Visible Surface Ray Tracing Algorithm

In this example below you will see how to do a Visible Surface Ray Tracing Algorithm with some HTML / CSS and Javascript

Sec 4-13, PECG, D.F.RogersRay Tracing algorithm used as hidden surface removal algorithm Viewpoint is located at infinity on the positive z axis, rays are parallel to the z axis, scene has been transformed to image space

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This awesome code was written by arcollector, you can see more from this user in the personal repository.
You can find the original code on Codepen.io
Copyright arcollector ©
  • HTML
  • CSS
  • JavaScript
<!DOCTYPE html>
<html lang="en" >

<head>
  <meta charset="UTF-8">
  <title>Visible Surface Ray Tracing Algorithm</title>
  
  
  
      <link rel="stylesheet" href="css/style.css">

  
</head>

<body>

  <html>
  <head></head>
  <body>
<table class="framebuffer"></table>
  </body>
</html>
  
  

    <script  src="js/index.js"></script>




</body>

</html>

/*Downloaded from https://www.codeseek.co/arcollector/visible-surface-ray-tracing-algorithm-okzvB */
.framebuffer {
  border-collapse: collapse;
  border: 1px solid #000;
  table-layout: fixed;
  margin: 0 auto;
}

.framebuffer td {
  border: 1px solid #000;
  width: 10px;
  height: 10px;
}

/*Downloaded from https://www.codeseek.co/arcollector/visible-surface-ray-tracing-algorithm-okzvB */
// --------------------------------------------
// 
// --------------------------------------------
var Vector = function( x,y,z,w ) {
	this.x = x;
	this.y = y;
	this.z = z;
	this.w = typeof w === 'undefined' ? 1 : w;
	return this;
};

Vector.prototype.length = function() {
	return Math.sqrt(this.x*this.x+this.y*this.y+this.z*this.z);
};

Vector.prototype.normalize = function() {
	var l = this.length();
	this.x /= l;
	this.y /= l;
	this.z /= l;
	return this;
};

Vector.prototype.copy = function() {
	return new Vector(this.x,this.y,this.z);
};

Vector.prototype.toString = function() {
	console.log( "Purple,Point[" +
		"{" + ((Math.abs(this.x)<=1e-6)?0:this.x) + "," + ((Math.abs(this.y)<=1e-6)?0:this.y) + "," + ((Math.abs(this.z)<=1e-6)?0:this.z) + "}" +
		"]," 
	);
};

Vector.prototype.transform = function( m ) {
	var x = this.x*m._00 + this.y*m._01 + this.z*m._02 + this.w*m._03;
	var y = this.x*m._10 + this.y*m._11 + this.z*m._12 + this.w*m._13;
	var z = this.x*m._20 + this.y*m._21 + this.z*m._22 + this.w*m._23;
	var w = this.x*m._30 + this.y*m._31 + this.z*m._32 + this.w*m._33;
	
	this.x = x/w;
	this.y = y/w;
	this.z = z/w;
	this.w = 1;
};

// --------------------------------------------
// 
// --------------------------------------------
var vectorToRGB = function( v ) {
  return "rgb(" + v.x + "," + v.y + "," + v.z + ")";
};

// --------------------------------------------
// 
// --------------------------------------------
var frameBuffer = [];
var WIDTH = 32;
var HEIGHT = 32;
var BACKGROUND_COLOR = new Vector(0,0,0); // black
var $table = document.querySelector('.framebuffer');
for( var y = 0; y < HEIGHT; y++ ) {
  var $tr = document.createElement( 'tr' )
  for( var x = 0; x < WIDTH; x++ ) {
    var $td = document.createElement( 'td');
    $td.style.backgroundColor = vectorToRGB(BACKGROUND_COLOR);
    $td.setAttribute( 'title', '('+x+','+(-y+HEIGHT-1)+')');
    $tr.appendChild($td);
  }
  $table.appendChild($tr);
}

