/* VECTOR */
function Vector(size,values)
{
this.size = size;
this.values = new Array(this.size);
for (var i=0;i<this.size;i++)
this.values[i]=0.0;
if (values)
{
if (values instanceof Vector)
values=values.values;
for (var i=0;i<Math.min(this.size,values.length);i++)
this.values[i]=values[i];
}
}
Vector.prototype.resized=function(size)
{
return new Vector(size,this);
};
Vector.prototype.multiplyScalar=function(b)
{
var c=new Vector(this.size);
for (var i in this.values)
c.values[i]=(this.values[i]*b);
return c;
};
Vector.prototype.divideScalar=function(b)
{
var c=new Vector(this.size);
for (var i in this.values)
c.values[i]=(this.values[i]/b);
return c;
};
Vector.prototype.addVector=function(b)
{
var c=new Vector(this.size);
for (var i in this.values)
c.values[i]=(this.values[i]+b.values[i]);
return c;
};
Vector.prototype.subtractVector=function(b)
{
var c=new Vector(this.size);
for (var i in this.values)
c.values[i]=(this.values[i]-b.values[i]);
return c;
};
Vector.prototype.length2=function()
{
var l2=0.0;
for (var i in this.values)
l2+=(this.values[i]*this.values[i]);
return l2;
};
Vector.prototype.length=function()
{
return Math.sqrt(this.length2());
};
Vector.prototype.dot=function(b)
{
var d=0.0;
for (var i in this.values)
d+=(this.values[i]*b.values[i]);
return d;
};
Vector.prototype.cross=function(b)
{
if (this.size!=3 || b.size!=3)
throw new Error("Cross product is only defined for vectors with a length of 3");
var c=new Vector(3);
c.values[0]=(this.values[1]*b.values[2])-(this.values[2]*b.values[1]);
c.values[1]=(this.values[2]*b.values[0])-(this.values[0]*b.values[2]);
c.values[2]=(this.values[0]*b.values[1])-(this.values[1]*b.values[0]);
return c;
};
Vector.prototype.normalized=function()
{
return this.divideScalar(this.length());
};
Vector.prototype.negated=function()
{
var c=new Vector(this.size);
for (var i in this.values)
c.values[i]=-this.values[i];
return c;
};
/* MATRIX */
function degreesToRadians(degrees)
{
return (degrees*(Math.PI/180));
}
function Matrix(rows,columns,values)
{
this.rows = rows;
this.columns = columns;
this.values = new Array(this.rows*this.columns);
for (var i=0;i<this.rows;i++) for (var j=0;j<this.columns;j++)
this.set(i,j,(i==j? 1.0:0.0));
if (values)
{
if (values instanceof Matrix)
{
for (var i=0;i<Math.min(this.rows,values.rows);i++)
for (var j=0;j<Math.min(this.columns,values.columns);j++)
this.set(i,j,values.get(i,j));
return;
}
if (values.length>(this.rows*this.columns))
throw Error("Too many arguments for matrix constructor");
var k=0;
for (var j=0;j<this.columns;j++) for (var i=0;i<this.rows;i++)
this.set(i,j,values[k++]);
}
}
Matrix.prototype.get=function(i,j)
{
return this.values[i + j*this.rows];
};
Matrix.prototype.set=function(i,j,value)
{
this.values[i + j*this.rows]=value;
};
Matrix.prototype.resized=function(rows,columns)
{
return new Matrix(rows,columns,this);
};
Matrix.prototype.multiplyMatrix=function(b)
{
if (this.columns!=b.rows)
throw new Error("Cannot multiply matrices: size mismatch");
var c=new Matrix(this.rows,b.columns);
for (var i=0;i<this.rows;i++) for (var j=0;j<b.columns;j++)
{
var sum=0.0;
for (var k=0;k<this.columns;k++)
sum+=(this.get(i,k)*b.get(k,j));
c.set(i,j,sum);
}
return c;
};
Matrix.prototype.multiplyVector=function(b)
