SVG Animation Examples with Sources: Page #2 - 2013
Tutorial by Examples
SVG Animation Example: Simple 3D Text
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()"
onresize="resize()"
onmousemove="mouseMove(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var O = "";
var nx=ny=xm=ym=0;
var nShadow = 25;
function makeShadow(n,O)
{
this.obj = document.createElementNS(xmlns,"text");
this.O = O;
this.zOOm = 1.01 + (n/500);
this.obj.zoom = this.zOOm;
r = parseInt(255/nShadow) * n/2;
g = parseInt(255/nShadow) * n/2;
b = parseInt(255/nShadow) * n;
if(n>0)this.obj.color = "RGB("+(r)+","+(g)+","+(b)+")";
this.obj.setAttributeNS(null,"fill",this.obj.color);
this.obj.setAttributeNS(null,"font-family","ariel");
this.obj.setAttributeNS(null,"font-size","80");
Msg = document.createTextNode("BoGoToBoGo");
this.obj.appendChild(Msg);
document.getElementById("textShadow").appendChild(this.obj);
this.position = function(){
with(this){
obj.left = (400-xm)*(1 - zOOm);
obj.top = (400-ym)*(1 - zOOm);
this.obj.setAttributeNS(null,"x",obj.left);
this.obj.setAttributeNS(null,"y",obj.top);
if(O)O.position();
}
}
}
function startUp()
{
resize();
xm = nx / 2;
ym = ny / 2;
for(i=0;i<nShadow;i++)O = new makeShadow(i,O);
O.position();
}
function mouseMove(event)
{
xm = event.clientX;
ym = event.clientY;
O.position();
}
function resize()
{
nx = screen.width;
ny = screen.height;
}
]]>
</script>
<rect width="100%" height="100%" fill="white"/>
<g id="textShadow" transform="translate(100,200)">
</g>
</svg>
SVG Animation Example: SVG Digital Clock
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()">
<script>
<![CDATA[
/* Evolved from DHTML version
@ http://www.dhteumeuleu.com */
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var backX0;
var backY0;
var backWidth;
var backHeight;
var O=[];
var TM=[];
var Tm=[];
var A = 1000;
var digits = [
" ### # #### #### # ###### ### ##### ### ### ",
"# # # # ## ## # # ## ## # ",
"# # # # ## ## # ## ## # # ",
"# # # ### ### ######### #### # ### #### ",
"# # # # # # ## # ## # # # ",
"# # # # # # ## # ## ## # ",
" ### # ######### ##### ### # ### ### "
];
function startUp() {
var myBack = document.getElementById("backGround");
backX0 = myBack.getAttributeNS(null,"x");
backY0 = myBack.getAttributeNS(null,"y");
backWidth = myBack.getAttributeNS(null,"width");
backHeight = myBack.getAttributeNS(null,"height");
dayDisplay();
timer();
/*
k 0 1 2 3 4 5 6 7 -> 1st args of Cdigit
display * * : * * : * * -> 2nd args of Cdigit
('10' for ':')
*/
var k=0;
for(var i=0;i<6;i++){
O[k] = new Cdigit(k++, TM[i]);
if(i==1 || i==3) O[k] = new Cdigit(k++, 10);
}
mainloop();
}
/* Input for Cdigit
N = 0-7
d = 0-9 or 10 */
function Cdigit(N,d){
// digit prototype: 5 x 7 dots for each of digit from 0 to 9
this.O = [];
for(var i=0;i<7;i++){
for(var j=0;j<5;j++){
if(digits[i].charAt(5*d+j)!=" "){
this.O.push(
// COjb(this.a, this.z)
new CObj((
(28*N)+(j*5))/(180/Math.PI),
-42+i*12
)
);
}
}
}
}
function CObj(a,z){
// create led element
this.o = document.createElementNS(xmlns,"circle");
document.getElementById("clock3D").appendChild(this.o);
this.a=a;
this.z=z;
this.plot=true;
}
// leds lighting
// main 3D function
CObj.prototype.anim=function() {
// z axis rotation
var x=Math.sin(A+this.a)*100;
var y=Math.cos(A+this.a)*100;
// simple 3D
var x1=y;
var zz=this.z;
var y1=-zz;
zz=x;
// 2D projection
var r=396/(396+zz);
x=Math.round(backWidth/2-x1/r)+parseFloat(backX0);
y=Math.round(backHeight/2-y1/r)+parseFloat(backY0);
// leds lighting
if(zz>0){
this.o.setAttributeNS(null,"fill","#ff0000");
this.o.setAttributeNS(null,"cx",x);
this.o.setAttributeNS(null,"cy",y);
this.o.setAttributeNS(null,"r","5");
this.o.setAttributeNS(null,"opacity","1.0");
}
else {
this.o.setAttributeNS(null,"fill","#00ff00");
this.o.setAttributeNS(null,"cx",x);
this.o.setAttributeNS(null,"cy",y);
this.o.setAttributeNS(null,"r","5");
this.o.setAttributeNS(null,"opacity","0.3");
}
}
function mainloop() {
// rotation speed
A-=Math.PI/120;
// refresh time
k=0;
for(var i=0;i<6;i++){
if(TM[i]!=Tm[i]){
Tm[i]=TM[i];
// destroy objects
for(var j in O[k].O)document.getElementById("clock3D").removeChild(O[k].O[j].o);
delete O[k];
// create new digit
O[k] = new Cdigit(k, TM[i]);
}
// skip colons
k+=(i==1 || i==3)?2:1;
}
// call animation
for(var i in O){
for(var j in O[i].O){
O[i].O[j].anim();
}
}
setTimeout("mainloop()",20);
}
function timer(){
// HH:MM:SS
T = new Date();
h = T.getHours();
m = T.getMinutes();
s = T.getSeconds();
TM = [
Math.floor(h/10),
h%10,
Math.floor(m/10),
m%10,
Math.floor(s/10),
s%10
];
setTimeout("timer()" ,1000);
}
function dayDisplay()
{
var dayName =
new Array("Sunday","Monday","Tuesday","Thursday",
"Friday","Saturday");
var monthName =
new Array("January","February","March","April","May","June","July",
"August","September","October","November","December");
var today = new Date();
document.getElementById("date").firstChild.nodeValue =
dayName[today.getDay()-1]+", "
+ monthName[today.getMonth()]+" "
+ today.getDate()+", "+today.getFullYear();
}
]]>
</script>
<rect id="backGround" x="50" y="50" width="300" height="200" fill="black" stroke="#444" stroke-width="5"/>
<rect id="backGround" x="53" y="53" width="294" height="194" fill="none" stroke="#fff" stroke-width="1"/>
<g id="clock3D">
<circle id="red" cx="-150" cy="-150" r="4" fill="red"/>
<circle id="green" cx="-150" cy="-150" r="4" fill="green" opacity="0.3"/>
</g>
<text id="date" x="80" y="240" font-size="20" fill="white">
date
<animate attributeName="opacity" dur="5s"
values="1;0;1" repeatCount="indefinite"/>
</text>
</svg>
SVG Picture Animation Example: Deformation -Renoir
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
width="100%"
height="100%"
onload="startUp()"
onmousemove="mouseMove(evt)"
onresize="resize()"
onmousedown="mouseDown()"
ondrag="mouseDrag()"
onmouseup="mouseUp()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var scr;
var O;
var MP;
var P;
var xm;
var ym;
var mpw;
var mph;
var sx = 0;
var sy = 0;
var X;
var Y;
var drag = false;
var xd = 0;
var yd = 0;
function CObj(N, parent) {
this.S = (N + 1) * P;
var cliprect = document.createElementNS(xmlns,"rect");
cliprect.setAttributeNS(null,"x",-Math.round(mpw/X-this.S/2));
cliprect.setAttributeNS(null,"y",-Math.round(mph/Y-this.S/2));
cliprect.setAttributeNS(null,"width",Math.round(this.S));
cliprect.setAttributeNS(null,"height",Math.round(this.S));
cliprect.setAttributeNS(null,"fill","none");
cliprect.setAttributeNS(null,"id","rect"+N);
definitions = document.getElementById("myDefs");
definitions.appendChild(cliprect);
this.cliprect = cliprect;
var clippath = document.createElementNS(xmlns,"clipPath");
clippath.setAttributeNS(null,"id","clip"+N);
var clipuse = document.createElementNS(xmlns,"use");
clipuse.setAttributeNS(xlinkns,"xlink:href","#rect"+N);
clippath.appendChild(clipuse);
pathgroup = document.getElementById("clipPathGroup");
pathgroup.appendChild(clippath);
this.clippath = clippath;
var clippedimage = document.createElementNS(xmlns,"use");
clippedimage.setAttributeNS(null,"id","clippedImage"+N);
clippedimage.setAttributeNS(xlinkns,"xlink:href","#myImage");
clippedimage.setAttributeNS(null,"clip-path","url(#clip"+N+")");
var imagegroup = document.getElementById("imageGroup");
imagegroup.insertBefore(clippedimage,imagegroup.firstChild);
this.clippedimage = clippedimage;
this.S = this.S * .5;
this.PX = xm;
this.PY = ym;
this.x = 0;
this.y = 0;
this.sx = 0;
this.sy = 0;
this.parent = parent;
if (N<NBi) {
this.O = new CObj(N+1,this);
}
}
CObj.prototype.anim = function () {
if (this.parent) {
var x0 = this.parent.x;
var y0 = this.parent.y;
}
else {
if (drag) {
var x0 = xm;
var y0 = ym;
} else {
var x0 = xd+sx;
var y0 = yd+sy;
}
}
var ddx = (x0-this.PX) * .5;
var ddy = (y0-this.PY) * .5;
this.x = this.PX+=ddx;
this.y = this.PY+=ddy;
this.left = Math.round(this.x - this.S);
this.top = Math.round(this.y - this.S);
if (this.O) {
this.O.cliprect.setAttributeNS(null,"x",this.left);
this.O.cliprect.setAttributeNS(null,"y",this.top);
this.O.clippedimage.setAttributeNS
(null,"x",this.x-window.innerWidth/4);
this.O.clippedimage.setAttributeNS
(null,"y",this.y-window.innerHeight/4);
this.O.anim();
}
}
function startUp()
{
alert("Works for IE only at this time.\n Drag mouse to play this picture aniamtion - http:\\www.bogotobogo.com");
scr = document.documentElement;
MP = document.getElementById("myImage");
xd = xm = window.innerWidth/2;
yd = ym = window.innerHeight/2;
scr.ondrag = mouseDrag ();
scr.onmousedown = mouseDown();
scr.onmouseup = mouseUp();
N = 0;
NBi = 30;
mpw = parseInt(MP.getAttributeNS(null,"width"))
*window.innerWidth/100;
mph = parseInt(MP.getAttributeNS(null,"height")) *window.innerHeight/100;
X = 2;
Y = 2.2;
P = Math.max(mpw, mph)/NBi;
O = new CObj(0);
setInterval("randomxy()",30);
}
function randomxy()
{
sx += Math.random() * 4 - 2;
sy += Math.random() * 4 - 2;
O.anim();
}
function mouseMove(e)
{
xm=e.clientX;
ym=e.clientY;
sx = 0;
sy = 0;
}
function mouseDown()
{
drag = true;
return false;
}
function mouseUp()
{
drag = false;
xd = xm;
yd = ym;
return false;
}
function mouseDrag()
{
return false;
}
function resize()
{
xm = window.innerWidth/2;
ym = window.innerHeight/2;
}
]]> </script>
<defs id="myDefs">
<image id="myImage" xlink:href="../images/Renoir.jpg" width="50%" height="50%" preserveAspectRatio="none" />
<!-- Javascript will generate ...
<rect id="rect1" ..../>
-->
</defs>
<g id="clipPathGroup">
<!-- Javascript will generate ...
<clipPath id="clip1">
<use xlink:href="#rect1">
</clipPath>
-->
</g>
<g id="imageGroup">
<!-- Javascript will generate ...
<use id="clippedImage1" xlink:href="#myImage" clip-path="url(#clip1)" />
-->
</g>
</svg>
SVG Animation Example: SVG Interactive Map of Europe with ViewBox
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"
"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd" [
<!ATTLIST svg
xmlns:a3 CDATA #IMPLIED
a3:scriptImplementation CDATA #IMPLIED>
<!ATTLIST script
a3:scriptImplementation CDATA #IMPLIED>
]>
<svg viewBox="0 0 600 600" preserveAspectRatio="none"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:a3="http://ns.adobe.com/AdobeSVGViewerExtensions/3.0/"
a3:scriptImplementation="Adobe"
onload="init(evt)"
onzoom="updateTracker(evt)"
onscroll="updateTracker(evt)"
onresize="updateTracker(evt)">
<script type="text/ecmascript" a3:scriptImplementation="Adobe"><![CDATA[
/* Evolved from http://www.kevlindev.com */
/*****
*
* Globals
*
*****/
var elems = {
tracker: false,
trans: true,
scale: true,
mx: true,
my: true,
ux: true,
uy: true
};
var frame = {
x_trans: 0,
y_trans: 0,
zoom : 1,
x_scale: 1,
y_scale: 1
};
var countryName;
/*****
*
* init
*
*****/
function init(e) {
if ( window.svgDocument == null )
svgDocument = e.target.ownerDocument;
// Find nodes by id and store in elems object
for (var id in elems) getElement(id, elems[id]);
// Update our tracking rectangle
updateTracker(null);
countryName = document.getElementById("countryName");
}
/*****
*
* getElement
*
*****/
function getElement(id, useFirstChild) {
// Find the node with the specified id
var node = svgDocument.getElementById(id);
if ( useFirstChild ) {
// Grab first child of node
// This is used to get the text node of tspan and text elements
elems[id] = node.firstChild;
} else {
// Don't need first child so use the node we just found
elems[id] = node;
}
}
/*****
*
* updateTracker
*
*****/
function updateTracker(e) {
// Get the top-most SVG element
var SVGRoot = svgDocument.documentElement;
// Get the current zoom and pan settings
var trans = SVGRoot.currentTranslate;
var scale = SVGRoot.currentScale;
// Determine the translation needed to move the upper-left
// corner of our tracking rectangle to the upper-left of the
// current view.
