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original.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<style>
.slidecontainer {
width: 100%; /* Width of the outside container */
}
/* The slider itself */
.slider {
-webkit-appearance: none; /* Override default CSS styles */
appearance: none;
width: 100%; /* Full-width */
height: 25px; /* Specified height */
background: #d3d3d3; /* Grey background */
outline: none; /* Remove outline */
opacity: 0.7; /* Set transparency (for mouse-over effects on hover) */
-webkit-transition: .2s; /* 0.2 seconds transition on hover */
transition: opacity .2s;
}
/* Mouse-over effects */
.slider:hover {
opacity: 1; /* Fully shown on mouse-over */
}
/* The slider handle (use -webkit- (Chrome, Opera, Safari, Edge) and -moz- (Firefox) to override default look) */
.slider::-webkit-slider-thumb {
-webkit-appearance: none; /* Override default look */
appearance: none;
width: 25px; /* Set a specific slider handle width */
height: 25px; /* Slider handle height */
background: #4CAF50; /* Green background */
cursor: pointer; /* Cursor on hover */
}
.slider::-moz-range-thumb {
width: 25px; /* Set a specific slider handle width */
height: 25px; /* Slider handle height */
background: #4CAF50; /* Green background */
cursor: pointer; /* Cursor on hover */
}
</style>
<script>
function p3( x, y, z ) { return { x:x, y:y, z:z }; }
function p2( x, y ) { return { x:x, y:y, z:0 }; }
function origin() { return p3(0,0,0); }
function xaxis() { return p3(1,0,0); }
function yaxis() { return p3(0,1,0); }
function zaxis() { return p3(0,0,1); }
function add( a, b ) { return p3( a.x + b.x, a.y + b.y, a.z + b.z ); }
function sub( a, b ) { return p3( a.x - b.x, a.y - b.y, a.z - b.z ); }
function mul( a, f ) { return p3( a.x * f, a.y * f, a.z * f ); }
function dot( a, b ) { return a.x * b.x + a.y * b.y + a.z * b.z; }
function len2( a ) { return dot(a,a); }
function dist( a, b ) { return Math.sqrt( len2( sub( a, b ) ) ); }
function assign( a, b ) { a.x = b.x; a.y = b.y; a.z = b.z; }
function normalize( a ) { return mul( a, 1 / Math.sqrt( len2( a ) ) ); }
function cross( a, b ) { return p3( a.y * b.z - a.z * b.y, a.z*b.x - a.x * b.z, a.x * b.y - a.y * b.x ); }
function mid( a, b ) { return mul( add( a, b ), 0.5 ); }
function angle( p1, p2, p3 ) { var a = dist(p2,p3); var b = dist(p1,p2); var c = dist(p1,p3); return Math.acos( ( c*c - a*a - b*b ) / ( -2*a*b ) ); }
function rot2d( v, theta ) { var s = Math.sin(theta); var c = Math.cos(theta); return p2( v.x*c - v.y*s, v.x*s + v.y*c ); }
function clear() {
verts = [];
verts2d = [];
edges = [];
faces = [];
angles = [];
}
function getMousePos(canvas, evt) {
var rect = canvas.getBoundingClientRect();
return p2( evt.clientX - rect.left, evt.clientY - rect.top );
}
function onMouseMove( evt ) {
var pos = getMousePos( canvas, evt );
view_height = 1.3 * ( canvas.height / 2.0 - pos.y ) / canvas.height;
repositionCamera();
}
function onMouseDown( evt ) {
var pos = getMousePos( canvas, evt );
isSpinning = !isSpinning;
if( animationRequestID && isSpinning ) animate();
}
function onMouseUp( evt ) {
redraw();
}
function repositionCamera() {
var look_at = p3(0,0,0);
var d = 40;
var vd = d * view_height;
var hd = Math.sqrt( d*d - vd*vd );
camera.p = p3( hd*Math.cos(theta), hd*Math.sin(theta), vd );
camera.z = normalize( sub( look_at, camera.p ) );
var up = p3(0,0,1);
camera.x = normalize( cross( camera.z, up ) );
camera.y = normalize( cross( camera.x, camera.z ) );
}
function pointInRect( p, rect ) {
return p.x > rect.x && p.x < ( rect.x + rect.width ) &&
p.y > rect.y && p.y < ( rect.y + rect.height );
}
function add_vert( p ) {
verts.push( p );
}
function make_edge(i,j) {
edges.push( [i,j] );
}
function make_face3(i,j,k) {
faces.push( [i,j,k] );
make_edge(i,j);
make_edge(j,k);
make_edge(k,i);
}
function make_face4(i,j,k,m) {