// --------------------------------------------
// 
// --------------------------------------------
var Matrix4x4 = function( v1,v2,v3,v4 ) {
	v1 = v1 || new Vector(1,0,0,0);
	v2 = v2 || new Vector(0,1,0,0);
	v3 = v3 || new Vector(0,0,1,0);
	v4 = v4 || new Vector(0,0,0,1);
	
	this._00 = v1.x; this._10 = v2.x; this._20 = v3.x; this._30 = v4.x; 
	this._01 = v1.y; this._11 = v2.y; this._21 = v3.y; this._31 = v4.y; 
	this._02 = v1.z; this._12 = v2.z; this._22 = v3.z; this._32 = v4.z; 
	this._03 = v1.w; this._13 = v2.w; this._23 = v3.w; this._33 = v4.w;
	return this;
};

Matrix4x4.prototype.multiply = function( m ) {
	var _00 = this._00*m._00 + this._10*m._01 + this._20*m._02 + this._30*m._03; 
	var _10 = this._00*m._10 + this._10*m._11 + this._20*m._12 + this._30*m._13; 
	var _20 = this._00*m._20 + this._10*m._21 + this._20*m._22 + this._30*m._23; 
	var _30 = this._00*m._30 + this._10*m._31 + this._20*m._32 + this._30*m._33; 
	
	var _01 = this._01*m._00 + this._11*m._01 + this._21*m._02 + this._31*m._03; 
	var _11 = this._01*m._10 + this._11*m._11 + this._21*m._12 + this._31*m._13; 
	var _21 = this._01*m._20 + this._11*m._21 + this._21*m._22 + this._31*m._23; 
	var _31 = this._01*m._30 + this._11*m._31 + this._21*m._32 + this._31*m._33; 
	
	var _02 = this._02*m._00 + this._12*m._01 + this._22*m._02 + this._32*m._03; 
	var _12 = this._02*m._10 + this._12*m._11 + this._22*m._12 + this._32*m._13; 
	var _22 = this._02*m._20 + this._12*m._21 + this._22*m._22 + this._32*m._23; 
	var _32 = this._02*m._30 + this._12*m._31 + this._22*m._32 + this._32*m._33; 
	
	var _03 = this._03*m._00 + this._13*m._01 + this._23*m._02 + this._33*m._03; 
	var _13 = this._03*m._10 + this._13*m._11 + this._23*m._12 + this._33*m._13; 
	var _23 = this._03*m._20 + this._13*m._21 + this._23*m._22 + this._33*m._23; 
	var _33 = this._03*m._30 + this._13*m._31 + this._23*m._32 + this._33*m._33; 
	
	this._00 = _00; this._10 = _10; this._20 = _20; this._30 = _30;
	this._01 = _01; this._11 = _11; this._21 = _21; this._31 = _31;
	this._02 = _02; this._12 = _12; this._22 = _22; this._32 = _32;
	this._03 = _03; this._13 = _13; this._23 = _23; this._33 = _33;
	
	return this;
};

Matrix4x4.prototype.transpose = function() {
	return new Matrix4x4(
		new Vector( this._00,this._10,this._20,this._30 ),
		new Vector( this._01,this._11,this._21,this._31 ),
		new Vector( this._02,this._12,this._22,this._32 ),
		new Vector( this._03,this._13,this._23,this._33 )
	);
};

Matrix4x4.prototype.toString = function() {
	console.log(
		"mat = {\n" +
			"{" + this._00 + "," + this._10 + "," + this._20 + "," + this._30 + "},\n" +
			"{" + this._01 + "," + this._11 + "," + this._21 + "," + this._31 + "},\n" +
			"{" + this._02 + "," + this._12 + "," + this._22 + "," + this._32 + "},\n" +
			"{" + this._03 + "," + this._13 + "," + this._23 + "," + this._33 + "},\n" +
		"}"
	);
};