// The zeros are used to reinforce that we are translating
// the origin of the rectangle to the upper-left corner of the
// current view.
frame.x_trans = ( 0.0 - trans.x ) / scale;
frame.y_trans = ( 0.0 - trans.y ) / scale;
// Now that we have moved the rectangle's corner to the
// upper-left position, let's scale the rectangle to fit
// the current view. X and Y scales are maintained seperately
// to handle possible anamorphic scaling from the viewBox
frame.zoom = scale;
frame.x_scale = 1 / scale;
frame.y_scale = 1 / scale;
// Get the current viewBox
var vbox = SVGRoot.getAttributeNS(null, "viewBox");
if ( vbox ) {
// We have a viewBox so, update our translation and scale
// to take the viewBox into account
// Break the viewBox parameters into an array to make life easier
var params = vbox.split(/\s+/);
// Determine the scaling from the viewBox
// Note that these calculations assume that the outermost
// SVG element has height and width attributes set to 100%.
var h_scale = window.innerWidth / params[2];
var v_scale = window.innerHeight / params[3];
// Update our previously calculated transform
frame.x_trans = frame.x_trans / h_scale + parseFloat(params[0]);
frame.y_trans = frame.y_trans / v_scale + parseFloat(params[0]);
frame.x_scale = frame.x_scale / h_scale;
frame.y_scale = frame.y_scale / v_scale;
}
// Apply changes to the tracking rectangle
updateTrackerTransform();
}
/*****
*
* updateCursor
*
*****/
function updateCursor(e) {
// Get the mouse x and y coordinates
var x = e.clientX;
var y = e.clientY;
// Calculate the user-coordinate using the scaling and
// translation values we calculated for the tracking
// rectangle
var nx = x * frame.x_scale + frame.x_trans;
var ny = y * frame.y_scale + frame.y_trans;
// Update the cursor position
// elems.cursor.setAttributeNS(null, "cx", nx);
// elems.cursor.setAttributeNS(null, "cy", ny);
// Update our text fields
elems.mx.data = parseInt(x);
elems.my.data = parseInt(y);
elems.ux.data = parseInt(nx);
elems.uy.data = parseInt(ny);
}
/*****
*
* updateTrackerTransform
*
*****/
function updateTrackerTransform()
{
// Build the text versions of the translate and scale transformation
var trans = "translate(" + parseInt(frame.x_trans) + "," + parseInt(frame.y_trans) + ")"
var scale = "scale(" + 1/frame.zoom.toFixed(1) + "," + 1/frame.zoom.toFixed(1) + ")";
// Apply the transformation to our tracking rectangle
elems.tracker.setAttributeNS(null, "transform", trans + " " + scale);
// Update our text fields
elems.trans.data = trans;
elems.scale.data = scale;
}
function mouseOver(e)
{
// Get the mouse x and y coordinates
var x = e.clientX;
var y = e.clientY;
// Calculate the user-coordinate using the scaling and
// translation values we calculated for the tracking
// rectangle
var nx = x * frame.x_scale + frame.x_trans;
var ny = y * frame.y_scale + frame.y_trans;
var obj = e.target;
obj.setAttributeNS(null,"style","fill: rgb(254, 254, 233); stroke: red;stroke-width: 2;");
countryName.setAttributeNS(null,"x",nx);
countryName.setAttributeNS(null,"y",ny);
countryName.firstChild.nodeValue =obj.getAttributeNS(null,"id");
}
function mouseOut(e)
{
var obj = e.target;
obj.setAttributeNS(null,"style","fill: rgb(254, 254, 233); stroke: rgb(100, 100, 100); stroke-width: 0.4252; stroke-miterlimit: 1;");
countryName.firstChild.nodeValue ="";
}
]]></script>
<!-- A group of elements collectively refered to as the tracker -->
<g id="tracker">
<!-- Draw a visible rectangle to show the tracking area -->
<rect x="0" y="0" width="100%" height="100%" fill="#008080" opacity="0.25"/>
<!-- Draw a panel to display transformation info for the end-user -->
<rect x="2" y="2" width="196" height="6em" fill="white" fill-opacity="0.4" stroke="black"/>
<text>
<tspan x="5" dy="1em">translate= </tspan><tspan id="trans"> </tspan>
<tspan x="5" dy="1em">scale = </tspan><tspan id="scale"> </tspan>
<tspan x="5" dy="1em">mouse x = </tspan><tspan id="mx"> </tspan>
<tspan x="5" dy="1em">mouse y = </tspan><tspan id="my"> </tspan>
<tspan x="5" dy="1em">user x = </tspan><tspan id="ux"> </tspan>
<tspan x="5" dy="1em">user y = </tspan><tspan id="uy"> </tspan>
</text>
<!--
- This is the actual tracking rectangle. This is all that is needed
- to track the cursor. Just place the "tracker" id here and remove
- this group and all of the other elements in this group
-->
<rect x="0" y="0" width="100%" height="100%" opacity="0" onmousemove="updateCursor(evt)"/>
</g>
<!-- Map -->
<g id="Europa" onmousemove="updateCursor(evt)" opacity="0.7"
transform="translate(50,150)">
<rect width="449.40454" height="368.61963" x="0.0" y="0.0" style="stroke: rgb(100, 100, 100); stroke-width: 0.4252;
fill: rgb(50,100,255); fill-rule: evenodd;" id="rect7"/>
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SVG Animation Example: Battle of the Bulge - SMIL Path Animation
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<!-- Created with Inkscape (http://www.inkscape.org/) -->
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<!--
Map source:
http://en.wikipedia.org/wiki/Battle_of_the_Bulge
War Front Source: http://memory.loc.gov/ammem/collections/maps/wwii/essay1.html
Note) War front is not accurate in my simulation.
-->
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<text
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id="tspan7288">20</tspan></text>
<text
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id="text7290"
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style="font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-indent:0;text-align:start;text-decoration:none;line-height:normal;letter-spacing:normal;word-spacing:normal;text-transform:none;direction:ltr;block-progression:tb;writing-mode:lr-tb;text-anchor:start;opacity:1;fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;marker:none;marker-start:none;marker-mid:none;marker-end:none;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;visibility:visible;display:inline;overflow:visible;enable-background:accumulate;font-family:Bitstream Vera Sans;-inkscape-font-specification:Bitstream Vera Sans"><tspan
x="787.0838"
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id="tspan7292">30</tspan></text>
<text
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id="text7294"
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id="tspan7296">MILES</tspan></text>
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id="tspan7384">FRANCE</tspan></text>
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id="tspan7388">Roer R</tspan></text>
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id="tspan7392">Ourthe R</tspan></text>
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style="font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-indent:0;text-align:start;text-decoration:none;line-height:normal;letter-spacing:normal;word-spacing:normal;text-transform:none;direction:ltr;block-progression:tb;writing-mode:lr-tb;text-anchor:start;opacity:1;fill:#74afbc;fill-opacity:0.93333333;fill-rule:nonzero;marker:none;marker-start:none;marker-mid:none;marker-end:none;visibility:visible;display:inline;overflow:visible;enable-background:accumulate;font-family:Bitstream Vera Sans;-inkscape-font-specification:Bitstream Vera Sans"><tspan
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id="tspan7396">ALBERT CANAL</tspan></text>
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x="415.7338"
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id="tspan7400">FIFTEENTH</tspan></text>
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style="font-size:20px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-indent:0;text-align:start;text-decoration:none;line-height:normal;letter-spacing:normal;word-spacing:normal;text-transform:none;direction:ltr;block-progression:tb;writing-mode:lr-tb;text-anchor:start;opacity:1;fill:#b00000;fill-opacity:1;fill-rule:nonzero;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;marker:none;marker-start:none;marker-mid:none;marker-end:none;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;visibility:visible;display:inline;overflow:visible;enable-background:accumulate;font-family:Bitstream Vera Sans;-inkscape-font-specification:Bitstream Vera Sans"><tspan
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</path>
</g>
</svg>
SVG Math Animation Example: Apollonian Gasket (-3,5,8,8)- Soddy(three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var drawingScale = 200*3;
var circles = new Array();
var curvaturePool = [-3];
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = 1;
var lenTangentArray = 3;
var nStage = 0;
function startup(evt)
{
init();
// Setting up initial configuration
// 1st circle at the origin (0,0). Vertex A
// The center of circle 2 and 3 are B and C, respectively.
var Ax = 0.0;
var Ay = 0.0;
// The three curvatures are:
var curvA = 5;
var curvB = 8;
var curvC = 8;
// The three radii are:
var a = 1/curvA;
var b = 1/curvB;
var c = 1/curvC;
/* To calculate the center position of circle 2 (B) and 3 (C),
we need the half angle A */
angleA2 = Math.asin (b/(a+b));
var By = b;
var Bx = (a+b)*Math.cos(angleA2);
var Cy = -b;
var Cx = Bx;
// curvature of the outer circumcircle
curvD=soddy(a,b,c,4);
// center of the outer circumcircle
Dx = -1/curvD - a;
Dy = 0.0;
// Now, put the data into circle object
O = {x:0, y:0, curvature:1, tangents:[], stage:0};
circles[0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[3]= O;
// 4th circle: outer circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[5]= O;
circles[5].curvature=soddy(1/circles[1].curvature,1/circles[2].curvature,1/circles[3].curvature,5);
// Now we have a configuration to start
// To get 5th circle,
currentCircle = 5;
findApollonian(2,3,4,1,currentCircle);
for(i=1;i<=currentCircle;i++) {
drawCircle(i);
curvaturePool.push(circles[i].curvature);
}
displayStatus();
}
function soddy(r1,r2,r3,n)
{
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it tells you it's done for the stage");
*/
nextCircle(currentCircle);
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage)*2;
totalCirclesText.firstChild.nodeValue=Math.pow(3,nStage+1)+2;
}
}
function nextCircle()
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
ilen = 1;
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[i].tangents.length;
}
}
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4);
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv);
if(isThere==1) {
st1=circles[i1].stage;
st2=circles[i2].stage;
st3=circles[i3].stage;
st4=circles[i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1) continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle++;
O = {x:0, y:0, curvature:1, tangents:[]};
circles[currentCircle] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle);
drawCircle(currentCircle);
curvaturePool.push(circles[currentCircle].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n1==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n1==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n1==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n2==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n2==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n2==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n3==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n3==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n3==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n4==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n4==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n4==circles[n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv)
{
for(var i=0;i<curvaturePool.length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo)
{
var curv = getCurvature(i1,i2,i3,i4);
circles[iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo);
circles[iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo);
circles[iApollo].y = imagy;
// setup tangents
//new circle
circles[iApollo].tangents.push(i1);
circles[iApollo].tangents.push(i2);
circles[iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[i1].tangents.push(iApollo);
circles[i2].tangents.push(iApollo);
circles[i3].tangents.push(iApollo);
// stage
circles[iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = circles[i4prime].curvature;
if(flag==1)
{
z1 = circles[i1].x;
z2 = circles[i2].x;
z3 = circles[i3].x;
z4 = circles[i4].x;
}
else
{
z1 = circles[i1].y;
z2 = circles[i2].y;
z3 = circles[i3].y;
z4 = circles[i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function heron(a,b,c)
{
var s = 0.5 * (a + b + c);
var delta = Math.sqrt(s*(s-a)*(s-b)*(s-c));
return delta;
}
function drawCircle(i)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[i].x);
label.setAttributeNS(null,"y",drawingScale*circles[i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
//var txtNode = document.createTextNode(circles[i].curvature);
var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="40"
x="80" y="50">
Apollonian Gasket (-3,5,8,8)
</text>
</g>
<g id="Apollo" transform="translate(200,270)">
</g>
<text id="status" y="480" font-size="20">
<tspan x="100" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<tspan x="100" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="100" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(0,445)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="ZoomInCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="560">
<tspan x="100" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="100" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="100" dy="1em">
I haven't got to stage 8 with my algorithm. It seems to take forever.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Apollonian Gasket (-1,2,2,3)- Soddy (three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var drawingScale = 200;
var circles = new Array();
var curvaturePool = [-1];
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = 1;
var lenTangentArray = 3;
var nStage = 0;
function startup(evt)
{
init();
// Setting up initial configuration
// 1st circle at the origin (0,0). Vertex A
// The center of circle 2 and 3 are B and C, respectively.
var Ax = 0.0;
var Ay = 0.0;
// The three curvatures are:
var curvA = 2;
var curvB = 2;
var curvC = 3;
// The three radii are:
var a = 1/curvA;
var b = 1/curvB;
var c = 1/curvC;
var Bx = a+b;
var By = 0.0;
/* To calculate the center position of circle 3 (C),
we need the angle A */
angleA = Math.acos(a/(a+c));
var Cx = a;
var Cy = (a+c)*Math.sin(angleA);
// curvature of the outer circumcircle
curvD=soddy(a,b,c,4);
// center of the outer circumcircle
Dx = a;
Dy = 0.0;
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[3]= O;
// 4th circle: outer circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[5]= O;
circles[5].curvature=soddy(1/circles[1].curvature,1/circles[2].curvature,1/circles[3].curvature,5);
// Now we have a configuration to start
// To get 5th circle,
currentCircle = 5;
findApollonian(1,2,4,3,currentCircle);
for(i=1;i<=currentCircle;i++) {
drawCircle(i);
curvaturePool.push(circles[i].curvature);
}
displayStatus();
}
function soddy(r1,r2,r3,n)
{
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it is telling you it's done for the stage");
*/
nextCircle(currentCircle);
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage)*2;
totalCirclesText.firstChild.nodeValue=Math.pow(3,nStage+1)+2;
}
}
function nextCircle()
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
ilen = 1;
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[i].tangents.length;
}
}
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4);
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv);
if(isThere==1) {
st1=circles[i1].stage;
st2=circles[i2].stage;
st3=circles[i3].stage;
st4=circles[i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1) continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle++;
O = {x:0, y:0, curvature:1, tangents:[]};
circles[currentCircle] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle);
drawCircle(currentCircle);
curvaturePool.push(circles[currentCircle].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n1==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n1==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n1==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n2==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n2==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n2==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n3==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n3==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n3==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n4==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n4==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n4==circles[n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv)
{
for(var i=0;i<curvaturePool.length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo)
{
var curv = getCurvature(i1,i2,i3,i4);
circles[iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo);
circles[iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo);
circles[iApollo].y = imagy;
// setup tangents
//new circle
circles[iApollo].tangents.push(i1);
circles[iApollo].tangents.push(i2);
circles[iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[i1].tangents.push(iApollo);
circles[i2].tangents.push(iApollo);
circles[i3].tangents.push(iApollo);
// stage
circles[iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = circles[i4prime].curvature;
if(flag==1)
{
z1 = circles[i1].x;
z2 = circles[i2].x;
z3 = circles[i3].x;
z4 = circles[i4].x;
}
else
{
z1 = circles[i1].y;
z2 = circles[i2].y;
z3 = circles[i3].y;
z4 = circles[i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function heron(a,b,c)
{
var s = 0.5 * (a + b + c);
var delta = Math.sqrt(s*(s-a)*(s-b)*(s-c));
return delta;
}
function drawCircle(i)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[i].x);
label.setAttributeNS(null,"y",drawingScale*circles[i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
//var txtNode = document.createTextNode(circles[i].curvature);
var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="40"
x="80" y="50">
Apollonian Gasket (-1,2,2,3)
</text>
</g>
<g id="Apollo" transform="translate(200,270)">
</g>
<text id="status" y="480" font-size="20">
<tspan x="100" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<tspan x="100" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="100" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(0,445)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="ZoomInCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="560">
<tspan x="100" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="100" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="100" dy="1em">
I haven't got to stage 8 with my algorithm. It seems to take forever.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Apollonian Gasket (-15,32,32,33)- Soddy (three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var drawingScale = 200*15;
var circles = new Array();
var curvaturePool = [-1];
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = 1;
var lenTangentArray = 3;
var nStage = 0;
function startup(evt)
{
init();
// Setting up initial configuration
// 1st circle at the origin (0,0). Vertex A
// The center of circle 2 and 3 are B and C, respectively.
