JavaScript preprocessors can help make authoring JavaScript easier and more convenient. For instance, CoffeeScript can help prevent easy-to-make mistakes and offer a cleaner syntax and Babel can bring ECMAScript 6 features to browsers that only support ECMAScript 5.

Any URL's added here will be added as `<script>`

s in order, and run *before* the JavaScript in the editor. You can use the URL of any other Pen and it will include the JavaScript from that Pen.

You can apply a script from anywhere on the web to your Pen. Just put a URL to it here and we'll add it, in the order you have them, before the JavaScript in the Pen itself.

If the script you link to has the file extension of a preprocessor, we'll attempt to process it before applying.

You can also link to another Pen here, and we'll pull the JavaScript from that Pen and include it. If it's using a matching preprocessor, we'll combine the code before preprocessing, so you can use the linked Pen as a true dependency.

+ add another resource

If active, Pens will autosave every 30 seconds after being saved once.

If enabled, the preview panel updates automatically as you code. If disabled, use the "Run" button to update.

If enabled, your code will be formatted when you actively save your Pen. Note: your code becomes un-folded during formatting.

Visit your global Editor Settings.

` ````
<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);
```

999px

Also see: Tab Triggers