// --------------------------------------------
// 
// --------------------------------------------
var VectorLine = function( point, direction ) {
	this.point = point;
	this.direction = direction;
};

VectorLine.prototype.getMatrixOntoZAxis = function() {
	var point = this.point.copy();
	//point.normalize();
	
	var matrix = new Matrix4x4(
		new Vector(1,0,0,-point.x),
		new Vector(0,1,0,-point.y),
		new Vector(0,0,1,0),
		new Vector(0,0,0,1)
	);
	
	var inverseMatrix = new Matrix4x4(
		new Vector(1,0,0,point.x),
		new Vector(0,1,0,point.y),
		new Vector(0,0,1,0),
		new Vector(0,0,0,1)
	);
	
	/*var l = point.length();
	var l_yz = new Vector(0,point.y,point.z).length();
	var rotX = new Matrix4x4(
		new Vector(1,0,0,0),
		new Vector(0,point.z/l_yz,-point.y/l_yz,0),
		new Vector(0,point.y/l_yz,point.z/l_yz,0),
		new Vector(0,0,0,1)
	);
	var rotY = new Matrix4x4(
		new Vector(l_yz/l,0,-point.x/l,0),
		new Vector(0,1,0,0),
		new Vector(point.x/l,0,l_yz/l,0),
		new Vector(0,0,0,1)
	);
	
	var matrix = new Matrix4x4();
	matrix.multiply( rotX );
	matrix.multiply( rotY );
	
	var inverseMatrix = new Matrix4x4();
	inverseMatrix.multiply( rotY.transpose() );
	inverseMatrix.multiply( rotX.transpose() );*/
	
	/*var test = new Matrix4x4();
	test.multiply( matrix );
	test.multiply( inverseMatrix );
	test.toString();*/
	
	return  [ matrix, inverseMatrix ];
};

// --------------------------------------------
// 
// --------------------------------------------
var Polygon = function() {
	this.vertices = [];
	for( var i = 0, l = arguments.length-1; i < l; i++ ) {
		this.vertices[i] = arguments[i];
	}
	this.color = arguments[arguments.length-1];
	this.calcPlaneEquation();
	this.calcBoundingSphere();
	this.calcBoundingBox();
};

Polygon.prototype.calcPlaneEquation = function() {
	this.normal = new Vector(0,0,0);
	for( var i = 0, l = this.vertices.length-1; i < l; i++ ) {
		var vi = this.vertices[i];
		var vj = this.vertices[i+1];
		this.normal.x += (vi.y-vj.y)*(vi.z+vj.z);
		this.normal.y += (vi.z-vj.z)*(vi.x+vj.x);
		this.normal.z += (vi.x-vj.x)*(vi.y+vj.y);
	}
	var vi = this.vertices[this.vertices.length-1];
	var vj = this.vertices[0];
	this.normal.x += (vi.y-vj.y)*(vi.z+vj.z);
	this.normal.y += (vi.z-vj.z)*(vi.x+vj.x);
	this.normal.z += (vi.x-vj.x)*(vi.y+vj.y);
	//this.normal.normalize();
	this.A = this.normal.x;
	this.B = this.normal.y;
	this.C = this.normal.z;
	var v = this.vertices[0];
	this.D = -(this.A*v.x + this.B*v.y + this.C*v.z);
};

Polygon.prototype.displayPlaneEquation = function() {
	console.log( this.A+"x" + (this.B<0?"":"+")  + this.B+"y" + (this.C<0?"":"+") + this.C+"z" + (this.D<0?"":"+") + this.D + "=0" );
};

Polygon.prototype.transform = function( m ) {
	for( var i = 0, l = this.vertices.length; i < l; i++ ) {
		this.vertices[i].transform( m );
	}
	this.calcPlaneEquation();
};

