JS1k: The JavaScript code golfing competition

_=Math;X=Y=Z=100;V=3;W=a=r=0;d=1;
function R(t,l,j,u,C,v,w,m,D,x,y,g,z,E,h,k,c,b,e){function n(f,i){f=f*E+r;i=_.PI/2-i*E;return[j*l(i)*l(f)+X,j*l(i)*t(f)+Y,j*t(i)+Z]}function A(f,i,o,B,p,q,s){s=l(a);q=t(-a);for(e=0;e<4;e++){p=f[e][0]-u;o=f[e][1]-u;B=f[e][2]-u;f[e]=[p*s*y-o*q*y-B*x,p*q+o*s,p*s*x-o*q*x+B*y]}k.push(f)}h=z.getContext("2d");z.width=z.height=v;if(Y<=j||Y>=w-j){V=-V;d=-d}Z<=j?W=-W:W-=1.5;a-=0.04;r-=d*0.1;k=[];for(c=0;c<14;c++)for(b=0;b<7;b++)A([n(c,b),n(c+1,b),n(c+1,b-1),n(c,b-1),(c+b)%2?"red":"#fff"]);Y+=V;Z+=W;h[D]="#999";
h.fillRect(0,0,v,v);for(c=0;c<=w;c+=g)for(b=0;b<=w;b+=g){A([[c,b,0],[c+g,b,0],[c+g,b+g,0],[c+g,b,0],C]);A([[0,c,b],[0,c+g,b],[0,c+g,b+g],[0,c+g,b],C])}k.sort(function(f,i){return i[0][2]-f[0][2]});for(c in k){e=k[c];h.strokeStyle=h[D]=e[4];h.beginPath();h.moveTo(e[0][1]+m,-e[0][0]+m);for(b=1;b<=4;b++)h.lineTo(e[b%4][1]+m,-e[b%4][0]+m);h.stroke();h.fill()}}setInterval('R(_.sin,_.cos,50,200,"#90C",550,300,250,"fillStyle",-1,-.3,15,document.getElementById("c"),_.PI/7)',33);

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// X=P0,Y=P1,Z=P2,V=V1,W=V2,a=yaw,r=rot, d=rotation direction
// X, Y, Z are the centre of the ball
// V and W are the velocity in y and z directions repsectively
// a is the yaw, r the rotation and d the rotation direction
_ = Math,X=Y=Z=100,V=3,W=a=r=0,d=1;
function R(sin, cos, radius, Q, lineColour, w, gridSize, dw, fillStyle, sinPitch, cosPitch, fifteen,
	canvas, fact, context, sphere, i, j, tmp)
 {
	context = canvas.getContext('2d'), // just assume it exists!
	canvas.width = canvas.height = w;
	
	// Performs a translation from spherical to cartesion coordinates, together with an origin shift.
	function T(theta, phi) {
		theta = theta * fact + r;
		phi = _.PI / 2 - phi * fact;
		return [radius * cos(phi) * cos(theta) + X, radius * cos(phi) * sin(theta) + Y, radius * sin(phi) + Z] 
	};
	
	// Handle bounce off walls etc.
	if (Y <= radius || Y >= gridSize - radius) 
		V = -V, d = -d;
		
	Z <= radius ? W = -W : W -= 1.5;

	// Update camera yaw, and rotation of ball.
	a -= .04;
	r -= d * .1;

	// Create a model of our sphere. No space in 1k to make it smooth, can be done by increasing the facet count
	// but requires dividing i and j in the colour calculation which adds bytes etc.
	sphere = [];
	for(i = 0; i < 14; i++)
	  for(j = 0; j < 7; j++)
		cameraTranslateAndPush(
			[T(i, j), T(i + 1, j), T(i + 1, j - 1), T(i, j - 1),
				(i+j) % 2 ? 'red' : '#fff']);
			
	Y += V; Z += W;
	
	// Clear and color background.
	context[fillStyle] = '#999'; 
	context.fillRect(0,0,w,w);
	
	// Draws the grid, sticks to 4 points avoiding array length queries later on.
	for(i = 0; i <= gridSize; i += fifteen)
		for(j = 0; j <= gridSize; j += fifteen)
			cameraTranslateAndPush([[i,j,0],[i + fifteen, j,0],[i+fifteen,j+fifteen,0],[i+fifteen,j,0], lineColour]),
			cameraTranslateAndPush([[0,i,j],[0, i + fifteen, j],[0,i+fifteen,j+fifteen],[0,i+fifteen,j], lineColour])

	// Painter's algorithm: sort on distance from camera, for brevity, pick first z coordinate.
	sphere.sort(function(a, b) {
		return b[0][2] - a[0][2];
		} 
	);

	// Draw, starting with objects furthest away.
	for(i in sphere)
	{
		tmp = sphere[i];
		context.strokeStyle = context[fillStyle] =  tmp[4];
		context.beginPath();

		context.moveTo(tmp[0][1] + dw, -tmp[0][0] + dw);
		for(j = 1; j <= 4; j++)
			context.lineTo(tmp[j % 4][1] + dw, -tmp[j % 4][0] + dw); // uses % trick to draw back to starting point		
		
		context.stroke();
		context.fill();	
	}
	
	// Performs the camera translation given yaw and pitch (for brevity, I had to hardcode the pitch - it is precalculated).
	function cameraTranslateAndPush(poly, x, y, z, x0, sinYaw, cosYaw) {
		cosYaw = cos(a);
		sinYaw = sin(-a);
		for(tmp = 0; tmp < 4; tmp++) // reuse tmp variable
		{
			x0 = poly[tmp][0] - Q;
			y = poly[tmp][1] - Q;
			z = poly[tmp][2] - Q;
			
			poly[tmp] = [x0 * cosYaw * cosPitch - y * sinYaw * cosPitch - z * sinPitch, x0 * sinYaw + y * cosYaw, x0 * cosYaw * sinPitch - y * sinYaw * sinPitch + z * cosPitch];	
		}
	
		sphere.push(poly);
	}
	
}
setInterval('R(_.sin,_.cos,50,200,"#90C",550,300,250,"fillStyle",-1,-.3,15,document.getElementById("c"),_.PI/7)',33); // note: heavy rounding of pitch