Canvas.setpenopacity(.2);

const canvas_size = 95;
const turtle_dim = 32;
const num_iterations = 100;
const turtles = [];

const brown_rot = 360;
const brown_for_min = 1;
const brown_for_max = 10;

const light_position = [-2,3,-4];
const ro = [0,0,-3.5];
const sphere_pos = [-.2,0,0];

for (let x=0; x<turtle_dim; x++) {
    for (let y=0; y<turtle_dim; y++) {
        turtles.push( new Turtle( (x/turtle_dim * 2 - 1 ) * canvas_size,
                                  (y/turtle_dim * 2 - 1 ) * canvas_size));
    }   
}

function get_image_intensity(x,y) {
    x /= canvas_size;
    y /= canvas_size;
    
    const rd = vec_normalize([x,-y,2]);
    let normal;
    let light = 0;
    let hit;
    let plane_hit = false;
    
    let dist = intersect_sphere(ro, rd, sphere_pos, 1);
    if (dist > 0) {
        hit = vec_add(ro, vec_mul(rd, dist));
        normal = vec_normalize(hit);
    } else {
        dist = 10000;
    }
    if (rd[1] < 0) {
        const plane_dist = -1/rd[1];
       if (plane_dist < dist) {
            dist = plane_dist;
            plane_hit = true;
            hit = vec_add(ro, vec_mul(rd, dist));
            normal = [0,1,0];
        }
    } 
    
    if (dist > 0 && dist < 100) {
        let vec_to_light = vec_sub(hit, light_position);
        const light_dist_sqr = vec_dot(vec_to_light, vec_to_light);
        
        vec_to_light = vec_mul(vec_to_light, -1/Math.sqrt(light_dist_sqr));
        
        let light = vec_dot(normal, vec_to_light);
        light *= 30 / light_dist_sqr;
        
        // shadow ?
        if (plane_hit && intersect_sphere(hit, vec_to_light, sphere_pos, 1) > 0) {
            light = 0;
        }
        
        return Math.sqrt(Math.min(1, Math.max(0,light)));
    } else {
        return 0;
    }
}

function move_turtle(t) {
    // brownian movement, random rotation:
    t.penup();
    t.goto( (Math.random()-.5)*2*canvas_size, (Math.random()-.5)*2*canvas_size);
    t.right( Math.random() * brown_rot );
    // distance dependent on brightness scene
    const int = 1 - get_image_intensity( t.xcor(), t.ycor() );
    const dist = brown_for_min + (brown_for_max-brown_for_min) * int;
    
    t.backward(dist/2);
    t.pendown();
    t.forward(dist);
}

// The walk function will be called until it returns false.
function walk(i) {
    for (let j=0; j<turtles.length; j++) {
        move_turtle(turtles[j]);
    }
    return i < num_iterations;
}

// math functions
function vec_normalize(a) {
    const l = Math.sqrt(vec_dot(a,a));
    return [a[0]/l,a[1]/l,a[2]/l];
}

function vec_add(a, b) {
    return [a[0]+b[0], a[1]+b[1], a[2]+b[2]]
}

function vec_mul(a, b) {
    return [a[0]*b, a[1]*b, a[2]*b]
}

function vec_sub(a, b) {
    return [a[0]-b[0], a[1]-b[1], a[2]-b[2]]
}

function vec_dot(a, b) {
    return a[0]*b[0]+a[1]*b[1]+a[2]*b[2];
}

function intersect_sphere(ro, rd, center, radius) {
    const oc = vec_sub(ro, center);
	const b = vec_dot( oc, rd );
	const c = vec_dot( oc, oc ) - radius * radius;
	const h = b*b - c;
	if( h<0 ) return -1;
	return -b - Math.sqrt( h );
}