A Pen By
Michael Jasper

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` ````
<canvas id="c"></canvas>
```

` ````
// Tiny Raytracer (C) Gabriel Gambetta 2013
// ----------------------------------------
//
// Configuration and scene
//
// Size of the canvas. w is also reused as a "big constant" / "+infinity"
var w = 600;
// Sphere: radius, [cx, cy, cz], R, G, B, specular exponent, reflectiveness
// R, G, B in [0, 9], reflectiveness in [0..9].
var spheres = [
w, [ 0, -w, 0], 9, 9, 0, w, 2, // Yellow sphere
1, [ 0, 0, 3], 9, 0, 0, w, 3, // Red sphere
1, [-2, 1, 4], 0, 9, 0, 9, 4, // Green sphere
1, [ 2, 1, 4], 0, 0, 9, w, 5 // Blue sphere
];
// Ambient light.
var ambient_light = 2;
// Point lights: intensity, [x, y, z]
// Intensities should add to 10, including ambient.
var lights = [
8, [2, 2, 0]
];
// -----------------------------------------------------------------------------
// Shorten some names.
var math = Math;
var sqrt = math.sqrt;
var max = math.max;
// Global variables.
var out_idx = 0;
// Closure doesn't rename vars unless they're declared with "var", which takes
// space. So most vars are 1-letter and global:
//
// C: sphere center
// L: light vector
// N: surface normal at intersection
// X: intersection point
// a: quadratic equation constant
// b: quadratic equation constant
// c: color channel
// d: quadratic equation discriminant
// e: loop variable
// f: candidate parameter t
// h: half-width of the canvas
// i: illumination
// j: (ray origin) - (sphere center)
// k: <N, L>
// l: light index in loop
// n: <N, N>
// q: sphere index in loop
// r: sphere radius
// s: closest intersection sphere index
// t: closest intersection t
// u: intensity of lights[l]
// v: closest sphere found in loop
//
// The exceptions are vars that need to be initialized here (we still pay the
// "a=", so we pay a single "var" above, and use nice names) and some vars in
// trace_ray, which is recursive, so some of it vars can't be global.
// Get to the raw pixel data.
var canvas = document.getElementById("c");
var context2d = canvas.getContext("2d");
var image_data = context2d.getImageData(0, 0, w, w);
var raw_data = image_data.data;
canvas.width = canvas.height = w;
// Dot product.
function dot(A, B) {
return A[0]*B[0] + A[1]*B[1] + A[2]*B[2];
}
// Helper: A_minus_Bk(A, B, k) = A - B*k. Since it's used more with k < 0,
// using - here saves a couple of bytes later.
function A_minus_Bk (A, B, k) {
return [A[0] - B[0]*k, A[1] - B[1]*k, A[2] - B[2]*k];
}
// Find nearest intersection of the ray from B in direction D with any sphere.
// "Interesting" parameter values must be in the range [t_min, t_max].
// Returns the index within spheres of the center of the hit sphere, 0 if none.
// The parameter value for the intersection is in the global variable t.
function closest_intersection(B, D, t_min, t_max) {
t = w; // Min distance found.
// Quadratic equation coefficients are K1, K2, K3. K1 is constant for the ray.
a = 2*dot(D, D); // 2*K1
// For each sphere.
// Get the radius and test for end of array at the same time;
// spheres[n] == undefined ends the loop.
// q points to the 2nd element of the sphere because of q++; +6 skips to next
// sphere.
for (v = q = 0; r = spheres[q++]; q += 6) {
b = -2*dot(j = A_minus_Bk(B, spheres[q], 1), D); // -K2; also j = origin - center
// Compute sqrt(Discriminant) = sqrt(K2*K2 - 4*K1*K3), go ahead if there are
// solutions.
if ( d = sqrt(b*b - 2*a*(dot(j, j) - r*r)) ) {
// Compute the two solutions.
for (e = 2; e--; d = -d) {
f = (b - d)/a; // f = (-K2 - d) / 2*K1
if (t_min < f && f < t_max && f < t) {
v = q;
t = f;
}
}
}
}
// Return index of closest sphere in range; t is global
return v;
}
// Trace the ray from B with direction D considering hits in [t_min, t_max].