var Ax = 0.0;
var Ay = 0.0;
// The three curvatures are:
var curvA = 32;
var curvB = 32;
var curvC = 33;
// The three radii are:
var ra = 1/curvA;
var rb = 1/curvB;
var rc = 1/curvC;
var Bx = ra+rb;
var By = 0.0;
// sides of the triangles with 3 vertices
var sideA = rb + rc;
var sideB = ra + rc;
var sideC = ra + rb;
// angles
var angleA = angle(1,sideA,sideB,sideC);
var angleB = angle(2,sideA,sideB,sideC);
var angleC = angle(3,sideA,sideB,sideC);
/* To calculate the center position of circle 3 (C),
we need the angle A */
var Cx = sideB*Math.cos(angleA);
var Cy = sideB*Math.sin(angleA);
// Area of the triangle
delta = getTriangleArea(sideA,sideB,sideC);
// three points on the Soddy lines, not needed for this example
midSideAx = rb*Math.cos(angleB);
midSideAy = rb*Math.sin(angleB);
midSideBx = ra*Math.cos(angleA);
midSideBy = ra*Math.sin(angleA);
midSideCx = ra;
midSideCy = 0;
// The distance from midC (midSideCx,midSideCy)
// is the y-coordinates of Inner Soddy center
// center of the Inner Soddy circle
Dx = ra;
Dy = trilinear(sideA,sideB,sideC);
// curvature of the inner Soddy circle
var curvD=soddy(ra,rb,rc,5);
// center of the outer circumcircle
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[3]= O;
// 4th circle: inner circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[5]= O;
circles[5].curvature=soddy(1/circles[1].curvature,1/circles[2].curvature,1/circles[3].curvature,4);
// Now we have a configuration to start
// To get coordinates of the 5th circle,
currentCircle = 5;
findApollonian(1,2,3,4,currentCircle);
for(i=1;i<=currentCircle;i++) {
drawCircle(i);
curvaturePool.push(circles[i].curvature);
}
displayStatus();
}
function trilinear(a,b,c)
{
// angles
var A = angle(1,a,b,c);
var B = angle(2,a,b,c);
var C = angle(3,a,b,c);
// trilinear coordinates
alpha = 1/Math.cos(A/2)*Math.cos(B/2)*Math.cos(C/2)+1;
beta = 1/Math.cos(B/2)*Math.cos(C/2)*Math.cos(A/2)+1;
gamma = 1/Math.cos(C/2)*Math.cos(A/2)*Math.cos(B/2)+1;
//area
var delta = getTriangleArea(a,b,c);
var k = 2*delta/(alpha*a+beta*b+gamma*c);
// In this case, we need to return c' i.e. k*gamma
return k*gamma;
}
function getTriangleArea(a,b,c)
{
s = (a+b+c)/2;
area = Math.sqrt( s*(s-a)*(s-b)*(s-c) );
return area;
}
function angle(n,a,b,c)
{
var cos;
if(n==1)
cos = (-a*a+b*b+c*c)/(2*b*c);
else if(n==2)
cos = (a*a-b*b+c*c)/(2*a*c);
else if(n==3)
cos = (a*a+b*b-c*c)/(2*a*b);
return Math.acos(cos);
}
function soddy(r1,r2,r3,n)
{
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it is telling you it's done for the stage");
*/
nextCircle(currentCircle);
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage)*2;
totalCirclesText.firstChild.nodeValue=Math.pow(3,nStage+1)+2;
}
}
function nextCircle()
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
ilen = 1;
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[i].tangents.length;
}
}
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4);
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv);
if(isThere==1) {
st1=circles[i1].stage;
st2=circles[i2].stage;
st3=circles[i3].stage;
st4=circles[i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1) continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle++;
O = {x:0, y:0, curvature:1, tangents:[]};
circles[currentCircle] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle);
drawCircle(currentCircle);
curvaturePool.push(circles[currentCircle].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n1==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n1==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n1==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n2==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n2==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n2==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n3==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n3==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n3==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n4==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n4==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n4==circles[n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv)
{
for(var i=0;i<curvaturePool.length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo)
{
var curv = getCurvature(i1,i2,i3,i4);
circles[iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo);
circles[iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo);
circles[iApollo].y = imagy;
// setup tangents
//new circle
circles[iApollo].tangents.push(i1);
circles[iApollo].tangents.push(i2);
circles[iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[i1].tangents.push(iApollo);
circles[i2].tangents.push(iApollo);
circles[i3].tangents.push(iApollo);
// stage
circles[iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = circles[i4prime].curvature;
if(flag==1)
{
z1 = circles[i1].x;
z2 = circles[i2].x;
z3 = circles[i3].x;
z4 = circles[i4].x;
}
else
{
z1 = circles[i1].y;
z2 = circles[i2].y;
z3 = circles[i3].y;
z4 = circles[i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function heron(a,b,c)
{
var s = 0.5 * (a + b + c);
var delta = Math.sqrt(s*(s-a)*(s-b)*(s-c));
return delta;
}
function drawCircle(i)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[i].x);
label.setAttributeNS(null,"y",drawingScale*circles[i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
//var txtNode = document.createTextNode(circles[i].curvature);
var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="40"
x="40" y="50">
Apollonian Gasket (-15,32,32,33)
</text>
</g>
<g id="Apollo" transform="translate(200,220)">
</g>
<text id="status" y="480" font-size="20">
<tspan x="100" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<tspan x="100" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="100" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(0,445)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="StageCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="560">
<tspan x="100" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="100" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="100" dy="1em">
I haven't got to stage 8 with my algorithm. It seems to take forever.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Apollonian Gasket (-15,32,32,33)-Core section: Soddy (three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var totalCircles=0;
var drawingScale = 200*80;
var circles = new Array();
var curvaturePool = [-1];
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = 1;
var lenTangentArray = 3;
var curvLimit;
var nStage = 0;
function startup(evt)
{
init();
// Setting up initial configuration
// 1st circle at the origin (0,0). Vertex A
// The center of circle 2 and 3 are B and C, respectively.
var Ax = 0.0;
var Ay = 0.0;
// The three curvatures are:
var curvA = 32;
var curvB = 32;
var curvC = 33;
// In this case, we need the circles in the center region
// So, we do not want to make outer circle.
// Put a limit to the curvature < curvA.
curvLimit = curvA;
// The three radii are:
var ra = 1/curvA;
var rb = 1/curvB;
var rc = 1/curvC;
var Bx = ra+rb;
var By = 0.0;
// sides of the triangles with 3 vertices
var sideA = rb + rc;
var sideB = ra + rc;
var sideC = ra + rb;
// angles
var angleA = angle(1,sideA,sideB,sideC);
var angleB = angle(2,sideA,sideB,sideC);
var angleC = angle(3,sideA,sideB,sideC);
/* To calculate the center position of circle 3 (C),
we need the angle A */
var Cx = sideB*Math.cos(angleA);
var Cy = sideB*Math.sin(angleA);
// Area of the triangle
delta = getTriangleArea(sideA,sideB,sideC);
// three points on the Soddy lines
//side BC
var midax = (ra+rb)-rb*Math.cos(angleB);
var miday = rb*Math.sin(angleB);
//side AC
var midbx = ra*Math.cos(angleA);
var midby = ra*Math.sin(angleA);
//side AB
var midcx = ra;
var midcy = 0;
// The distance from midC (midcx,midcy)
// is the y-coordinates of Inner Soddy center
// center of the Inner Soddy circle
var Dx = ra;
var Dy = trilinear(sideA,sideB,sideC);
// curvature of the inner Soddy circle
var curvD=soddy(ra,rb,rc,5);
// center of the outer circumcircle
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[3]= O;
// 4th circle: inner circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[1,2,3,4], stage:0};
circles[5]= O;
// Now we have a configuration to start
// To get coordinates of the 5th circle
currentCircle = 5;
findApollonian(1,2,4,3,currentCircle);
drawArc(midbx,midby,midcx,midcy,ra,ra);
drawArc(midcx,midcy,midax,miday,rb,rb);
drawArc(midax,miday,midbx,midby,rc,rc);
drawCircle(4);
drawCircle(5);
curvaturePool.push(circles[1].curvature);
curvaturePool.push(circles[2].curvature);
curvaturePool.push(circles[3].curvature);
curvaturePool.push(circles[4].curvature);
curvaturePool.push(circles[5].curvature);
displayStatus();
}
function trilinear(a,b,c)
{
// angles
var A = angle(1,a,b,c);
var B = angle(2,a,b,c);
var C = angle(3,a,b,c);
// trilinear coordinates
alpha = 1/Math.cos(A/2)*Math.cos(B/2)*Math.cos(C/2)+1;
beta = 1/Math.cos(B/2)*Math.cos(C/2)*Math.cos(A/2)+1;
gamma = 1/Math.cos(C/2)*Math.cos(A/2)*Math.cos(B/2)+1;
//area
var delta = getTriangleArea(a,b,c);
var k = 2*delta/(alpha*a+beta*b+gamma*c);
// In this case, we need to return c' i.e. k*gamma
return k*gamma;
}
function getTriangleArea(a,b,c)
{
s = (a+b+c)/2;
area = Math.sqrt( s*(s-a)*(s-b)*(s-c) );
return area;
}
function angle(n,a,b,c)
{
var cos;
if(n==1)
cos = (-a*a+b*b+c*c)/(2*b*c);
else if(n==2)
cos = (a*a-b*b+c*c)/(2*a*c);
else if(n==3)
cos = (a*a+b*b-c*c)/(2*a*b);
return Math.acos(cos);
}
function soddy(r1,r2,r3,n)
{
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it is telling you it's done for the stage");
*/
nextCircle(currentCircle);
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
totalCircles = parseInt(totalCirclesText.firstChild.nodeValue);
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage-1)*5;
totalCircles+=parseInt(circlesText.firstChild.nodeValue);
totalCirclesText.firstChild.nodeValue=totalCircles;
}
}
function nextCircle()
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
ilen = 1;
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[i].tangents.length;
}
}
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4);
// Special limit not to make outer circle
// which can generate children afterwards.
if(curv < curvLimit) {
continue;
}
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv);
if(isThere==1) {
/*
st1=circles[i1].stage;
st2=circles[i2].stage;
st3=circles[i3].stage;
st4=circles[i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1) continue;
*/
continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle++;
O = {x:0, y:0, curvature:1, tangents:[]};
circles[currentCircle] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle);
drawCircle(currentCircle);
curvaturePool.push(circles[currentCircle].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n1==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n1==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n1==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n2==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n2==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n2==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n3==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n3==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n3==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n4==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n4==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n4==circles[n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv)
{
for(var i=0;i<curvaturePool.length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo)
{
var curv = getCurvature(i1,i2,i3,i4);
if(curv <curvLimit) return;
circles[iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo);
circles[iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo);
circles[iApollo].y = imagy;
// setup tangents
//new circle
circles[iApollo].tangents.push(i1);
circles[iApollo].tangents.push(i2);
circles[iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[i1].tangents.push(iApollo);
circles[i2].tangents.push(iApollo);
circles[i3].tangents.push(iApollo);
// stage
circles[iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = circles[i4prime].curvature;
if(flag==1)
{
z1 = circles[i1].x;
z2 = circles[i2].x;
z3 = circles[i3].x;
z4 = circles[i4].x;
}
else
{
z1 = circles[i1].y;
z2 = circles[i2].y;
z3 = circles[i3].y;
z4 = circles[i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function heron(a,b,c)
{
var s = 0.5 * (a + b + c);
var delta = Math.sqrt(s*(s-a)*(s-b)*(s-c));
return delta;
}
function drawArc(fromX,fromY,toX,toY,rX,rY)
{
var obj = document.createElementNS(xmlns,"path");
var fromX = fromX*drawingScale;
var fromY = fromY*drawingScale;
var toX = toX*drawingScale;
var toY = toY*drawingScale;
var rX = rX*drawingScale;
var rY = rY*drawingScale;
var str ="M"+fromX+","+fromY+" A "+rX+","+rY+" 0 0 0,"+toX+","+toY;
obj.setAttributeNS(null,"d",str);
obj.setAttributeNS(null,"stroke","black");
obj.setAttributeNS(null,"stroke-width","1");
obj.setAttributeNS(null,"fill","none");
document.getElementById("Apollo").appendChild(obj);
}
function drawCircle(i)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[i].x);
label.setAttributeNS(null,"y",drawingScale*circles[i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
//var txtNode = document.createTextNode(circles[i].curvature);
var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="40"
x="60" y="50">
Apollonian Gasket (-15,32,32,33)
</text>
</g>
<g id="Apollo" transform="translate(-180,60)">
</g>
<text id="status" y="480" font-size="20">
<tspan x="180" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<tspan x="180" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="180" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(80,460)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="StageCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="560">
<tspan x="100" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="100" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="100" dy="1em">
I haven't got to stage 8 with my integral packing algorithm. It seems to take forever.