faces.push( [i,j,k,m] );
make_edge(i,j);
make_edge(j,k);
make_edge(k,m);
make_edge(m,i);
}
function make_zome() {
clear();
var H = height * R; // height of first ring
var P = bulge * R; // shift outwards of first ring
var Z = -10; // vertical position of base
// add the base ring of vertices
for(var i=0;i<N;i++) {
var a = i*2*Math.PI / N;
add_vert( p3( R * Math.sin(a), R * Math.cos(a), Z ) );
}
// add the next ring of vertices
for(var i=0;i<N;i++) {
var b = (i+0.5)*2*Math.PI / N;
add_vert( p3( (R+P) * Math.sin(b), (R+P) * Math.cos(b), Z+H ) );
make_face3( i, (i+1)%N, N+i );
}
angles.push( angle( verts[0], verts[N], verts[1] ) );
// add the remaining rings
for(var r=2;r<M;r++) {
for(var i=0;i<N;i++) {
var ia = (r-1)*N+i;
var ib = (r-2)*N+(i+1)%N;
var ic = (r-1)*N+(i+1)%N;
var id = r*N+i;
var a = verts[ ia ];
var b = verts[ ib ];
var c = verts[ ic ];
var d = add(b,mul(sub(mid(a,c),b),1+K)); // make a kite (rhombus if K=1)
add_vert( d );
make_face4( ia, ib, ic, id );
if( i == 0 ) {
angles.push( angle(a,b,c) );
}
}
}
}
function init() {
canvas = document.getElementById('canvas');
ctx = canvas.getContext('2d');
theta = Math.PI / 2;
view_height = 0.5;
camera = { p:p3(0,3,-6),
x:p3(1,0,0),
y:p3(0,1,0),
z:p3(0,0,1),
f:canvas.height,
pp:p2(canvas.width/2-100,canvas.height/2)
};
repositionCamera();
var width_slider = document.getElementById("width_slider");
width_slider.updatefromvalue = function() {
R = parseFloat(this.value);
document.getElementById("width_label").innerHTML = "Width: "+R;
}
width_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
width_slider.updatefromvalue();
var height_slider = document.getElementById("height_slider");
height_slider.updatefromvalue = function() {
height = parseFloat(this.value);
document.getElementById("height_label").innerHTML = "Height: "+height;
}
height_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
height_slider.updatefromvalue();
var bulge_slider = document.getElementById("bulge_slider");
bulge_slider.updatefromvalue = function() {
bulge = parseFloat(this.value);
document.getElementById("bulge_label").innerHTML = "Bulge: "+bulge;
}
bulge_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
bulge_slider.updatefromvalue();
var rings_slider = document.getElementById("rings_slider");
rings_slider.updatefromvalue = function() {
M = parseFloat(this.value);
document.getElementById("rings_label").innerHTML = "Number of rings: "+M;
}
rings_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
rings_slider.updatefromvalue();
var triangles_slider = document.getElementById("triangles_slider");
triangles_slider.updatefromvalue = function() {
N = parseFloat(this.value);
document.getElementById("triangles_label").innerHTML = "Number of triangles: "+N;
}
triangles_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
triangles_slider.updatefromvalue();
var kite_slider = document.getElementById("kite_slider");
kite_slider.updatefromvalue = function() {
K = parseFloat(this.value);
document.getElementById("kite_label").innerHTML = "Kite ratio: "+K;
}
kite_slider.oninput = function() {
this.updatefromvalue();
make_zome();
}
kite_slider.updatefromvalue();
make_zome();
redraw();
canvas.addEventListener( 'mousemove', onMouseMove, false );
canvas.addEventListener( 'touchmove', onMouseMove, false );
canvas.addEventListener( 'touchstart', onMouseDown, false );
canvas.addEventListener( 'mousedown', onMouseDown, false );
canvas.addEventListener( 'touchend', onMouseUp, false );
canvas.addEventListener( 'mouseup', onMouseUp, false );
canvas.addEventListener( 'mouseout', onMouseUp, false );
isSpinning = true;
animate();
}
function camera_projection( p, camera ) {
var ray = sub( p, camera.p ); // the ray from camera center to point
var cp = p3( dot( camera.x, ray ), dot( camera.y, ray ), dot( camera.z, ray ) ); // into camera space
