camera.js

/*
 * Perspective camera implementation.
 * Derived from https://github.com/osresearch/papercraft/blob/master/camera.c
 */

function m44_mult(a,b)
{
	let c = [
		[0,0,0,0],
		[0,0,0,0],
		[0,0,0,0],
		[0,0,0,0],
	];
	for(let i = 0 ; i < 4 ; i++)
		for(let j = 0 ; j < 4 ; j++)
			for(let k = 0 ; k < 4 ; k++)
				c[i][j] += a[i][k] * b[k][j];

	return c;
}


function Camera(eye,lookat,up,fov)
{
	this.eye = eye;
	this.lookat = lookat;
	this.up = up;
	this.fov = fov;
	this.generation = 0;
	this.width = width;
	this.height = height;

	// project a point from model space to camera space
	this.project = function(v_in,v_out=null)
	{
		let v = [v_in.x, v_in.y, v_in.z, 1];
		let p = [0,0,0,0];

		for(let i = 0 ; i < 4 ; i++)
			for(let j = 0 ; j < 4 ; j++)
				p[i] += this.matrix[i][j] * v[j];

		// if the projected point has negative z, this means
		// it is behind us and can be discarded
		if (p[2] <= 0)
			return;

		let x = p[0] / p[3];
		let y = p[1] / p[3];
		let z = p[2] / p[3];
		if (!v_out)
			return createVector(x,y,z);

		// update in place to avoid an allocation
		v_out.x = x;
		v_out.y = y;
		v_out.z = z;
		return v_out;
	}

	// Update the camera projection matrix with eye/lookat/fov
	this.update_matrix = function()
	{
		// compute the three basis vectors for the camera

		// w is the Z axis from the eye to the destination point
		let w = p5.Vector.sub(this.eye, this.lookat).normalize();

		// u is the X axis to the right side of the camera
		let u = this.up.cross(w).normalize();

		// v is the Y axis aligned with the UP axis
		let v = w.cross(u).normalize();

		let cam = [
			[ u.x, u.y, u.z, -u.dot(this.eye) ],
			[ v.x, v.y, v.z, -v.dot(this.eye) ],
			[ w.x, w.y, w.z, -w.dot(this.eye) ],
			[ 0,   0,   0,   1 ],
		];

		let scale = 1000.0 / tan(this.fov * PI / 180 / 2);
		let near = 1;
		let far = 200;
		let f1 = - far / (far - near);
		let f2 = - far * near / (far - near);

		let perspective = [
			[ scale, 0, 0, 0 ],
			[ 0, scale, 0, 0 ],
			[ 0, 0, f2, -1 ],
			[ 0, 0, f1,  0 ],
		];

		this.matrix = m44_mult(perspective, cam);
		this.u = u;
		this.v = v;
		this.w = w;

		console.log("Camera matrix: " + this.matrix);
		this.generation++;
	}

	this.update_matrix();
}