</tspan>
<tspan x="100" dy="1em">
It appears Google Chrome is the fastest among browsers for these examples.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Apollonian Gasket (0,0,1,1)- Soddy (three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly and my circle packing algorithm is not efficient.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var drawingScale = 100;
var circles = new Array();
var curvaturePool = [0.0001];
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = 1;
var lenTangentArray = 3;
var nStage = 0;
function startup(evt)
{
init();
// Setting up initial configuration
// 1st circle at the origin (-1,0). Vertex A
// The center of circle 2 and 3 are B and C, respectively.
var Ax = -1.0;
var Ay = 0.0;
// The three curvatures are:
var curvA = 1;
var curvB = 1;
var curvC = 0.0001;
var curvD = 0.0001;
// The three radii are:
var a = 1/curvA;
var b = 1/curvB;
var c = 1/curvC;
var By = 0.0;
var Bx = 1.0;;
// top circle with 0 curvature (line)
var Cy = -9999;
var Cx = 0.0;
// center of the outer circumcircle
Dx = 0.0;
Dy = 9999;
// Now, put the data into circle object
O = {x:0, y:0, curvature:1, tangents:[], stage:0};
circles[0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[3]= O;
// 4th circle: outer circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[5]= O;
circles[5].curvature=soddy(1/circles[1].curvature,1/circles[2].curvature,1/circles[3].curvature,5);
// Now we have a configuration to start
// To get 5th circle,
currentCircle = 5;
findApollonian(1,2,3,4,currentCircle);
for(i=1;i<=currentCircle;i++) {
drawCircle(i);
curvaturePool.push(circles[i].curvature);
}
displayStatus();
}
function soddy(r1,r2,r3,n)
{
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it tells you it's done for the stage");
*/
nextCircle(currentCircle);
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage)*2;
totalCirclesText.firstChild.nodeValue=Math.pow(3,nStage+1)+2;
}
}
function nextCircle()
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
ilen = 1;
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[i].tangents.length;
}
}
for(var i=1;i<=currentCircle;i++) {
if(circles[i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4);
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv);
if(isThere==1) {
st1=circles[i1].stage;
st2=circles[i2].stage;
st3=circles[i3].stage;
st4=circles[i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1)continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle++;
O = {x:0, y:0, curvature:1, tangents:[], id:currentCircle};
circles[currentCircle] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle);
drawCircle(currentCircle);
curvaturePool.push(circles[currentCircle].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n1==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n1==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n1==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n2==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n2==circles[n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n2==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n3==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n3==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[n4].tangents.length;i++) {
if(n3==circles[n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[n1].tangents.length;i++) {
if(n4==circles[n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[n2].tangents.length;i++) {
if(n4==circles[n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[n3].tangents.length;i++) {
if(n4==circles[n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv)
{
for(var i=0;i<curvaturePool.length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo)
{
var curv = getCurvature(i1,i2,i3,i4);
circles[iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo);
circles[iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo);
circles[iApollo].y = imagy;
// setup tangents
//new circle
circles[iApollo].tangents.push(i1);
circles[iApollo].tangents.push(i2);
circles[iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[i1].tangents.push(iApollo);
circles[i2].tangents.push(iApollo);
circles[i3].tangents.push(iApollo);
// stage
circles[iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = circles[i4prime].curvature;
if(flag==1)
{
z1 = circles[i1].x;
z2 = circles[i2].x;
z3 = circles[i3].x;
z4 = circles[i4].x;
}
else
{
z1 = circles[i1].y;
z2 = circles[i2].y;
z3 = circles[i3].y;
z4 = circles[i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4)
{
b1 = circles[i1].curvature;
b2 = circles[i2].curvature;
b3 = circles[i3].curvature;
b4 = circles[i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function heron(a,b,c)
{
var s = 0.5 * (a + b + c);
var delta = Math.sqrt(s*(s-a)*(s-b)*(s-c));
return delta;
}
function drawCircle(i)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[i].x);
label.setAttributeNS(null,"y",drawingScale*circles[i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
var txtNode = document.createTextNode(circles[i].curvature);
//var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="40"
x="80" y="50">
Apollonian Gasket (0,0,1,1)
</text>
</g>
<g id="Apollo" transform="translate(220,200)">
</g>
<text id="status" y="370" font-size="20">
<tspan x="100" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<tspan x="100" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="100" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(0,335)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="ZoomInCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="450">
<tspan x="100" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="100" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="100" dy="1em">
I haven't got to stage 8 with my algorithm. It seems to take forever.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Nested Apollonian Gasket [n,n+1,n(n+1),n(n+1)+1] (n=2,10) - Soddy (three tangential Circles) and Descartes' theorem. It may be slow because it's calculating circles on the fly and my circle packing algorithm is not efficient.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var stageText;
var circlesText;
var totalCirclesText;
var redStop;
var drawingScale = 350;
var circles = new Array();
var curvaturePool = new Array();
var circlesMap = [3,1,2,5,4];
var O = {};
var currentCircle = new Array();
var nStage = 0;
var startN = 2;
var numberOfNest= 10;
function startup(evt)
{
init();
//
// A at the bottom, B on top of a with same x
// C right side of A and B
//
// B
// C
// A
//
for(inest=0;inest<numberOfNest;inest++) {
// The three curvatures are:
var curvA = startN + 1;
var curvB = startN*(startN+1);
var curvC = startN*(startN+1)+1;
var ra = 1/curvA;
var rb = 1/curvB;
var rc = 1/curvC;
// Setting up initial configuration
// 1st circle (0,ra) centered. This center is Vertex A
// The center of circle 2 and 3 are B and C, respectively.
// The three radii are:
var Ax = 0.0;
var Ay = ra;
var Bx = 0.0;
var By = 2*ra+rb;
// sides of the triangles with 3 vertices
var sideA = rb + rc;
var sideB = ra + rc;
var sideC = ra + rb;
// angles
var angleA = angle(1,sideA,sideB,sideC);
var angleB = angle(2,sideA,sideB,sideC);
var angleC = angle(3,sideA,sideB,sideC);
/* To calculate the center position of circle 3 (C),
we need the angle A */
var Cx = sideB*Math.sin(angleA);
var Cy = Ay + sideB*Math.cos(angleA);
// three points on the Soddy lines
// on BC
var midax = rb*Math.sin(angleB);
var miday = By-rb*Math.cos(angleB);
// on AC
var midbx = ra*Math.sin(angleA);
var midby = Ay + ra*Math.cos(angleA);
// on AB
var midcx = 0.0;
var midcy = Ay + ra;
// curvature of the inner Soddy circle
var curvD=soddy(ra,rb,rc,4);
// take outer circle as 4th circle since it's aligned in y-axis
Dy = ra + rb;
Dx = 0.0;
// Now we have all the information on the circles A,B,C and 4th outer circle D
circles[inest] = new Array(numberOfNest);
curvaturePool[inest] = new Array(numberOfNest);
currentCircle[inest] = 1;
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[inest][0]= O; //junk
// valid index starts from 1 not 0
O = {x:Ax, y:Ay, curvature:curvA, tangents:[2,3,4], stage:0};
circles[inest][1]= O;
O = {x:Bx, y:By, curvature:curvB, tangents:[1,3,4], stage:0};
circles[inest][2]= O;
O = {x:Cx, y:Cy, curvature:curvC, tangents:[1,2,4], stage:0};
circles[inest][3]= O;
// 4th circle: outer circle
O = {x:Dx, y:Dy, curvature:curvD, tangents:[1,2,3], stage:0};
circles[inest][4]= O;
// Apollonian 5th
O = {x:0, y:0, curvature:0, tangents:[], stage:0};
circles[inest][5]= O;
// 5th circle is inner circle, we get the curvature using soddy()
circles[inest][5].curvature=soddy(1/circles[inest][1].curvature,1/circles[inest][2].curvature,1/circles[inest][3].curvature,5);
// Now we have a configuration to start
// To get coordinates of the 5th circle,
currentCircle[inest] = 5;
findApollonian(1,2,3,4,currentCircle[inest],inest);
for(i=1;i<=currentCircle[inest];i++) {
drawCircle(i,inest);
curvaturePool[inest].push(circles[inest][i].curvature);
}
displayStatus();
startN++;
}
}
function trilinear(n,a,b,c)
{
// angles
var A = angle(1,a,b,c);
var B = angle(2,a,b,c);
var C = angle(3,a,b,c);
// trilinear coordinates
alpha = 1/Math.cos(A/2)*Math.cos(B/2)*Math.cos(C/2)+1;
beta = 1/Math.cos(B/2)*Math.cos(C/2)*Math.cos(A/2)+1;
gamma = 1/Math.cos(C/2)*Math.cos(A/2)*Math.cos(B/2)+1;
//area
var delta = getTriangleArea(a,b,c);
var k = 2*delta/(alpha*a+beta*b+gamma*c);
if(n==1) return k*alpha;
else if(n==2) return k*beta;
else if(n==3) return k*gamma;
}
function getTriangleArea(a,b,c)
{
s = (a+b+c)/2;
area = Math.sqrt( s*(s-a)*(s-b)*(s-c) );
return area;
}
function angle(n,a,b,c)
{
var cos;
if(n==1)
cos = (-a*a+b*b+c*c)/(2*b*c);
else if(n==2)
cos = (a*a-b*b+c*c)/(2*a*c);
else if(n==3)
cos = (a*a+b*b-c*c)/(2*a*b);
return Math.acos(cos);
}
function soddy(r1,r2,r3,n)
{
// n=4: outer, n=5: inner
var r;
if(n==4) {
r = r1*r2*r3/
( (r1*r2+r2*r3+r1*r3) - 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)) )
}
if(n==5) {
r = r1*r2*r3/
((r1*r2+r2*r3+r1*r3) + 2*Math.sqrt(r1*r2*r3*(r1+r2+r3)))
}
curv = 1/r
return curv;
}
function stageUp()
{
nStage++;
/*
if(nStage>=4) alert("It will be getting slower and slower.\n If you see the red highlight at the center of the button, it is telling you it's done for the stage");
*/
for(inest=0;inest<numberOfNest;inest++) {
nextCircle(inest);
}
displayStatus();
}
function init()
{
stageText = document.getElementById("stage");
stageText.firstChild.nodeValue=0;
/*
circlesText = document.getElementById("circles");
circlesText.firstChild.nodeValue=5;
totalCirclesText = document.getElementById("totalCircles");
totalCirclesText.firstChild.nodeValue=5;
*/
redStop = document.getElementById("RedStop");
}
function displayStatus()
{
stageText.firstChild.nodeValue=nStage;
/*
if(nStage==0) {
circlesText.firstChild.nodeValue=5;
totalCirclesText.firstChild.nodeValue=5;
}
else {
circlesText.firstChild.nodeValue=Math.pow(3,nStage)*2;
totalCirclesText.firstChild.nodeValue=Math.pow(3,nStage+1)+2;
}
*/
}
function nextCircle(inest)
{
var fourCircles = [];
var iStartingCircle = [];
var nSC = 0;
var lenTangentArray = 3;
ilen = 1;
for(var i=1;i<=currentCircle[inest];i++) {
if(circles[inest][i].tangents.length >= lenTangentArray) {
lenTangentArray = circles[inest][i].tangents.length;
}
}
for(var i=1;i<=currentCircle[inest];i++) {
if(circles[inest][i].tangents.length < lenTangentArray) {
iStartingCircle[nSC] = i;
nSC++;
}
}
for(var ns=0;ns<nSC;ns++)
{
iStart = iStartingCircle[ns];
ilen = circles[inest][iStart].tangents.length;
var isThere = 0;
var isTangent = 1;
var isNewFour = 1;
for(var i=0;i<ilen;i++) {
i1 = iStart;
//i4 as one Apollonian
i4 = circles[inest][iStart].tangents[i];
for(var j=0;j<ilen;j++) {
if(j==i) {
continue;
}
i2 = circles[inest][iStart].tangents[j];
for(var k=0;k<ilen;k++) {
if(k==j || k==i) {
continue;
}
i3 = circles[inest][iStart].tangents[k];
/* (1) Check if the first three circles (i1,i2,i3) are neighbors. i1 has i2,i3 but i2 and i3 may not touching each other (2) Check if i4 touches i1,i2,i3.*/
isTangent = checkTangency(i1,i2,i3,i4,inest);
if(isTangent==0) {
continue;
}
var curv = getCurvature(i1,i2,i3,i4,inest);
// Check if this circle has been made in the previous stages.
isThere=checkCurvature(curv,inest);
if(isThere==1) {
st1=circles[inest][i1].stage;
st2=circles[inest][i2].stage;
st3=circles[inest][i3].stage;
st4=circles[inest][i4].stage;
if( st1!=nStage-1 && st2!=nStage-1 && st3!=nStage-1 && st3!=nStage-1) continue;
}
//Check if the 4 circles are in current set
if(fourCircles.length>0){
isNewFour = checkFourCircles(i1,i2,i3,i4,fourCircles);
}
if(isNewFour==0) {
continue;
}
fourCircles.push(i1);
fourCircles.push(i2);
fourCircles.push(i3);
fourCircles.push(i4);
}
}
}
}
nset = fourCircles.length/4;
for(var i=0;i<nset;i++) {
currentCircle[inest]++;
O = {x:0, y:0, curvature:1, tangents:[]};
circles[inest][currentCircle[inest]] = O;
i1 = fourCircles[4*i];
i2 = fourCircles[4*i+1];
i3 = fourCircles[4*i+2];
i4 = fourCircles[4*i+3];
findApollonian(i1,i2,i3,i4,currentCircle[inest],inest);
drawCircle(currentCircle[inest],inest);
curvaturePool[inest].push(circles[inest][currentCircle[inest]].curvature);
}
}
/* Check if a set of 4 circles are already in the set */
function checkFourCircles(n0,n1,n2,n3,cset)
{
// return 0: duplicate
// 1: new - OK to put it into the list
nset = cset.length/4;
narr = [n0,n1,n2];
narr.sort();
for(var i=0;i<nset;i++) {
// compare Apollonian first
// if it's different, the two can't be the same
if(n3!=cset[4*i+3]) continue;
var carr = [cset[4*i],cset[4*i+1],cset[4*i+2]];
carr.sort();
if(narr[0]==carr[0]&&
narr[1]==carr[1]&&
narr[2]==carr[2]) {
return 0;
}
}
return 1;
}
/* Check (1) circle n3 is in the tangents array of n2, vise versa.
(2) circles n1, n2 and n3 shares n4
The conditions (1) and (2) should be met to get an Apollonian */
function checkTangency(n1,n2,n3,n4,inest)
{
var pass = 0;
var passlimit = 12;
// n1 in n2
for(var i=0;i<circles[inest][n2].tangents.length;i++) {
if(n1==circles[inest][n2].tangents[i]) {
pass++;
break;
}
}
// n1 in n3
for(var i=0;i<circles[inest][n3].tangents.length;i++) {
if(n1==circles[inest][n3].tangents[i]) {
pass++;
break;
}
}
// n1 in n4
for(var i=0;i<circles[inest][n4].tangents.length;i++) {
if(n1==circles[inest][n4].tangents[i]) {
pass++;
break;
}
}
// n2 in n1
for(var i=0;i<circles[inest][n1].tangents.length;i++) {
if(n2==circles[inest][n1].tangents[i]) {
pass++;
break;
}
}
// n2 in n3
for(var i=0;i<circles[inest][n3].tangents.length;i++) {
if(n2==circles[inest][n3].tangents[i]) {
pass++;
break;
}
}
// n2 in n4
for(var i=0;i<circles[inest][n4].tangents.length;i++) {
if(n2==circles[inest][n4].tangents[i]) {
pass++;
break;
}
}
// n3 in n1
for(var i=0;i<circles[inest][n1].tangents.length;i++) {
if(n3==circles[inest][n1].tangents[i]) {
pass++;
break;
}
}
// n3 in n2
for(var i=0;i<circles[inest][n2].tangents.length;i++) {
if(n3==circles[inest][n2].tangents[i]) {
pass++;
break;
}
}
// n3 in n4
for(var i=0;i<circles[inest][n4].tangents.length;i++) {
if(n3==circles[inest][n4].tangents[i]) {
pass++;
break;
}
}
// n4 in n1
for(var i=0;i<circles[inest][n1].tangents.length;i++) {
if(n4==circles[inest][n1].tangents[i]) {
pass++;
break;
}
}
// n4 in n2
for(var i=0;i<circles[inest][n2].tangents.length;i++) {
if(n4==circles[inest][n2].tangents[i]) {
pass++;
break;
}
}
// n4 in n3
for(var i=0;i<circles[inest][n3].tangents.length;i++) {
if(n4==circles[inest][n3].tangents[i]) {
pass++;
break;
}
}
if(pass>=passlimit) {
return 1;
}
return 0;
}
// Check if a circle already been made in the previous stages.