{
if (this.columns!=b.size)
throw new Error("Cannot multiply matrix and vector: size mismatch");
var c=new Vector(b.size);
for (var i=0;i<this.rows;i++)
{
var sum=0.0;
for (var k=0;k<this.columns;k++)
sum+=(this.get(i,k)*b.values[k]);
c.values[i]=sum;
}
return c;
};
Matrix.rotationX3=function(r)
{
r=degreesToRadians(r);
var c=Math.cos(r);
var s=Math.sin(r);
return new Matrix(3,3, [
1.0, 0.0, 0.0,
0.0, c, s,
0.0, -s, c
]);
};
Matrix.rotationY3=function(r)
{
r=degreesToRadians(r);
var c=Math.cos(r);
var s=Math.sin(r);
return new Matrix(3,3, [
c, 0.0, -s,
0.0, 1.0, 0.0,
s, 0.0, c
]);
};
Matrix.rotationZ3=function(r)
{
r=degreesToRadians(r);
var c=Math.cos(r);
var s=Math.sin(r);
return new Matrix(3,3, [
c, s, 0.0,
-s, c, 0.0,
0.0, 0.0, 1.0
]);
};
Matrix.scale3=function(x,y,z)
{
return new Matrix(3,3, [
x, 0.0, 0.0,
0.0, y, 0.0,
0.0, 0.0, z
]);
};
Matrix.translation4=function(x,y,z)
{
return new Matrix(4,4, [
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
x, y, z, 1.0
]);
};
Matrix.perspective4=function(fov,aspect,near,far)
{
fov=degreesToRadians(fov);
var f=(1.0/Math.tan(fov/2));
return new Matrix(4,4, [
(f/aspect), 0.0, 0.0, 0.0,
0.0, f, 0.0, 0.0,
0.0, 0.0, ((far+near)/(near-far)), -1.0,
0.0, 0.0, ((2*far*near)/(near-far)), 0.0
]);
};
/* RENDER */
var CAMERA_DIRECTION=new Vector(3,[0.0,0.0,1.0]);
function clamp(value,min,max)
{
if (value<min)
return min;
if (value>max)
return max;
return value;
}
function render(context,projection,modelView,vertices,faces)
{
function DrawFace(normal,depth2,points)
{
this.normal = normal;
this.depth2 = depth2;
this.points = points;
}
/* Backface culling: */
var drawFaces=[];
for (var i in faces)
{
/* Transform points to model+view space: */
var points=[];
for (var j in faces[i])
{
var vertex=new Vector(4,vertices[faces[i][j]]);
vertex.values[3]=1.0;
vertex=modelView.multiplyVector(vertex);
vertex=vertex.divideScalar(vertex.values[3]);
points.push(new Vector(3,vertex.values));
}
/* Calculate normal: */
var u=(points[2].subtractVector(points[0]));
var v=(points[2].subtractVector(points[1]));
var normal=u.cross(v).normalized();
/* Calculate center: */
var center=(points[0].addVector(points[1]).addVector(points[2])).divideScalar(3.0);
/* Save front facing faces: */
if (normal.dot(center)<0.0)
drawFaces.push(new DrawFace(normal,center.length2(),points));
}
/* Sort faces back to front: */
drawFaces.sort(function(a,b) {
return (b.depth2-a.depth2);
});
/* Draw faces: */
for (var i in drawFaces)
{
/* Transform points to projection space: */
var points=[];
for (var j in drawFaces[i].points)
{
var vertex=new Vector(4,drawFaces[i].points[j]);
vertex.values[3]=1.0;
vertex=projection.multiplyVector(vertex);
vertex=vertex.divideScalar(vertex.values[3]);
points.push(new Vector(3,vertex.values));
}
/* Draw face: */
context.beginPath();
context.moveTo(points[0].values[0],points[0].values[1]);
context.lineTo(points[1].values[0],points[1].values[1]);
context.lineTo(points[2].values[0],points[2].values[1]);
context.closePath();
/* Lighting: */
var intensity = clamp(drawFaces[i].normal.dot(CAMERA_DIRECTION),0.0,1.0);
var value = parseInt(255*intensity);
var color = ("#"+value.toString(16)+"0000");
context.fillStyle=color;
context.fill();
context.strokeStyle=color;
context.stroke();
}