return p3( cp.x * camera.f / cp.z + camera.pp.x,
canvas.height - ( cp.y * camera.f / cp.z + camera.pp.y ),
cp.z );
}
function redraw() {
drawMesh();
drawNet();
}
function point( p ) {
ctx.beginPath();
ctx.arc( p.x, p.y, 2, 0, 2.0 * Math.PI );
ctx.fill();
}
function drawMesh() {
// project the mesh onto the screen
for( var iVert = 0; iVert < verts.length; ++iVert ) {
verts2d[ iVert ] = camera_projection( verts[ iVert ], camera );
}
ctx.strokeStyle = "rgb(200,200,200)";
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.strokeRect(0, 0, canvas.width, canvas.height);
// draw the faces
ctx.fillStyle = "rgba(200,210,255,0.2)";
for( var iFace = 0; iFace < faces.length; ++iFace ) {
var a = verts2d[ faces[iFace][0] ];
ctx.beginPath();
ctx.moveTo( a.x, a.y );
for( var i = 1; i < faces[iFace].length; ++i ) {
a = verts2d[ faces[iFace][i] ];
ctx.lineTo( a.x, a.y );
}
ctx.fill();
}
// draw the edges
ctx.strokeStyle = "rgb(200,200,200)";
ctx.beginPath();
for( var i = 0; i < edges.length; ++i ) {
var a = verts2d[ edges[i][0] ];
var b = verts2d[ edges[i][1] ];
ctx.moveTo( a.x, a.y );
ctx.lineTo( b.x, b.y );
}
ctx.stroke();
// draw the verts
ctx.fillStyle = "rgb(0,0,0)";
for( var i = 0; i < verts2d.length; ++i )
point( verts2d[i], "" );
}
function drawNet() {
ctx.strokeStyle = "rgb(0,0,0)";
ctx.beginPath();
// first triangle:
var a = p2(500,580);
var b = p2(a.x+R*10,580);
var angle = angles[0];
var h = 0.5*dist(a,b) / Math.tan(angles[0]/2);
var c = add(mid(a,b),p2(0,-h));
ctx.moveTo( a.x, a.y );
ctx.lineTo( b.x, b.y );
ctx.lineTo( c.x, c.y );
ctx.lineTo( a.x, a.y );
// remaining rhombi
for(var i=1;i<angles.length;i++) {
var angle = angles[i];
var bc = sub(c,b);
var rotated_bc = rot2d
var new_b = add( b, rot2d(bc, angle) );
var new_c = add(b,mul(sub(mid(c,new_b),b),1+K)); // make a kite (rhombus if K=1)
ctx.moveTo( c.x, c.y );
ctx.lineTo( b.x, b.y );
ctx.lineTo( new_b.x, new_b.y );
ctx.lineTo( new_c.x, new_c.y );
ctx.lineTo( c.x, c.y );
b = new_b;
c = new_c;
}
ctx.stroke();
}
function drawRect( x, y, w, h ) {
ctx.beginPath();
ctx.rect( x, y, w, h );
ctx.fill();
ctx.stroke();
}
function animate() {
if( isSpinning ) {
// rotate round
theta += 0.004;
repositionCamera();
}
redraw();
animationRequestID = requestAnimationFrame( animate );
}
window.onload = init;
</script>
<noscript>
<p>For full functionality of this site it is necessary to enable JavaScript.
Here are the <a href="http://www.enable-javascript.com/" target="_blank">
instructions how to enable JavaScript in your web browser</a>.
</p></noscript>
</head>
<body>
<table border="0">
<tr>
<td><canvas id="canvas" width="800" height="600">(Canvas drawing not supported by your browser.)</canvas></td>
<td width="300px" valign="center">
<p id="width_label">Width:</p>
<div class="slidecontainer"><input type="range" min="0.3" max="15" value="10" step="0.001" class="slider" id="width_slider"></div>
<p id="height_label">Height:</p>
<div class="slidecontainer"><input type="range" min="0.0" max="0.7" value="0.3" step="0.0001" class="slider" id="height_slider"></div>
<p id="bulge_label">Bulge:</p>
<div class="slidecontainer"><input type="range" min="-1" max="1" value="0.035" step="0.0001" class="slider" id="bulge_slider"></div>
<p id="rings_label">Number of rings:</p>
<div class="slidecontainer"><input type="range" min="2" max="30" value="8" step="1" class="slider" id="rings_slider"></div>
<p id="triangles_label">Number of triangles:</p>
<div class="slidecontainer"><input type="range" min="3" max="30" value="12" step="1" class="slider" id="triangles_slider"></div>
<p id="kite_label">Kite ratio:</p>
<div class="slidecontainer"><input type="range" min="0.1" max="3" value="1" step="0.001" class="slider" id="kite_slider"></div>
</td>
</tr>
</table>
<p>
Source code: <a href="https://github.com/timhutton/zomes">https://github.com/timhutton/zomes</a>
</p>
</body>
</html>