// It's done by comparing the curvatures.
function checkCurvature(cv,inest)
{
for(var i=0;i<curvaturePool[inest].length;i++) {
if( Math.round(cv) == Math.round(curvaturePool[inest][i]) ) return 1;
}
return 0;
}
// input: i1,i2,i3 = tangent circles
// i4 = one of Apollonian cicle
function findApollonian(i1,i2,i3,i4,iApollo,inest)
{
var curv = getCurvature(i1,i2,i3,i4,inest);
circles[inest][iApollo].curvature = curv;
var realx = getCoord(1,i1,i2,i3,i4,iApollo,inest);
circles[inest][iApollo].x = realx;
var imagy = getCoord(2,i1,i2,i3,i4,iApollo,inest);
circles[inest][iApollo].y = imagy;
// setup tangents
//new circle
circles[inest][iApollo].tangents.push(i1);
circles[inest][iApollo].tangents.push(i2);
circles[inest][iApollo].tangents.push(i3);
// updates existing tangents of existing circles
circles[inest][i1].tangents.push(iApollo);
circles[inest][i2].tangents.push(iApollo);
circles[inest][i3].tangents.push(iApollo);
// stage
circles[inest][iApollo].stage = nStage;
circlesMap.push(iApollo);
circlesMap.push(i1);
circlesMap.push(i2);
circlesMap.push(i3);
circlesMap.push(i4);
}
function getCoord(flag,i1,i2,i3,i4,i4prime,inest)
{
b1 = circles[inest][i1].curvature;
b2 = circles[inest][i2].curvature;
b3 = circles[inest][i3].curvature;
b4 = circles[inest][i4].curvature;
b4prime = circles[inest][i4prime].curvature;
if(flag==1)
{
z1 = circles[inest][i1].x;
z2 = circles[inest][i2].x;
z3 = circles[inest][i3].x;
z4 = circles[inest][i4].x;
}
else
{
z1 = circles[inest][i1].y;
z2 = circles[inest][i2].y;
z3 = circles[inest][i3].y;
z4 = circles[inest][i4].y;
}
z4prime = (2*b1*z1+2*b2*z2+2*b3*z3-b4*z4)/b4prime;
return z4prime;
}
function getCurvature(i1,i2,i3,i4,inest)
{
b1 = circles[inest][i1].curvature;
b2 = circles[inest][i2].curvature;
b3 = circles[inest][i3].curvature;
b4 = circles[inest][i4].curvature;
b4prime = 2*b1+2*b2+2*b3-b4;
return b4prime;
}
function drawCircle(i,inest)
{
var obj = document.createElementNS(xmlns,"circle");
obj.setAttributeNS(null,"id","circle"+i);
obj.setAttributeNS(null,"cx",drawingScale*circles[inest][i].x);
obj.setAttributeNS(null,"cy",drawingScale*circles[inest][i].y);
obj.setAttributeNS(null,"r",drawingScale*Math.abs(1/circles[inest][i].curvature));
obj.setAttributeNS(null,"fill","none");
obj.setAttributeNS(null,"stroke","black");
if(nStage==1) obj.setAttributeNS(null,"stroke","red");
if(nStage==2) obj.setAttributeNS(null,"stroke","green");
if(nStage==3) obj.setAttributeNS(null,"stroke","blue");
if(nStage==4) obj.setAttributeNS(null,"stroke","purple");
obj.setAttributeNS(null,"stroke-width","1");
document.getElementById("Apollo").appendChild(obj);
/*
if(parseInt(circles[inest][i].curvature) > 0) {
var label = document.createElementNS(xmlns,"text");
label.setAttributeNS(null,"id","label"+i);
label.setAttributeNS(null,"x",drawingScale*circles[inest][i].x);
label.setAttributeNS(null,"y",drawingScale*circles[inest][i].y);
label.setAttributeNS(null,"font-size","12");
label.setAttributeNS(null,"fill","black");
//var txtNode = document.createTextNode(circles[inest][i].curvature);
var txtNode = document.createTextNode(i);
label.appendChild(txtNode);
if(nStage<3) document.getElementById("Apollo").appendChild(label);
}
*/
}
function mouseOverRed()
{
redStop.setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
redStop.setAttributeNS(null,"stop-color", "red");
}
]]>
</script>
<g id="title">
<text id="category" font-size="32"
y="50">
<tspan x="130">Nested Apollonian Gasket </tspan>
<tspan font-size="20" x="170" dy="1.5em">[-n,n+1,n(n+1),n(n+1)+1](n=2,10)</tspan>
</text>
</g>
<g id="Apollo" transform="translate(300,100)">
</g>
<text id="status" y="480" font-size="20">
<tspan x="150" dy="1em">Current Stage (usually up to 5-7): </tspan><tspan id="stage"> 0</tspan>
<!--
<tspan x="150" dy="1em">Circles at This Stage: </tspan><tspan id="circles"> 5</tspan>
<tspan x="150" dy="1em">Total Circles:</tspan><tspan id="totalCircles"> 5</tspan>
-->
</text>
<!-- button -->
<defs>
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
</defs>
<g id="upButton" transform="translate(50,440)"
onclick="stageUp()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="StageCircle" cx = "50" cy="50" r="20" fill="url(#RedG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="subNote">
<text font-size="14" y="530">
<tspan x="90" dy="0em">
Note: As the stage number going up, it's getting slower and slower.
</tspan>
<tspan x="90" dy="1em">
Since it's generating circles on the fly, your browser may suffer at higher stage.
</tspan>
<tspan x="90" dy="1em">
I haven't got to stage 8 with my algorithm. It seems to take forever.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Pythagorean (Pythagoras') Theorem - SMIL
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
]]>
</script>
<g id="title">
</g>
<g id="Pythagoras" transform="translate(100,100)">
<text id="title" font-family="serif" font-size="40" x="-30" y="-30">
Pythagorean theorem
</text>
<!-- background big square -->
<rect id="BigSquare" x="0" y="0" width="350" height="350"
stroke="lime" stroke-width="1" fill="green"/>
<g id="abcSquare">
<!-- a^2 -->
<text x = "90" y = "65" font-family="serif" font-size = "30" fill = "white" opacity="0">2
<animate attributeName="opacity" keyTimes="0;0.3;0.5;1" values="0;0;1;1" begin="2s" dur="20s" repeatCount="1" fill="freeze"/>
</text>
<text x = "50" y = "85" font-family="serif" font-size = "60" fill = "white" opacity="0">
a
<animate attributeName="opacity" keyTimes="0;0.3;0.5;1" values="0;0;1;1" begin="2s" dur="20s" repeatCount="1" fill="freeze"/>
</text>
<!-- b^2 -->
<text x = "260" y = "95" font-family="serif" font-size = "30" fill = "white" opacity="0">2
<animate attributeName="opacity" keyTimes="0;0.8;0.9;1" values="0;0;1;1" begin="2s" dur="20s" repeatCount="1" fill="freeze"/>
</text>
<text x = "220" y = "115" font-family="serif" font-size = "60" fill = "white" opacity="0">
b
<animate attributeName="opacity" keyTimes="0;0.8;0.9;1" values="0;0;1;1" begin="2s" dur="20s" repeatCount="1" fill="freeze"/>
</text>
<!-- c^2 -->
<text x = "185" y = "155" font-family="serif" font-size = "30" fill = "white" opacity="0">
2
<animate attributeName="opacity" keyTimes="0;0.25;0.4;1" values="1;1;0;0" begin="0s" dur="20s" repeatCount="1" fill="freeze" />
</text>
<text x = "145" y = "175" font-family="serif" font-size = "60" fill = "white" opacity="0">
c
<animate attributeName="opacity" keyTimes="0;0.25;0.4;1" values="1;1;0;0" begin="0s" dur="20s" repeatCount="1" fill="freeze"/>
</text>
</g>
<!-- partition between a^2 and b^2-->
<path id="triangleA" d="M150 0 L150 150" fill="none"
stroke="white" stroke-width="2" opacity="0">
<animate attributeName="opacity" keyTimes="0;0.3;0.5;1" values="0;0;1;1" begin="2s" dur="20s" repeatCount="1" fill="freeze"/>
</path>
<!--lower left-->
<path id="triangleA" d="M0 150 L0 350 150 350 z" fill="lime"
stroke="white" stroke-width="2"/>
<!--lower right-->
<path id="triangleB" d="M150 350 L350 200 350 350 z" fill="lime"
stroke="white" stroke-width="2">
</path>
<!--upper left-->
<path id="triangleC" d="M0 0 L0 150 200 0 z" fill="lime"
stroke="white" stroke-width="2">
<animateTransform attributeName="transform" type="rotate"
cx="0" cy="150" begin="2s" dur="10s" values="0,0,150;90,0,150" fill="freeze" repeatCount="1"/>
</path>
<!--upper right-->
<path id="triangleD" d="M200 0 L350 200 350 0 z" fill="lime"
stroke="white" stroke-width="2">
<animateTransform attributeName="transform" type="rotate"
cx="0" cy="150" dur="10s" values="0,350,200;-90,350,200" fill="freeze" repeatCount="1"
begin="12"
/>
</path>
</g>
<g id="Note">
<text font-family="serif" font-size="28" y="500" fill="black">
<tspan x="65" dy="0em">
Dark green area remains the same.
</tspan>
<tspan x="150" dy="1em">
It's c-squared.
</tspan>
</text>
</g>
</svg>
SVG Math Animation Example: Pythagorean (Pythagoras') Theorem - SMIL Proof #2
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
viewBox="0 0 2000 1600"
width="100%"
height="100%"
xml:space="preserve"
onload = "startUp(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
function startUp(evt)
{}
]]>
</script>
<g id="title">
</g>
<text id="title" font-family="serif" font-size="100" x="100" y="200">
Pythagorean theorem #2
</text>
<g id="Pythagoras" transform="translate(800,1000) rotate(90)">
<!-- 1st stage of animation -trianlge moving -->
<!-- side 5 square excluding moving triangle -->
<path id="Square5A" d="M-300 0 L0 400 -400 700 -400 300 -700 300 z" fill="green" stroke="none">
<animate id="Square5AColor" attributeName="fill" begin="para4MovingA.begin" dur="10s" repeatCount="1" fill="freeze"
keyTimes="0;1"
values="white;white" />
</path>
<!-- moving triangle -->
<path id="Square5BTriangle" d="M-400 700 L-400 300 -700 300 z" fill="green" stroke="none">
<animate id="triangleMove" attributeName="d" begin="1s" dur="3s" repeatCount="1" fill="freeze"
values=
"M-400 700 L-400 300 -700 300 z;
M0 400 L0 0 -300 0 z" />
<animate id="triangleColorChange" attributeName="fill" begin="1s" dur="3s" repeatCount="1" fill="freeze"
keyTimes="0;0.1;0.9;1"
values="green;lime;lime;green" />
<animate id="Square5BTriangleColor" attributeName="fill" begin="para4MovingA.begin" dur="10s" repeatCount="1" fill="freeze"
keyTimes="0;1"
values="white;white" />
</path>
<!-- 2nd stage of animation -2 parallelograms moving -->
<path id="parallel4" fill="green" stroke="none">
<animate id="para4MovingA" attributeName="d"
begin="triangleMove.end+1" dur="10s" fill="freeze"
keyTimes="0;0.4;0.6;1"
values=
"M0 0 L0 400 -400 700 -400 300 z;
M400 -300 L400 100 0 400 0 0 z;
M400 -300 L400 100 0 400 0 0 z;
M400 0 L400 400 0 400 0 0 z"/>
</path>
<path id="parallel3" fill="green" stroke="none">
<animate id="para4MovingB" attributeName="d"
begin="triangleMove.end+1"
dur="10s" fill="freeze"
keyTimes="0;0.4;0.6;1"
values=
"M0 0 L-300 0 -700 300 -400 300 z;
M400 -300 L100 -300 -300 0 0 0 z;
M400 -300 L100 -300 -300 0 0 0 z;
M0 -300 -300 -300 -300 0 0 0 z"/>
</path>
<!-- Square5,4,3 are the fixture. They are not moving parts -->
<path id="Square5" d="M-300 0 L0 400 -400 700 -700 300 z" fill="none" stroke="black" stroke-width="2">
<animate id="Square5ColorChange" attributeName="fill"
begin="para4MovingA.end" dur="2s" repeatCount="indefinite" fill="freeze"
keyTimes="0;0.25;0.75;1"
values="lime;green;lime;green" />
</path>
<path id="Square4" d="M0 0 L0 400 400 400 400 0 z" fill="none" stroke="black" stroke-width="2">
<animate id="Square5ColorChange" attributeName="fill"
begin="para4MovingB.end" dur="2s" repeatCount="indefinite" fill="freeze"
keyTimes="0;0.5;0.75;1"
values="lime;green;lime;green" />
</path>
<path id="Square3" d="M-300 0 L0 0 0 -300 -300 -300 z" fill="none" stroke="black" stroke-width="2">
<animate id="Square5ColorChange" attributeName="fill"
begin="para4MovingB.end" dur="2s" repeatCount="indefinite" fill="freeze"
keyTimes="0;0.5;0.75;1.0"
values="lime;green;lime;green" />
</path>
</g>
</svg>
SVG Math Animation Example: Cycloid with Javascript
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onresize="resize()"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var wWidth;
var wHeight;
var RPS = 0.2;
var X = 0;
var Y = 0;
var RWheel = 1.0;
var Routside = RWheel;
var Rmiddle = RWheel/2.0;
var dotSize = 0.1;
var Scale = 30;
var wheel;
var oDot;
var mDot;
var cDot;
var oCycloid;
var mCycloid;
var cCycloid;
var connector;
var T = 0.0;
var Counter = 0;
var Omega = RPS *2*Math.PI;
var Tinc = 25;
var oPathString="";
var mPathString="";
var cPathString="";
var connectorPathString="";
var phi = Math.PI;
function startup(evt)
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
wheel = document.getElementById("Wheel");
oDot = document.getElementById("OutsideDot");
mDot = document.getElementById("MiddleDot");
cDot = document.getElementById("CenterDot");
oCycloid= document.getElementById("OutsideCycloid");
mCycloid= document.getElementById("MiddleCycloid");
cCycloid= document.getElementById("CenterCycloid");
connector= document.getElementById("Connector");
calculateXY();
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
wheel.setAttributeNS(null,"r",RWheel*Scale);
var x = X+Routside*Math.cos(Omega*T+phi);
var y = Y+Routside*Math.sin(Omega*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
oDot.setAttributeNS(null,"r",dotSize*Scale);
oPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+
" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos(Omega*T+phi);
var y = Y+Rmiddle*Math.sin(Omega*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
mDot.setAttributeNS(null,"r",dotSize*Scale);
mPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
cDot.setAttributeNS(null,"r",dotSize*Scale);
setInterval("Animate()",Tinc);
}
function calculateXY()
{
T = Counter*Tinc/1000;
X = 2*Math.PI*RWheel*RPS*T;
Y = 0.0;
}
function Animate()
{
Counter++;
calculateXY();
if( X*Scale > wWidth-2*RWheel*Scale-Scale)
{
return;
}
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
var x = X+Routside*Math.cos(Omega*T+phi);
var y = Y+Routside*Math.sin(Omega*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
oPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+
" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos(Omega*T+phi);
var y = Y+Rmiddle*Math.sin(Omega*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
mPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString +=" L"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
}
function resize()
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
}
]]>
</script>
<g id="title">
<text font-size="40" x="60" y="50">Simple Cycloid
</text>
</g>
<g id="MyCycloid" transform="translate(50,120)">
<circle id="Wheel" stroke-width="2" stroke="black" fill="none"/>
<circle id="OutsideDot" stroke-width="2" stroke="none" fill="red"/>
<circle id="MiddleDot" stroke-width="2" stroke="none" fill="blue"/>
<circle id="CenterDot" stroke-width="2" stroke="none" fill="black"/>
<path id="OutsideCycloid" stroke-width="2" stroke="red" fill="none"/>
<path id="MiddleCycloid" stroke-width="1" stroke="blue" fill="none" opacity="0.5"/>
<path id="CenterCycloid" stroke-width="1" stroke="gray" fill="none" opacity="0.1"/>
<path id="Connector" stroke-width="1" stroke="green" fill="none"/>
</g>
</svg>
SVG Math Animation Example: N-Cusp Epicycloid with Javascript
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onresize="resize()"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var wWidth;
var wHeight;
var RPS = 1.0;
var baseTheta = 0.0;
var X = 0;
var Y = 0;
var RBase = 8.0;
var RWheel = 3.0;
var Routside = RWheel;
var Rmiddle = RWheel/2.0;
var dotSize = RWheel/10.0;
var Scale = 10;
var wheel;
var oDot;
var mDot;
var cDot;
var oCycloid;
var mCycloid;
var cCycloid;
var connector;
var T = 0.0;
var Counter = 0;
var Omega = RPS *2*Math.PI;
var baseOmega = Omega *RWheel/RBase;
var Tinc = 25;
var oPathString="";
var mPathString="";
var cPathString="";
var connectorPathString="";
var phi = 0;
var basePhi = 0;
// Do not make more path string after 1-cycle
var NPath = 1000/Tinc/RPS*Math.max(RBase,RWheel)+1;
function startup(evt)
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
base = document.getElementById("Base");
wheel = document.getElementById("Wheel");
oDot = document.getElementById("OutsideDot");
mDot = document.getElementById("MiddleDot");
cDot = document.getElementById("CenterDot");
oCycloid= document.getElementById("OutsideCycloid");
mCycloid= document.getElementById("MiddleCycloid");
cCycloid= document.getElementById("CenterCycloid");
connector= document.getElementById("Connector");
base.setAttributeNS(null,"r",RBase*Scale);
calculateXY();
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
wheel.setAttributeNS(null,"r",RWheel*Scale);
var x = X+Routside*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega+Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
oDot.setAttributeNS(null,"r",dotSize*Scale);
oPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
connectorPathString =
"M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega+Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
mDot.setAttributeNS(null,"r",dotSize*Scale);
mPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
cDot.setAttributeNS(null,"r",dotSize*Scale);
setInterval("Animate()",Tinc);
}
function calculateXY()
{
// calculate the center coordinates of the Wheel.