}
/* MESH */
var mesh =
{
"vertices" :
[
[0.4375,0.1640624701976776,0.765625],
[-0.4375,0.1640624701976776,0.765625],
[0.5,0.09374997019767761,0.6875],
[-0.5,0.09374997019767761,0.6875],
[0.546875,0.05468747392296791,0.578125],
[-0.546875,0.05468747392296791,0.578125],
[0.3515625,-0.02343752607703209,0.6171875],
[-0.3515625,-0.02343752607703209,0.6171875],
[0.3515625,0.031249968335032463,0.71875],
[-0.3515625,0.031249968335032463,0.71875],
[0.3515625,0.1328124701976776,0.78125],
[-0.3515625,0.1328124701976776,0.78125],
[0.2734375,0.1640624701976776,0.796875],
[-0.2734375,0.1640624701976776,0.796875],
[0.203125,0.09374997019767761,0.7421875],
[-0.203125,0.09374997019767761,0.7421875],
[0.15625,0.05468747019767761,0.6484375],
[-0.15625,0.05468747019767761,0.6484375],
[0.078125,0.2421874701976776,0.65625],
[-0.078125,0.2421874701976776,0.65625],
[0.140625,0.2421874701976776,0.7421875],
[-0.140625,0.2421874701976776,0.7421875],
[0.2421875,0.2421874701976776,0.796875],
[-0.2421875,0.2421874701976776,0.796875],
[0.2734375,0.3281249701976776,0.796875],
[-0.2734375,0.3281249701976776,0.796875],
[0.203125,0.3906249701976776,0.7421875],
[-0.203125,0.3906249701976776,0.7421875],
[0.15625,0.4374999701976776,0.6484375],
[-0.15625,0.4374999701976776,0.6484375],
[0.3515625,0.515625,0.6171875],
[-0.3515625,0.515625,0.6171875],
[0.3515625,0.4531249701976776,0.71875],
[-0.3515625,0.4531249701976776,0.71875],
[0.3515625,0.3593749701976776,0.78125],
[-0.3515625,0.3593749701976776,0.78125],
[0.4375,0.3281249701976776,0.765625],
[-0.4375,0.3281249701976776,0.765625],
[0.5,0.3906249701976776,0.6875],
[-0.5,0.3906249701976776,0.6875],
[0.546875,0.4374999701976776,0.578125],
[-0.546875,0.4374999701976776,0.578125],
[0.625,0.2421874701976776,0.5625],
[-0.625,0.2421874701976776,0.5625],
[0.5625,0.2421874701976776,0.671875],
[-0.5625,0.2421874701976776,0.671875],
[0.46875,0.2421874701976776,0.7578125],
[-0.46875,0.2421874701976776,0.7578125],
[0.4765625,0.2421874701976776,0.7734375],
[-0.4765625,0.2421874701976776,0.7734375],
[0.4453125,0.3359374701976776,0.78125],
[-0.4453125,0.3359374701976776,0.78125],
[0.3515625,0.3749999701976776,0.8046875],
[-0.3515625,0.3749999701976776,0.8046875],
[0.265625,0.3359374701976776,0.8203125],
[-0.265625,0.3359374701976776,0.8203125],
[0.2265625,0.2421874701976776,0.8203125],
[-0.2265625,0.2421874701976776,0.8203125],
[0.265625,0.1562499701976776,0.8203125],
[-0.265625,0.1562499701976776,0.8203125],
[0.3515625,0.2421874701976776,0.828125],
[-0.3515625,0.2421874701976776,0.828125],
[0.3515625,0.11718746274709702,0.8046875],
[-0.3515625,0.11718746274709702,0.8046875],
[0.4453125,0.1562499701976776,0.78125],
[-0.4453125,0.1562499701976776,0.78125],
[0.0,0.4296874701976776,0.7421875],
[0.0,0.3515624701976776,0.8203125],
[0.0,-0.6796875596046448,0.734375],
[0.0,-0.3203125298023224,0.78125],
[0.0,-0.1875000298023224,0.796875],
[0.0,-0.7734375596046448,0.7187499403953552],
[0.0,0.4062499701976776,0.6015625],
[0.0,0.5703125,0.5703125],
[0.0,0.8984375,-0.5468749403953552],
[0.0,0.5625000596046448,-0.8515625],
[0.0,0.07031253725290298,-0.828125],
[0.0,-0.3828124701976776,-0.3515625298023224],
[0.203125,-0.1875000298023224,0.5625],
[-0.203125,-0.1875000298023224,0.5625],
[0.3125,-0.4375000298023224,0.5703125],
