// Global code will be evaluated once.
const turtle = new Turtle();

const canvas_size = 95;

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

function get_image_intensity(x,y) {
    x *= 2;
    y *= 2;
     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 draw_pixel(x, y, intensity, res) {
    const steps = 16;
    for (let i=0; i<steps; i++) {
        if (intensity < (i+1)/(steps)) {
            const radius = canvas_size/res * ( 1 - (i+.5)/(steps+.5));
            turtle.penup();
            turtle.goto( x * 2 * canvas_size + canvas_size/res, 
                         y * 2 * canvas_size - radius + canvas_size/res );
            turtle.pendown();
            turtle.circle(radius,360);
        }
    }
}

// The walk function will be called until it returns false.
function walk(i) {
    const res = 32;
    const x = (i % res) / res -.5;
    const y = ((i/res)|0) / res -.5;
        
    let int = 0;
    for (let j=0; j<2; j++) {
        for (let k=0; k<2; k++) {
            int += get_image_intensity(x + (j-.5)/res, y + (k-.5)/res);    
        }
    }
    draw_pixel(x, y, int/4, res);

    return i < res*res;
}

// 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 );
}