T = Counter*Tinc/1000;
X = (RBase+RWheel)*Math.cos(baseOmega*T+basePhi);
Y =(RBase+RWheel)*Math.sin(baseOmega*T+basePhi);
}
function Animate()
{
Counter++;
calculateXY();
if( X*Scale > wWidth-2*RWheel*Scale-Scale)
{
return;
}
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
var x = X+Routside*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega+Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
oPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
}
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+
" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega+Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
mPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString +=" L"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
}
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
}
function resize()
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
}
]]>
</script>
<g id="title">
<text font-size="40" x="120" y="50">N-cusp Epicycloid
</text>
</g>
<g id="MyCycloid" transform="translate(250,250)">
<circle id="Base" cx="0" cy="0" stroke-width="1" stroke="green" fill="lime" opacity="0.2"/>
<circle id="Wheel" stroke-width="1" stroke="black" fill="none"/>
<circle id="OutsideDot" stroke-width="1" stroke="none" fill="red"/>
<circle id="MiddleDot" stroke-width="1" stroke="none" fill="blue" opacity="0.0"/>
<circle id="CenterDot" stroke-width="1" stroke="none" fill="black"/>
<path id="OutsideCycloid" stroke-width="1" stroke="red" fill="none"/>
<path id="MiddleCycloid" stroke-width="1" stroke="blue" fill="none" opacity="0.0"/>
<path id="CenterCycloid" stroke-width="2" stroke="gray" fill="none" opacity="0.0"/>
<path id="Connector" stroke-width="1" stroke="green" fill="none"/>
</g>
</svg>
SVG Math Animation Example: Irrational Epicycloid with Javascript
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onresize="resize()"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var wWidth;
var wHeight;
var RPS = 1.0;
var baseTheta = 0.0;
var X = 0;
var Y = 0;
var RBase = 10.0;
var RWheel = Math.sqrt(5.0);
var Routside = RWheel;
var Rmiddle = RWheel/2.0;
var dotSize = RWheel/10.0;
var Scale = 10;
var wheel;
var oDot;
var mDot;
var cDot;
var oCycloid;
var mCycloid;
var cCycloid;
var connector;
var T = 0.0;
var Counter = 0;
var Omega = RPS *2*Math.PI;
var baseOmega = Omega *RWheel/RBase;
var Tinc = 25;
var oPathString="";
var mPathString="";
var cPathString="";
var connectorPathString="";
var phi = 0;
var basePhi = 0;
// make more path string after 1-cycle
// We can not impose limit to the NPath for irrational case
//var NPath = 1000/Tinc/RPS*Math.max(RBase,RWheel)+1;
// Just to keep it from slowing down to much
var NPath = 10000;
function startup(evt)
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
base = document.getElementById("Base");
wheel = document.getElementById("Wheel");
oDot = document.getElementById("OutsideDot");
mDot = document.getElementById("MiddleDot");
cDot = document.getElementById("CenterDot");
oCycloid= document.getElementById("OutsideCycloid");
mCycloid= document.getElementById("MiddleCycloid");
cCycloid= document.getElementById("CenterCycloid");
connector= document.getElementById("Connector");
base.setAttributeNS(null,"r",RBase*Scale);
calculateXY();
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
wheel.setAttributeNS(null,"r",RWheel*Scale);
var x = X+Routside*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega+Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
oDot.setAttributeNS(null,"r",dotSize*Scale);
oPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
connectorPathString =
"M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega+Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
mDot.setAttributeNS(null,"r",dotSize*Scale);
mPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
cDot.setAttributeNS(null,"r",dotSize*Scale);
setInterval("Animate()",Tinc);
}
function calculateXY()
{
// calculate the center coordinates of the Wheel.
T = Counter*Tinc/1000;
X = (RBase+RWheel)*Math.cos(baseOmega*T+basePhi);
Y =(RBase+RWheel)*Math.sin(baseOmega*T+basePhi);
}
function Animate()
{
Counter++;
calculateXY();
if( X*Scale > wWidth-2*RWheel*Scale-Scale)
{
return;
}
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
var x = X+Routside*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega+Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
oPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
}
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+
" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega+Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega+Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
mPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString +=" L"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
}
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
}
function resize()
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
}
]]>
</script>
<g id="title">
<text font-size="40" x="100" y="50">Irrational Epicycloid
</text>
</g>
<g id="MyCycloid" transform="translate(250,250)">
<circle id="Base" cx="0" cy="0" stroke-width="1" stroke="green" fill="lime" opacity="0.5"/>
<circle id="Wheel" stroke-width="1" stroke="black" fill="none"/>
<circle id="OutsideDot" stroke-width="1" stroke="none" fill="red"/>
<circle id="MiddleDot" stroke-width="1" stroke="none" fill="blue" opacity="0.0"/>
<circle id="CenterDot" stroke-width="1" stroke="none" fill="black"/>
<path id="OutsideCycloid" stroke-width="1" stroke="red" fill="none"/>
<path id="MiddleCycloid" stroke-width="1" stroke="blue" fill="none" opacity="0.0"/>
<path id="CenterCycloid" stroke-width="2" stroke="gray" fill="none" opacity="0.0"/>
<path id="Connector" stroke-width="1" stroke="green" fill="none"/>
</g>
</svg>
SVG Math Animation Example: N-Cusp Hypocycloid with Javascript
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onresize="resize()"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var wWidth;
var wHeight;
var RPS = 1.0;
var baseTheta = 0.0;
var X = 0;
var Y = 0;
var RBase = 6;
var RWheel = 1;
var Routside = RWheel;
var Rmiddle = RWheel/2.0;
var dotSize = RWheel/10.0;
var Scale = 25;
var wheel;
var oDot;
var mDot;
var cDot;
var oCycloid;
var mCycloid;
var cCycloid;
var connector;
var T = 0.0;
var Counter = 0;
var Omega = RPS *2*Math.PI;
var baseOmega = Omega *RWheel/RBase;
var Tinc = 25;
var oPathString="";
var mPathString="";
var cPathString="";
var connectorPathString="";
var phi = 0;
var basePhi = 0;
var NPath=1000;
function startup(evt)
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
base = document.getElementById("Base");
wheel = document.getElementById("Wheel");
oDot = document.getElementById("OutsideDot");
mDot = document.getElementById("MiddleDot");
cDot = document.getElementById("CenterDot");
oCycloid= document.getElementById("OutsideCycloid");
mCycloid= document.getElementById("MiddleCycloid");
cCycloid= document.getElementById("CenterCycloid");
connector= document.getElementById("Connector");
base.setAttributeNS(null,"r",RBase*Scale);
calculateXY();
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
wheel.setAttributeNS(null,"r",RWheel*Scale);
var x = X+Routside*Math.cos((baseOmega-Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega-Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
oDot.setAttributeNS(null,"r",dotSize*Scale);
oPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
connectorPathString =
"M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega-Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega-Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
mDot.setAttributeNS(null,"r",dotSize*Scale);
mPathString ="M"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
cDot.setAttributeNS(null,"r",dotSize*Scale);
setInterval("Animate()",Tinc);
}
function calculateXY()
{
// calculate the center coordinates of the Wheel.