[-0.3125,-0.4375000298023224,0.5703125],
[0.3515625,-0.6953125,0.5703124403953552],
[-0.3515625,-0.6953125,0.5703124403953552],
[0.3671875,-0.890625,0.5312499403953552],
[-0.3671875,-0.890625,0.5312499403953552],
[0.328125,-0.9453125,0.5234374403953552],
[-0.328125,-0.9453125,0.5234374403953552],
[0.1796875,-0.96875,0.5546874403953552],
[-0.1796875,-0.96875,0.5546874403953552],
[0.0,-0.984375,0.5781249403953552],
[0.4375,-0.1406250298023224,0.53125],
[-0.4375,-0.1406250298023224,0.53125],
[0.6328125,-0.03906252235174179,0.5390625],
[-0.6328125,-0.03906252235174179,0.5390625],
[0.828125,0.1484374850988388,0.4453125],
[-0.828125,0.1484374850988388,0.4453125],
[0.859375,0.4296874701976776,0.59375],
[-0.859375,0.4296874701976776,0.59375],
[0.7109375,0.4843749701976776,0.625],
[-0.7109375,0.4843749701976776,0.625],
[0.4921875,0.6015624403953552,0.6875],
[-0.4921875,0.6015624403953552,0.6875],
[0.3203125,0.7578124403953552,0.7343750596046448],
[-0.3203125,0.7578124403953552,0.7343750596046448],
[0.15625,0.7187499403953552,0.7578125596046448],
[-0.15625,0.7187499403953552,0.7578125596046448],
[0.0625,0.4921874701976776,0.75],
[-0.0625,0.4921874701976776,0.75],
[0.1640625,0.4140624701976776,0.7734375],
[-0.1640625,0.4140624701976776,0.7734375],
[0.125,0.3046874701976776,0.765625],
[-0.125,0.3046874701976776,0.765625],
[0.203125,0.09374997019767761,0.7421875],
[-0.203125,0.09374997019767761,0.7421875],
[0.375,0.015624969266355038,0.703125],
[-0.375,0.015624969266355038,0.703125],
[0.4921875,0.06249997019767761,0.671875],
[-0.4921875,0.06249997019767761,0.671875],
[0.625,0.1874999701976776,0.6484375],
[-0.625,0.1874999701976776,0.6484375],
[0.640625,0.2968749701976776,0.6484375],
[-0.640625,0.2968749701976776,0.6484375],
[0.6015625,0.3749999701976776,0.6640625],
[-0.6015625,0.3749999701976776,0.6640625],
[0.4296875,0.4374999701976776,0.71875],
[-0.4296875,0.4374999701976776,0.71875],
[0.25,0.4687499701976776,0.7578125],
[-0.25,0.4687499701976776,0.7578125],
[0.0,-0.7656250596046448,0.7343749403953552],
[0.109375,-0.7187500596046448,0.7343749403953552],
[-0.109375,-0.7187500596046448,0.7343749403953552],
[0.1171875,-0.8359375596046448,0.7109374403953552],
[-0.1171875,-0.8359375596046448,0.7109374403953552],
[0.0625,-0.8828125596046448,0.6953124403953552],
[-0.0625,-0.8828125596046448,0.6953124403953552],
[0.0,-0.8906250596046448,0.6874999403953552],
[0.0,-0.1953125298023224,0.75],
[0.0,-0.1406250298023224,0.7421875],
[0.1015625,-0.1484375298023224,0.7421875],
[-0.1015625,-0.1484375298023224,0.7421875],
[0.125,-0.2265625298023224,0.75],
[-0.125,-0.2265625298023224,0.75],
[0.0859375,-0.2890625298023224,0.7421875],
[-0.0859375,-0.2890625298023224,0.7421875],
[0.3984375,-0.04687502980232239,0.671875],
[-0.3984375,-0.04687502980232239,0.671875],
[0.6171875,0.05468747392296791,0.625],
[-0.6171875,0.05468747392296791,0.625],
[0.7265625,0.2031249701976776,0.6015625],
[-0.7265625,0.2031249701976776,0.6015625],
[0.7421875,0.3749999701976776,0.65625],
[-0.7421875,0.3749999701976776,0.65625],
[0.6875,0.4140624701976776,0.7265625],
[-0.6875,0.4140624701976776,0.7265625],
[0.4375,0.5468749403953552,0.796875],
[-0.4375,0.5468749403953552,0.796875],
[0.3125,0.6406249403953552,0.8359375],
[-0.3125,0.6406249403953552,0.8359375],