Polygon.prototype.calcCentroid = function() {
	this.center = new Vector(0,0,0);
	for( var i = 0, l = this.vertices.length; i < l; i++ ) {
		var v = this.vertices[i];
		this.center.x += v.x;
		this.center.y += v.y;
		this.center.z += v.z;
	}
	this.center.x /= this.vertices.length;
	this.center.y /= this.vertices.length;
	this.center.z /= this.vertices.length;
};

Polygon.prototype.calcBoundingSphere = function() {
	this.calcCentroid();
	var v = this.vertices[0];
	this.radius2 = Math.pow(this.center.x - v.x, 2) + Math.pow(this.center.y - v.y, 2) + Math.pow(this.center.z - v.z, 2); 
	this.radius = Math.sqrt( this.radius2 );
};

Polygon.prototype.displayBoundingSphere = function() {
	console.log( "Sphere center: " + "(" + this.center.x + "," + this.center.y + "," + this.center.z + ")" + "\n" +
		"Sphere radius: " + this.radius + "\n" +
		"Sphere radius^2: " + this.radius2
	);
};

Polygon.prototype.calcBoundingBox = function() {
	var v = this.vertices[0];
	this.min = new Vector(v.x,v.y,v.z);
	this.max = new Vector(v.x,v.y,v.z);
	for( var i = 1, l = this.vertices.length; i < l; i++ ) {
		var v = this.vertices[i];
		if( this.min.x > v.x ) {
			this.min.x = v.x;
		}
		if( this.max.x < v.x ) {
			this.max.x = v.x;
		}
		if( this.min.y > v.y ) {
			this.min.y = v.y;
		}
		if( this.max.y < v.y ) {
			this.max.y = v.y;
		}
		if( this.min.z > v.z ) {
			this.min.z = v.z;
		}
		if( this.max.z < v.z ) {
			this.max.z = v.z;
		}
	}
};

Polygon.prototype.displayBoundingBox = function() {
	console.log( this.min.x + "," + this.max.x + ", " +
		this.min.y + "," + this.max.y + ", " +
		this.min.z + "," + this.max.z 
	);
};

Polygon.prototype.transformBoundingBox = function( m ) {
	this.min.transform( m );
	this.max.transform( m );
};

// --------------------------------------------
// 
// --------------------------------------------
var VisibleSurfaceRayTracing = {
	
	objectsList: [],
	activeObjectList: [],
	intersectionList: [],
	
	calcDistanceSphereRay: function( poly, ray ) {
		return Math.pow(poly.center.x - ray.x, 2) + Math.pow(poly.center.y - ray.y, 2);
	},
	
	rayIntersectSphere: function( poly, ray ) {
		if( this.calcDistanceSphereRay(poly,ray) < poly.radius2 ) {
			return true;
		}
		return false;
	},
	