T = Counter*Tinc/1000;
X = (RBase-RWheel)*Math.cos(baseOmega*T+basePhi);
Y =(RBase-RWheel)*Math.sin(baseOmega*T+basePhi);
}
function Animate()
{
Counter++;
calculateXY();
if( X*Scale > wWidth-2*RWheel*Scale-Scale)
{
return;
}
wheel.setAttributeNS(null,"cx",X*Scale);
wheel.setAttributeNS(null,"cy",Y*Scale);
var x = X+Routside*Math.cos((baseOmega-Omega)*T+phi);
var y = Y+Routside*Math.sin((baseOmega-Omega)*T+phi);
oDot.setAttributeNS(null,"cx",x*Scale);
oDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
oPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
oCycloid.setAttributeNS(null,"d",oPathString);
}
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+
" L"+ Math.round(x*Scale)+","+Math.round(y*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
var x = X+Rmiddle*Math.cos((baseOmega-Omega)*T+phi);
var y = Y+Rmiddle*Math.sin((baseOmega-Omega)*T+phi);
mDot.setAttributeNS(null,"cx",x*Scale);
mDot.setAttributeNS(null,"cy",y*Scale);
if(Counter<=NPath) {
mPathString +=" L"+Math.round(x*Scale)+","+Math.round(y*Scale);
mCycloid.setAttributeNS(null,"d",mPathString);
cPathString +=" L"+Math.round(X*Scale)+","+Math.round(Y*Scale);
cCycloid.setAttributeNS(null,"d",cPathString);
}
cDot.setAttributeNS(null,"cx",X*Scale);
cDot.setAttributeNS(null,"cy",Y*Scale);
}
function resize()
{
wWidth = window.innerWidth;
wHeight = window.innerHeight;
}
]]>
</script>
<g id="title">
<text font-size="40" x="100" y="50">N-cusp Hypocycloid
</text>
</g>
<g id="MyCycloid" transform="translate(250,250)">
<circle id="Base" cx="0" cy="0" stroke-width="1" stroke="blue" fill="none" opacity="1.0"/>
<circle id="Wheel" stroke-width="2" stroke="black" fill="none"/>
<circle id="OutsideDot" stroke-width="1" stroke="none" fill="red"/>
<circle id="MiddleDot" stroke-width="1" stroke="none" fill="green" opacity="0.0"/>
<circle id="CenterDot" stroke-width="1" stroke="none" fill="black"/>
<path id="OutsideCycloid" stroke-width="1" stroke="red" fill="none" />
<path id="MiddleCycloid" stroke-width="1" stroke="green" fill="none" opacity="1.0"/>
<path id="CenterCycloid" stroke-width="2" stroke="gray" fill="none" opacity="0.2"/>
<path id="Connector" stroke-width="1" stroke="green" fill="none"/>
</g>
</svg>
SVG Math Animation Example: Trammel of Archimedes - Ellipse Tracing Mechanism
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/SVG/DTD/svg10.dtd" >
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
version="1.1"
width="100%"
height="100%"
xml:space="preserve"
onload = "startup(evt)">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var wWidth;
var wHeight;
//major, minor axis and focus
var a = 15;
var b = 5;
var c = Math.sqrt(Math.pow(a,2)-Math.pow(b,2));
var dotA = 1;
var dotB = 1;
var dotAsm = dotA/5.0;
var dotBsm = dotB/5.0;
var dotEllipse = 0.2;
var X ;
var Y ;
var Xa;
var Ya = 0;
var Xb = 0;
var Yb;
var Scale = 10;
var x_axis;
var y_axis;
var connector;
var ellipse;
var ellipseDot;
var baseA;
var baseB;
var baseAsm;
var baseBsm;
var T = 0.0;
var Counter = 0;
var Tinc = 25;
var ePathString="";
var connectorPathString="";
var RPS = 0.1;
var Omega = RPS *2*Math.PI;
var phi = 0;
var basePhi = 0;
// Do not make more path string after 1-cycle
var NPath = 1000/Tinc/RPS+1;
function startup(evt)
{
calculateXY();
x_axis = document.getElementById("x-axis");
y_axis = document.getElementById("y-axis");
connector = document.getElementById("Connector");
ellipse = document.getElementById("Ellipse");
ellipseDot = document.getElementById("EllipseDot");
baseA = document.getElementById("BaseA");
baseB = document.getElementById("BaseB");
baseAsm = document.getElementById("BaseAsm");
baseBsm = document.getElementById("BaseBsm");
x_axis.setAttributeNS(null,"d","M"+(-a-b)*Scale+",0"+
" L"+(a+b)*Scale+",0");
y_axis.setAttributeNS(null,"d","M0,"+(-a)*Scale+
" L0,"+a*Scale);
baseA.setAttributeNS(null,"cx",Xa*Scale);
baseA.setAttributeNS(null,"cy",Ya*Scale);
baseA.setAttributeNS(null,"r",dotA*Scale);
baseB.setAttributeNS(null,"cx",Xb*Scale);
baseB.setAttributeNS(null,"cy",Yb*Scale);
baseB.setAttributeNS(null,"r",dotB*Scale);
baseAsm.setAttributeNS(null,"cx",Xa*Scale);
baseAsm.setAttributeNS(null,"cy",Ya*Scale);
baseAsm.setAttributeNS(null,"r",dotAsm*Scale);
baseBsm.setAttributeNS(null,"cx",Xb*Scale);
baseBsm.setAttributeNS(null,"cy",Yb*Scale);
baseBsm.setAttributeNS(null,"r",dotBsm*Scale);
ellipseDot.setAttributeNS(null,"cx",X*Scale);
ellipseDot.setAttributeNS(null,"cy",Y*Scale);
ellipseDot.setAttributeNS(null,"r",dotEllipse*Scale);
ePathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
ellipse.setAttributeNS(null,"d",ePathString);
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+" L"+Math.round(Xb*Scale)+","+Math.round(Yb*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
setInterval("Animate()",Tinc);
}
function calculateXY()
{
T = Counter*Tinc/1000;
X = a*Math.cos(Omega*T+basePhi);
Y = b*Math.sin(Omega*T+basePhi);
if(X >= 0) Xa = X - Math.sqrt(b*b-Y*Y);
else if(X < 0)Xa = X + Math.sqrt(b*b-Y*Y);
if(Y >= 0) Yb = Y - Math.sqrt(a*a-X*X);
else if(Y < 0) Yb = Y + Math.sqrt(a*a-X*X);
}
function Animate()
{
Counter++;
calculateXY();
baseA.setAttributeNS(null,"cx",Xa*Scale);
baseA.setAttributeNS(null,"cy",Ya*Scale);
baseA.setAttributeNS(null,"r",dotA*Scale);
baseB.setAttributeNS(null,"cx",Xb*Scale);
baseB.setAttributeNS(null,"cy",Yb*Scale);
baseB.setAttributeNS(null,"r",dotB*Scale);
baseAsm.setAttributeNS(null,"cx",Xa*Scale);
baseAsm.setAttributeNS(null,"cy",Ya*Scale);
baseAsm.setAttributeNS(null,"r",dotAsm*Scale);
baseBsm.setAttributeNS(null,"cx",Xb*Scale);
baseBsm.setAttributeNS(null,"cy",Yb*Scale);
baseBsm.setAttributeNS(null,"r",dotBsm*Scale);
ellipseDot.setAttributeNS(null,"cx",X*Scale);
ellipseDot.setAttributeNS(null,"cy",Y*Scale);
ellipseDot.setAttributeNS(null,"r",dotEllipse*Scale);
if(Counter <= NPath) {
ePathString +=" L"+Math.round(X*Scale)+","+Math.round(Y*Scale);
ellipse.setAttributeNS(null,"d",ePathString);
}
connectorPathString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale)+" L"+Math.round(Xb*Scale)+","+Math.round(Yb*Scale);
connector.setAttributeNS(null,"d",connectorPathString);
}
]]>
</script>
<g id="title">
<text font-size="40" x="50" y="50">
<tspan>Trammel of Archimedes</tspan>
<tspan x="100" dy="1em" font-size="24">Ellipse Tracing Mechanism </tspan>
</text>
</g>
<g id="MyTrammel" transform="translate(250,250)">
<path id="x-axis" stroke-width="1" stroke="black" fill="none"/>
<path id="y-axis" stroke-width="1" stroke="black" fill="none"/>
<circle id="EllipseDot" cx="0" cy="0" stroke-width="1" stroke="purple" fill="red" opacity="1.0"/>
<circle id="BaseA" cx="0" cy="0" stroke-width="1" stroke="green" fill="lime" opacity="1.0"/>
<circle id="BaseB" cx="0" cy="0" stroke-width="1" stroke="blue" fill="aqua" opacity="1.0"/>
<circle id="BaseAsm" cx="0" cy="0" stroke-width="1" stroke="green" fill="green" opacity="1.0"/>
<circle id="BaseBsm" cx="0" cy="0" stroke-width="1" stroke="blue" fill="blue" opacity="1.0"/>
<path id="Ellipse" stroke-width="1" stroke="red" fill="none" opacity="1.0"/>
<path id="Connector" stroke-width="1" stroke="black" fill="white"/>
</g>
</svg>
SVG Animation Example: Opacity - Bubbles or Balloons in Purple
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg width="100%" height="100%"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()"
onmousemove="mouseMove(evt)"
onresize="resize()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
object = new Array()
var nw = nh = xm = ym = 0 ;
var Nbubble = 20 ;
var mouseCount = 0;
var Limit = 100;
function startUp()
{
resize();
for(i=0;i<Nbubble;i++) {
object[i] = new makeSphere(i);
}
setInterval("for (i in object)object[i].moveSphere()",20)
}
function makeSphere(N)
{
this.bubble = document.createElementNS(xmlns,"circle");
document.getElementById("GroupOfBubbles").appendChild(this.bubble);
this.r = (N * Limit / Nbubble);
this.x = -500;
this.y = 0;
this.moveSphere = function(){
with(this){
if (r >= Limit){
mouseCount--;
if (mouseCount<0){
x = Math.random() * nw;
y = Math.random() * nh;
}
else {
x = xm;
y = ym;
}
r = 0;
}
r += 3;
bubble.setAttributeNS(null,"cx",x);
bubble.setAttributeNS(null,"cy",y);
bubble.setAttributeNS(null,"r",r);
bubble.setAttributeNS(null,"fill","url(#rg)");
bubble.setAttributeNS(null,"opacity",(Limit - r) / Limit);
}
}
}
function resize()
{
nw = window.innerWidth;
nh = window.innerHeight;
}
function mouseMove(e)
{
xm = e.clientX;
ym = e.clientY;
mouseCount = 1;
}
]]>
</script>
<defs>
<radialGradient id="rg" cx="20%" cy="20%" r="100%" fx="30%" fy="30%" >
<stop stop-color="white" offset="0" stop-opacity="0.5"/>
<stop stop-color="fuchsia" offset="20%" stop-opacity="0.5"/>
<stop stop-color="purple" offset="80%" stop-opacity="0.5"/>
<stop stop-color="purple" offset="100%" stop-opacity="0.5"/>
</radialGradient>
</defs>
<rect height="100%" width="100%" fill="white"/>
<g id="GroupOfBubbles">
<circle id="myBubble" cx="-150" cy="-150" r="50" fill="url(#rg)" />
</g>
</svg>
SVG Animation Example: Path - Polygon vs. Circle (Area)
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg width="100%" height="100%"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var X;
var Y;
var Tinc = 1000;
var Limit = 360;
var Scale = 200;
var Npoly = 3;
var poly;
var txtArea;
var txtNpoly;
function startUp()
{
poly = document.getElementById("myPoly");
txtNpoly = document.getElementById("nPoly");
txtArea = document.getElementById("areaPoly");
document.getElementById("myCircle").setAttributeNS(null,"r",Scale);
setInterval("makeMeCircle()",Tinc)
}
function makeMeCircle()
{
if(Npoly > Limit) return;
var polyString = "";
var x0 = X = 1;
var y0 = Y = 0;
polyString ="M"+Math.round(X*Scale)+","+Math.round(Y*Scale);
for (var i=1;i<Npoly;i++) {
X = Math.cos(2*Math.PI*i/Npoly);
Y = Math.sin(2*Math.PI*i/Npoly);
polyString += " L"+ Math.round(X*Scale)+","+Math.round(Y*Scale);
}
polyString +=" z";
poly.setAttributeNS(null,"d",polyString);
txtNpoly.firstChild.nodeValue = "N: "+Npoly;
// calculate the outer edge length of sub-triangle
X = Math.cos(2*Math.PI/Npoly);
Y = Math.sin(2*Math.PI/Npoly);
var dist = Math.sqrt( (x0-X)*(x0-X)+(y0-Y)*(y0-Y) );
// area
area = heron(dist,1.0,1.0)* Npoly ;
txtArea.firstChild.nodeValue = "Filled: "+(area/Math.PI*100).toFixed(2)+"%";
Npoly++;
}
function heron(a,b,c)
{
var s = (a+b+c)/2.0;
return Math.sqrt( s*(s-a)*(s-b)*(s-c) );
}
]]>
</script>
<defs>
<radialGradient id="rg" cx="50%" cy="50%" r="100%" fx="50%" fy="50%" >
<stop stop-color="lime" offset="0%" stop-opacity="0.5"/>
<stop stop-color="lime" offset="20%" stop-opacity="0.5"/>
<stop stop-color="green" offset="80%" stop-opacity="0.5"/>
<stop stop-color="green" offset="100%" stop-opacity="0.5"/>
</radialGradient>
</defs>
<g id="Polygon" transform="translate(250,300)">
<text id="title" x="-180" y="-230" font-size="40"> N-Polygon vs Circle </text>
<circle id="myCircle" cx="0" cy="0" r="200" stroke="black" stroke-width="2" fill="none"/>
<path id="myPoly" stroke="green" stroke-width="1" fill="url(#rg)" />
<text id="nPoly" x="-70" y="-20" font-size="30" fill="black">
N: 0
</text>
<text id="areaPoly" x="-70" y="10" font-size="30" fill="black">
Filled: 0
</text>
</g>
</svg>
SVG Animation Example: Embracing Limit - Polygon Circumscribing Circle. Starting from incircle-> triangle->circumcircle->square->circumcircle->pentagon .... The ratio of final circumradius to initial inradius is 8.7000...