// If depth > 0, trace recursive reflection rays.
// Returns the value of the current color channel as "seen" through the ray.
function trace_ray(B, D, t_min, t_max, depth) {
// Find nearest hit; if no hit, return black.
if (!(s = closest_intersection(B, D, t_min, t_max)))
return 0;
// Compute "normal" at intersection: N = X - spheres[s]
N = A_minus_Bk(X = A_minus_Bk(B, D, -t), // intersection: X = B + D*t = B - D*(-t)
spheres[s], 1);
// Instead of normalizing N, we divide by its length when appropriate. Most of
// the time N appears twice, so we precompute its squared length.
n = dot(N, N);
// Start with ambient light only
i = ambient_light;
// For each light
for (l = 0; u = lights[l++]; ) { // Get intensity and check for end of array
// Compute vector from intersection to light (L = lights[l++] - X) and
// k = <N,L> (reused below)
k = dot(N, L = A_minus_Bk(lights[l++], X, 1));
// Add to lighting
i += u *
// If the pont isn't in shadow
// [t_min, t_max] = [epsilon, 1] - epsilon avoids self-shadow, 1
// doesn't look farther than the light itself.
!closest_intersection(X, L, 1/w, 1) * (
// Diffuse lighting, only if it's facing the point
// <N,L> / (|N|*|L|) = cos(alpha)
// Also, |N|*|L| = sqrt(<N,N>)*sqrt(<L,L>) = sqrt(<N,N>*<L,L>)
max(0, k / sqrt(dot(L, L)*n))
// Specular highlights
//
// specular = (<R,V> / (|R|*|V|)) ^ exponent
// = (<-R,-V> / (|-R|*|-V|)) ^ exponent
// = (<-R,D> / (|-R|*|D|)) ^ exponent
//
// R = 2*N*<N,L> - L
// M = -R = -2*N*<N,L> + L = L + N*(-2*<N,L>)
//
// If the resultant intensity is negative, treat it as 0 (ignore it).
+ max(0, math.pow( dot(M = A_minus_Bk(L, N, 2*k/n), D)
/ sqrt(dot(M, M)*dot(D, D)), spheres[s+4]))
);
}
// Compute the color channel multiplied by the light intensity. 2.8 maps
// the color range from [0, 9] to [0, 255] and the intensity from [0, 10]
// to [0, 1], because 2.8 ~ (255/9)/10
//
// spheres[s] = sphere center, so spheres[s+c] = color channel
// (c = [1..3] because ++c below)
var local_color = spheres[s+c]*i*2.8;
// If the recursion limit hasn't been hit yet, trace reflection rays.
// N = normal (non-normalized - two divs by |N| = div by <N,N>
// D = -view
// R = 2*N*<N,V>/<N,N> - V = 2*N*<N,-D>/<N,N> + D = D - N*(2*<N,D>/<N,N>)
var ref = spheres[s+5]/9;
return depth-- ? trace_ray(X,
A_minus_Bk(D, N, 2*dot(N, D)/n), // R
1/w, w, depth)*ref
+ local_color*(1 - ref)
: local_color;
}
// For each y; also compute h=w/2 without paying an extra ";"
for (y = h=w/2; y-- > -h;) {
// For each x
for (x = -h; x++ < h;) {
// One pass per color channel (!). This way we don't have to deal with
// "colors".
for (c = 0; ++c < 4;) {
// Camera is at (0, 1, 0)
//
// Ray direction is (x*vw/cw, y*vh/ch, 1) where vw = viewport width,
// cw = canvas width (vh and ch are the same for height). vw is fixed
// at 1 so (x/w, y/w, 1)
//
// [t_min, t_max] = [1, w], 1 starts at the projection plane, w is +inf
//
// 2 is a good recursion depth to appreciate the reflections without
// slowing things down too much
//
raw_data[out_idx++] = trace_ray([0, 1, 0], [x/w, y/w, 1], 1, w, 4);
}
raw_data[out_idx++] = 255; // Opaque alpha
}
}
context2d.putImageData(image_data, 0, 0);
```

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