[0.203125,0.6171874403953552,0.8515625],
[-0.203125,0.6171874403953552,0.8515625],
[0.1015625,0.4296874701976776,0.84375],
[-0.1015625,0.4296874701976776,0.84375],
[0.125,-0.10156253725290298,0.8125],
[-0.125,-0.10156253725290298,0.8125],
[0.2109375,-0.4453125298023224,0.7109375],
[-0.2109375,-0.4453125298023224,0.7109375],
[0.25,-0.7031250596046448,0.6874999403953552],
[-0.25,-0.7031250596046448,0.6874999403953552],
[0.265625,-0.8203125,0.6640624403953552],
[-0.265625,-0.8203125,0.6640624403953552],
[0.234375,-0.9140625,0.6328124403953552],
[-0.234375,-0.9140625,0.6328124403953552],
[0.1640625,-0.9296875,0.6328124403953552],
[-0.1640625,-0.9296875,0.6328124403953552],
[0.0,-0.9453125,0.6406249403953552],
[0.0,0.046874966472387314,0.7265625],
[0.0,0.2109374701976776,0.765625],
[0.328125,0.4765624701976776,0.7421875],
[-0.328125,0.4765624701976776,0.7421875],
[0.1640625,0.1406249701976776,0.75],
[-0.1640625,0.1406249701976776,0.75],
[0.1328125,0.2109374701976776,0.7578125],
[-0.1328125,0.2109374701976776,0.7578125],
[0.1171875,-0.6875000596046448,0.7343749403953552],
[-0.1171875,-0.6875000596046448,0.7343749403953552],
[0.078125,-0.4453125298023224,0.75],
[-0.078125,-0.4453125298023224,0.75],
[0.0,-0.4453125298023224,0.75],
[0.0,-0.3281250298023224,0.7421875],
[0.09375,-0.2734375298023224,0.78125],
[-0.09375,-0.2734375298023224,0.78125],
[0.1328125,-0.2265625298023224,0.796875],
[-0.1328125,-0.2265625298023224,0.796875],
[0.109375,-0.1328125298023224,0.78125],
[-0.109375,-0.1328125298023224,0.78125],
[0.0390625,-0.1250000298023224,0.78125],
[-0.0390625,-0.1250000298023224,0.78125],
[0.0,-0.2031250298023224,0.828125],
[0.046875,-0.1484375298023224,0.8125],
[-0.046875,-0.1484375298023224,0.8125],
[0.09375,-0.1562500298023224,0.8125],
[-0.09375,-0.1562500298023224,0.8125],
[0.109375,-0.2265625298023224,0.828125],
[-0.109375,-0.2265625298023224,0.828125],
[0.078125,-0.2500000298023224,0.8046875],
[-0.078125,-0.2500000298023224,0.8046875],
[0.0,-0.2890625298023224,0.8046875],
[0.2578125,-0.3125000298023224,0.5546875],
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var context = canvas.getContext("2d");
var screenMatrix;
var projection;
var screenProjection;
function resize()
{
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
var halfW=(canvas.width/2);
var halfH=(canvas.height/2);
/* Screen matrix: Maps from clip space to screen space. */
screenMatrix=new Matrix(4,4, [
halfW, 0.0, 0.0, 0.0,
0.0, -halfH, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,
halfW, halfH, 0.0, 1.0
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projection=Matrix.perspective4(45.0,(canvas.width/canvas.height),0.1,100.0)
screenProjection=screenMatrix.multiplyMatrix(projection);
}
addEventListener("resize",resize,false);
resize();
var r=0;
setInterval
(
function()
{
var translation = Matrix.translation4(0.0,0.0,-3.0);
var rotationY = Matrix.rotationY3(r).resized(4,4);
var rotationX = Matrix.rotationX3(r).resized(4,4);
var matrix = (translation.multiplyMatrix(rotationY.multiplyMatrix(rotationX)));
context.clearRect(0,0,canvas.width,canvas.height);
render(context,screenProjection,matrix,mesh.vertices,mesh.faces);
r+=1;
},
1
);
<canvas id="canvas"></canvas>
body
{
margin: 0px;
background-color: black;
}