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg width="100%" height="100%"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var ri = 1.0;
var r;
var Tinc = 1000;
var Limit = 7200;
var Scale = 20;
var Npoly = 3;
var poly;
var txtNpoly;
var txtRatio;
function startUp()
{
txtNpoly = document.getElementById("nPoly");
txtRatio = document.getElementById("ratio");
document.getElementById("circle0").setAttributeNS(null,"r",ri*Scale);
r = ri;
setInterval("beingCircumscribed()",Tinc)
}
function beingCircumscribed()
{
if(Npoly > Limit) return;
var R = r/Math.cos(Math.PI/Npoly);
var skip = 0;
if((R-r)*Scale < 0.1) skip = 1;
var polyString = "M"+R*Scale+","+"0";
for (var i=1;i<Npoly;i++) {
var X = R*Math.cos(2*Math.PI*i/Npoly);
var Y = R*Math.sin(2*Math.PI*i/Npoly);
polyString += " L"+ Math.round(X*Scale)+","+Math.round(Y*Scale);
}
polyString +=" z";
if(skip==0) {
var objp = document.createElementNS(xmlns,"path");
objp.setAttributeNS(null,"fill","none");
setStrokeColor(objp);
objp.setAttributeNS(null,"stroke-width","1");
objp.setAttributeNS(null,"d",polyString);
document.getElementById("Circumscribe").appendChild(objp);
var objc = document.createElementNS(xmlns,"circle");
objc.setAttributeNS(null,"cx","0");
objc.setAttributeNS(null,"cy","0");
objc.setAttributeNS(null,"r",R*Scale);
objc.setAttributeNS(null,"fill","none");
setStrokeColor(objc);
objc.setAttributeNS(null,"stroke-width","1");
document.getElementById("Circumscribe").appendChild(objc);
}
txtNpoly.firstChild.nodeValue = "N-polygon: "+Npoly;
txtRatio.firstChild.nodeValue = "r/ri: "+r.toFixed(5);
r = R;
Npoly++;
}
function heron(a,b,c)
{
var s = (a+b+c)/2.0;
return Math.sqrt( s*(s-a)*(s-b)*(s-c) );
}
function setStrokeColor(obj)
{
obj.setAttributeNS(null,"stroke",color());
}
function color(){
var r=Math.random()*(16777215);
return "#"+Math.floor(r).toString(16);
}
]]>
</script>
<g id="Circumscribe" transform="translate(250,300)">
<text id="title" x="-180" y="-250" font-size="40">
<tspan x="-140" dy="0"> Embracing Limit</tspan>
<tspan x="-140" font-size="30" dy="1.2em">(r/ri = 8.700036625...)</tspan>
</text>
<circle id="circle0" cx="0" cy="0" r="10" stroke="black" stroke-width="1" fill="none"/>
<text id="nPoly" x="-70" y="220" font-size="30" fill="black">
N-polygon: 0
</text>
<text id="ratio" x="-70" y="250" font-size="30" fill="black">
r/ri: 1.00000
</text>
</g>
</svg>
SVG Animation Example: Standing Wave - superposed two waves moving in opposite directions. Animated with variable frequency and wave number.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg width="100%" height="100%"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var t = 0;
// wave parameters
var f = 1.0;
var lambda = 1.5;
var k;
var omega;
// string geometry
var ym = 0.7;
var xLength = 3.0;
// drawing variables
var Scale = 100.0;
var st;
var end;
var nPoints = 360;
var nRatio = 6;
var nAmps = nPoints/nRatio;
var amps = new Array(nAmps);
// time interval
var Tinc=10;
function startUp()
{
for(var i=0;i<nAmps;i++) {
amps[i] = document.createElementNS(xmlns,"path");
amps[i].setAttributeNS(null,"fill","none");
amps[i].setAttributeNS(null,"stroke","red");
amps[i].setAttributeNS(null,"stroke-width","1");
document.getElementById("WaveGroup").appendChild(amps[i]);
}
st = document.getElementById("st");
end = document.getElementById("end")
setParams();
setInterval("motion()",Tinc)
}
function setParams()
{
k = 2*Math.PI/lambda;
omega = 2*Math.PI*f;
//Tinc = 1/f*1000/10;
t = 0.0;
}
function motion()
{
var rwString = "";
var lwString = "";
var swString = "";
var cString = "";
var aString = "";
iamps = 0;
for (var i=0;i<nPoints;i++) {
var X = i*xLength/(nPoints-1);
var Y = 2*ym*Math.cos(omega*t)*Math.sin(k*X);
var rY = ym*Math.sin(k*X-omega*t);
var lY = ym*Math.sin(k*X+omega*t);
var j = i % nRatio;
if(j == 0) {
//alert("nAmps="+nAmps+" i="+i);
aString = "M"+X*Scale+",0"+ " L"+X*Scale+","+Y*Scale;
amps[iamps++].setAttributeNS(null,"d",aString);
}
if(i==0) {
rwString ="M"+X*Scale+","+rY*Scale;
lwString ="M"+X*Scale+","+lY*Scale;
swString ="M"+X*Scale+","+Y*Scale;
cString ="M"+X*Scale+","+Y*Scale;
st.setAttributeNS(null,"cx",X*Scale);
st.setAttributeNS(null,"cy",Y*Scale);
}
else if(i>0) {
rwString += " L"+ Math.round(X*Scale)+","+Math.round(rY*Scale);
lwString += " L"+ Math.round(X*Scale)+","+Math.round(lY*Scale);
swString += " L"+ Math.round(X*Scale)+","+Math.round(Y*Scale);
if(i==nPoints-1) {
cString += " L"+ Math.round(X*Scale)+",0";
end.setAttributeNS(null,"cx",X*Scale);
end.setAttributeNS(null,"cy",Y*Scale);
}
}
}
document.getElementById("rightWave").setAttributeNS(null,"d",rwString);
document.getElementById("leftWave").setAttributeNS(null,"d",lwString);
document.getElementById("standingWave").setAttributeNS(null,"d",swString);
document.getElementById("centerLine").setAttributeNS(null,"d",cString);
//st.parentNode.removeChild(st);
document.getElementById("frequency").firstChild.nodeValue = "L=3m"+","+" frequency="+f.toFixed(1)+","+" lambda="+lambda.toFixed(1)+"m";
document.getElementById("waveEquation").firstChild.nodeValue = "y(x,t)="+(2*ym).toFixed(1)+"*cos("+omega.toFixed(2)+"t)sin("+k.toFixed(1)+"x)";
t += Tinc/1000;
}
function freqUp()
{
if(f>=1.0) f++;
else if(f<=0.9) f +=0.1;
setParams();
}
function freqDown()
{
if(f>1.0) f--;
else if(f<=1.0) f -=0.1;
if(f<0.1) f=0.1;
setParams();
}
function lambdaUp()
{
lambda += 0.5;
setParams();
}
function lambdaDown()
{
lambda -= 0.5;
if(lambda<0.5) lambda = 0.5;
setParams();
}
function mouseOverRed()
{
document.getElementById("RedStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOverGreen()
{
document.getElementById("GreenStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
document.getElementById("RedStop").setAttributeNS(null,"stop-color", "red");
}
function mouseOutGreen()
{
document.getElementById("GreenStop").setAttributeNS(null,"stop-color", "green");
}
function mouseOverPurple()
{
document.getElementById("PurpleStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOverLime()
{
document.getElementById("LimeStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOutPurple()
{
document.getElementById("PurpleStop").setAttributeNS(null,"stop-color", "purple");
}
function mouseOutLime()
{
document.getElementById("LimeStop").setAttributeNS(null,"stop-color", "lime");
}
]]>
</script>
<text id="title" x="70" y="40" font-size="40">
<tspan x="110" dy="0"> Standing Wave</tspan>
<tspan x="80" font-size="24" dy="1.2em">Two opposite waves superposed</tspan>
</text>
<g transform="translate(100,250)">
<g id="WaveGroup">
<path id="centerLine" stroke="black" stroke-width="1" fill="none"/>
<g transform="translate(0,0)">
<path id="rightWave" stroke="green" stroke-width="2" fill="none"/>
</g>
<g transform="translate(0,0)">
<path id="leftWave" stroke="lime" stroke-width="2" fill="none"/>
</g>
<path id="standingWave" stroke="blue" stroke-width="2" fill="none"/>
<circle id="st" r="1" stroke="red" stroke-width="2" fill="none"/>
<circle id="end" r="1" stroke="red" stroke-width="2" fill="none"/>
</g>
<text id="frequency" x="-20" y="240" font-size="24" fill="blue">
</text>
<text id="waveEquation" x="-10" y="270" font-size="24" fill="black">
</text>
<!-- buttons -->
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
<radialGradient id="GreenG">
<stop id="GreenStop" stop-color="green" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="green" offset="100%"/>
</radialGradient>
<radialGradient id="PurpleG">
<stop id="PurpleStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="purple" offset="100%"/>
</radialGradient>
<radialGradient id="LimeG">
<stop id="LimeStop" stop-color="green" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="lime" offset="100%"/>
</radialGradient>
<!--Freq-->
<g transform="translate(0,130)">
<text id="freqLabel" x="-30" y="60" font-size="24" fill="black">
Freq:
</text>
<g id="freqUp" onclick="freqUp()"
onmouseover="mouseOverGreen()"
onmouseout="mouseOutGreen()" >
<circle id="freqUpCircle" cx = "50" cy="50" r="20" fill="url(#GreenG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="freqDown" onclick="freqDown()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="freqDownCircle" cx = "100" cy="50" r="20" fill="url(#RedG)" />
<path d="M 90 50 L 110 50" fill="none" stroke="black" stroke-width="3"/>
</g>
</g>
<!-- lambda-->
<g transform="translate(230,130)">
<text id="lambdaLabel" x="-70" y="60" font-size="24" fill="black">
Lambda:
</text>
<g id="lambdaUp" onclick="lambdaUp()"
onmouseover="mouseOverLime()"
onmouseout="mouseOutLime()" >
<circle id="lambdaUpCircle" cx = "50" cy="50" r="20" fill="url(#LimeG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="lambdaDown" onclick="lambdaDown()"
onmouseover="mouseOverPurple()"
onmouseout="mouseOutPurple()">
<circle id="lambdaDownCircle" cx = "100" cy="50" r="20" fill="url(#PurpleG)" />
<path d="M 90 50 L 110 50" fill="none" stroke="black" stroke-width="3"/>
</g>
</g>
</g>
</svg>
SVG Animation Example: Sonic Boom - Animated with variable Mach number.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg width="100%" height="100%"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.1"
onload="startUp()"
onresize="resize()">
<script>
<![CDATA[
var xmlns="http://www.w3.org/2000/svg";
var xlinkns = "http://www.w3.org/1999/xlink";
var object = new Array();
var nw = nh = 0 ;
var time = 0.0;
var timeInc = 100;
// steps needed to fly across the browser
var nStep = 1000;
var Mach = 0.5;
var planeSpeed = 1.0;
var soundSpeed = 1.0;
var plane;
var xPos = 0.0;
var nWave = 0;
var eps = 0.000001;
function startUp()
{
init();
}
function init()
{
resize();
soundSpeed = nw*1.0/nStep*timeInc/1000.;
setParams();
setInterval("movePlane()",timeInc);
}
function setParams()
{
time = 0.0;
planeSpeed = soundSpeed * Mach;
document.getElementById("machLabel").firstChild.nodeValue = "Mach: "+ Mach.toFixed(1);
}
function movePlane()
{
xPos = planeSpeed*time;
plane = document.getElementById("plane");
plane.setAttributeNS(null,"transform","translate("+xPos+",0)");
object[nWave] = new makeWave()
for (i=0;i<object.length;i++) {
object[i].moveWave();
}
nWave++;
time += timeInc;
}
function makeWave()
{
this.wave = document.createElementNS(xmlns,"circle");
document.getElementById("GroupOfWaves").appendChild(this.wave);
this.r = 0.0;
this.x = xPos;
this.y = 0;
this.moveWave = function(){
with(this){
r += soundSpeed*timeInc;
wave.setAttributeNS(null,"r",r);
}
}
this.wave.setAttributeNS(null,"cx",this.x);
this.wave.setAttributeNS(null,"cy",this.y);
this.wave.setAttributeNS(null,"fill","none");
this.wave.setAttributeNS(null,"stroke","green");
this.wave.setAttributeNS(null,"stroke-width","1");
}
function resize()
{
nw = window.innerWidth;
nh = window.innerHeight;
}
function MachUp()
{
if(Mach >= (1.0-eps)) {
Mach += 0.5;
}
else if(Mach <= (0.9+eps)) {
Mach +=0.1;
}
remove();
setParams();
}
function MachDown()
{
if(Mach>1.0) Mach -= 0.5;
else if(Mach<=1.0) Mach -=0.1;
if(Mach<0.1) Mach=0.1;
remove();
setParams();
}
function remove(){
var GChildren=document.getElementById("GroupOfWaves").childNodes;
for (var i=GChildren.length-1;i>=0;i--){
var anyChild=GChildren.item(i)
document.getElementById("GroupOfWaves").removeChild(anyChild);
}
}
function mouseOverRed()
{
document.getElementById("RedStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOverGreen()
{
document.getElementById("GreenStop").setAttributeNS(null,"stop-color", "white");
}
function mouseOutRed()
{
document.getElementById("RedStop").setAttributeNS(null,"stop-color", "red");
}
function mouseOutGreen()
{
document.getElementById("GreenStop").setAttributeNS(null,"stop-color", "green");
}
]]>
</script>
<rect height="100%" width="100%" fill="white"/>
<g id="SpeedofSound" transform="translate(200,200)">
<g id="GroupOfWaves">
</g>
<g id="plane" >
<g id="planeInit" transform="scale(0.5)">
<path
d="M -58.044107,0.26904364 0.09133928,0.09846479 c 0,0 -6.48936928,-6.31739969 -20.41572828,-7.54695579 -16.622795,-1.4676241 -9.962229,0.7509972 -27.346556,-3.379336 -6.336304,-1.50544 -11.338107,-13.991707 -11.338107,-13.991707 l -6.754618,-1.929891 7.719563,27.01846864 z"
id="planePath"
style="fill:red;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
</g>
</g>
<g
id="girl" transform="translate(200,300)">
<path
d="M -0.24123634,0.08928235 C -6.2721448,-8.1127531 -6.5133811,-8.1127531 -6.5133811,-8.1127531 l -6.9958539,8.44327178"
id="path2824"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="m -6.5133811,-8.1127531 0,-11.3381079 -7.7195629,5.548436"
id="path2826"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="M -6.0309084,-19.450861 0,-14.384898"
id="path2828"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="m -68.028646,4.5521545 a 1.6886543,0.12061817 0 0 1 -0.0046,0.00891"
id="path3632"
style="fill:#ffffff;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
<rect
width="15.680362"
height="14.232944"
x="-51.624577"
y="-3.5292628"
id="rect3657"
style="opacity:0.01000001;color:#000000;fill:none;stroke:#b30000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none;stroke-dashoffset:0;marker:none;visibility:visible;display:inline;overflow:visible;enable-background:accumulate" />
<path
d="m -44.387486,-19.933334 a 9.4082174,8.9257441 0 1 1 -18.816435,0 9.4082174,8.9257441 0 1 1 18.816435,0 z"
transform="matrix(0.57416661,0,0,0.56466206,24.253697,-14.226172)"
id="path3689"
style="fill:#fffbc6;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
<path
d="m -58.620429,-14.023044 a 0.48247269,0.12061817 0 1 1 -0.964945,0 0.48247269,0.12061817 0 1 1 0.964945,0 z"
transform="translate(50.418394,-12.061817)"
id="path3697"
style="fill:#ffffff;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
<path
d="m -58.620429,-14.023044 a 0.48247269,0.12061817 0 1 1 -0.964945,0 0.48247269,0.12061817 0 1 1 0.964945,0 z"
transform="translate(54.278175,-11.941198)"
id="path3697-1"
style="fill:#ffffff;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
<path
d="m -6.5133811,-11.490062 c 0,-8.925744 0,-8.925744 0,-8.925744"
id="path3729"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="m -6.7309182,-30.330195 c -8.7569858,2.329371 -4.8649928,12.591687 -4.8649928,12.591687"
id="path3731"
style="fill:none;stroke:#000000;stroke-width:0.95260161px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="m -6.568473,-30.306495 c 6.99585339,0.176002 5.3071987,12.785525 5.3071987,12.785525"
id="path3731-7"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
d="m -9.5106917,-23.413117 c 3.230624,2.270409 6.235857,0 6.235857,0"
id="path3759"
style="fill:none;stroke:#000000;stroke-width:0.75;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
</g>
</g>
<linearGradient id="groundGradient">
<stop offset="0" stop-color="maroon"/>
<stop offset="1" stop-color="olive"/>
</linearGradient>
<g id="Ground" transform="translate(0,500)">
<rect x="0" y="0" height="100%" width="100%" fill="url(#groundGradient)" />
</g>
<g id="titleTextArea">
<rect x ="50" y="20" width="250" height="50" fill="white"/>
<text id="title" x="50" y="60" font-size="40">
<tspan x="70" dy="0"> Sonic Boom </tspan>
</text>
</g>
<!-- buttons -->
<radialGradient id="RedG">
<stop id="RedStop" stop-color="red" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="red" offset="100%"/>
</radialGradient>
<radialGradient id="GreenG">
<stop id="GreenStop" stop-color="green" offset="0"/>
<stop stop-color="white" offset="80%"/>
<stop stop-color="green" offset="100%"/>
</radialGradient>
<g id="buttonArea">
<rect x ="10" y="420" width="260" height="60" stroke="blue" stroke-width="2" fill="white"/>
<!--Mach-->
<g transform="translate(120,400)">
<text id="machLabel" x="-90" y="60" font-size="24" fill="black">
Mach:
</text>
<g id="MachUp" onclick="MachUp()"
onmouseover="mouseOverGreen()"
onmouseout="mouseOutGreen()" >
<circle id="MachUpCircle" cx = "50" cy="50" r="20" fill="url(#GreenG)" />
<path d="M 50 40 L 50 60 M 40 50 L 60 50" fill="none" stroke="black" stroke-width="3"/>
</g>
<g id="MachDown" onclick="MachDown()"
onmouseover="mouseOverRed()"
onmouseout="mouseOutRed()">
<circle id="MachCircle" cx = "100" cy="50" r="20" fill="url(#RedG)" />
<path d="M 90 50 L 110 50" fill="none" stroke="black" stroke-width="3"/>
</g>
</g>
</g>
</svg>
Just want to see the examples of SVG animations, go to SVG animation Home page.