	addObject: function( poly ) {
		this.objectsList.push( poly );
	},
	
	render: function() {
		var direction = new Vector(0,0,1);
		for( var y = 0; y < HEIGHT; y++ ) {
			for( var x = 0; x < WIDTH; x++ ) {
				var address = y*WIDTH+x;
				var ray = new Vector(x+.5,y+.5,0);
				//console.log( "Evaluating at point (" + ray.x + "," + ray.y + ")" );
				var line = new VectorLine(ray, direction);
				for( var i = 0, l = this.objectsList.length; i < l; i++ ) {
					var poly = this.objectsList[i];
					if( this.rayIntersectSphere(poly , ray) ) {
						this.activeObjectList.push( poly );
					}
				}
				if( this.activeObjectList.length ) {
					var m = line.getMatrixOntoZAxis();
					var transformation = m[0];
					var inverse = m[1];
					for( var i = 0, l = this.activeObjectList.length; i < l; i++ ) {
						var poly = this.activeObjectList[i];
						//console.log( "Testing poly with color (" + poly.color.x + "," + poly.color.y + "," + poly.color.z + ")" );
						poly.transformBoundingBox( transformation );
						if( Math.sign(poly.min.x) != Math.sign(poly.max.x) &&
						Math.sign(poly.min.y) != Math.sign(poly.max.y) ) {
							//console.log( "\tIntersection with bounding box" );
							if( this.pointInsidePoly( ray, poly ) ) {
								poly.transform( transformation );
								poly.calcPlaneEquation();
								var z = this.calcDepthValue( poly );
								//console.log( "\tIntersection depth at " + z );
								this.intersectionList.push( { poly: poly, z: z } );
								poly.transform( inverse );
							} else {
								//console.log( "\tPoint is outside" );
							}
						}
						poly.transformBoundingBox( inverse );
					}
					if( this.intersectionList.length ) {
						this.intersectionList.sort( this.sortFunc );
						frameBuffer[address] = this.intersectionList[0].poly.color;
					} else {
						frameBuffer[address] = BACKGROUND_COLOR;
					}
				} else {
					//console.log( "No polys intersect at this point" );
					frameBuffer[address] = BACKGROUND_COLOR;
				}
				this.intersectionList = [];
				this.activeObjectList = [];
				//console.log( "-----------" );
			}
		}
    
		$tds = $table.querySelectorAll( 'td' );
		var index = 0;
		for( var y = 0; y < HEIGHT; y++ ) {
			for( var x = 0; x < WIDTH; x++ ) {
				var address = (-y+HEIGHT-1)*WIDTH+x;
				$tds[address].style.backgroundColor = vectorToRGB(frameBuffer[index]);
				index++;
			}
		}
    
	},
	
	pointInsidePoly: function( ray, poly ) {
		var x = ray.x, y = ray.y;
		var vi = poly.vertices[0];
		var vj = poly.vertices[1];
		var x1 = vi.x, y1 = vi.y;
		var x2 = vj.x, y2 = vj.y;
		var prevSign = (x2-x1)*(y-y1)-(x-x1)*(y2-y1);
		prevSign = Math.abs(prevSign) <= 1e-6 ? 0 : Math.sign(prevSign);
		for( var i = 1, l = poly.vertices.length-1; i < l; i++ ) {
			vi = poly.vertices[i];
			vj = poly.vertices[i+1];
			x1 = vi.x, y1 = vi.y;
			x2 = vj.x, y2 = vj.y;
			var curSign = (x2-x1)*(y-y1)-(x-x1)*(y2-y1);
			curSign = Math.abs(curSign) <= 1e-6 ? 0 : Math.sign(curSign);
			if( prevSign != 0 && curSign != 0 && curSign != prevSign )  {
				return false;
			}
			prevSign = curSign;
		}
		vi = poly.vertices[poly.vertices.length-1];
		vj = poly.vertices[0];
		x1 = vi.x, y1 = vi.y;
		x2 = vj.x, y2 = vj.y;
		var curSign = (x2-x1)*(y-y1)-(x-x1)*(y2-y1);
		curSign = Math.abs(curSign) <= 1e-6 ? 0 : Math.sign(curSign);
		if( curSign != 0 && prevSign != 0 && prevSign != curSign ) {
			return false;
		}
		return true;
	},
	
	calcDepthValue: function( poly ) {
		return -poly.D/poly.C;
	},
	
	sortFunc: function( a, b ) {
		return b.z - a.z;
	},
	
};

// --------------------------------------------
// 
// --------------------------------------------
var triangle = new Polygon(
	new Vector(15,15,15),
	new Vector(25,25,5),
	new Vector(30,10,5),
	new Vector(0,255,0) // green
);
var rectangle = new Polygon(
	new Vector(10,5,10),
	new Vector(10,25,10),
	new Vector(25,25,10),
	new Vector(25,5,10),
	new Vector(255,0,0) // red
);

VisibleSurfaceRayTracing.addObject( rectangle );
VisibleSurfaceRayTracing.addObject( triangle );
VisibleSurfaceRayTracing.render();

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