### Raytraced Sphere with Quads

raytracing + quadtree subdivision

Special thanks to @reinder for the raytracing algorithm.

Would have worked on the first pass but rounding errors were making things wrong and ugly.

#raytracer #raytrace #dither #gradient #pixel

```// Forked from "FSD Raytraced Sphere #1" by imakerobots
// https://turtletoy.net/turtle/8f85afd31a

// Forked from "Floyd–Steinberg dithering" by imakerobots

// raytraced sphere part from https://turtletoy.net/turtle/11075dfee0
const canvas_size = 95;
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];

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 *= 20 / light_dist_sqr;  // changed the intensity a bit

if (plane_hit && intersect_sphere(hit, vec_to_light, sphere_pos, 1) > 0) {
light = 0.01;  // added some ambient light.  make 0 for none.
}

return Math.sqrt(Math.min(1, Math.max(0,light)));
} else {
return 0;
}
}

// 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 );
}

const iterations=800; // min=1 max=5000, step=10

// dithering part from https://turtletoy.net/turtle/d47e2bad0c
const opacity=0.1;
var brightest;
Canvas.setpenopacity(opacity);

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

function get_pixel(x,y) {
return get_image_intensity( x,y );
}

function get_image(x,y) {
y=Math.floor(y);
x=Math.floor(x);
return image[y*200+x];
}

Math.floor(x0),
Math.floor(y0),
Math.floor(x1),
Math.floor(y1),
0,
0
];

var w=Math.floor(x1-x0);
var h=Math.floor(y1-y0);
var size=w*h;
// find the average
for(var y=0;y<h;++y) {
for(var x=0;x<w;++x) {
}
}
// find the mean square error
for(var y=0;y<h;++y) {
for(var x=0;x<w;++x) {
var d = get_image(x0+x,y0+y) - quad[4];
}
}

}

}

}

var intensity = 1-(quad[4]/brightest);
if(intensity>0.01) {
// fill the quad
for(var i=0;i<intensity;i+=0.1) {
turtle.jump(left ,y-100);
turtle.goto(right,y-100);
}
}
}
}

var w2=w/2;
var h2=h/2;
if(w2<=1||h2<=1) {
return;
}
}

// precalculate the raytraced image.
var image=[];
for(var y=0;y<200;++y) {
for(var x=0;x<200;++x) {
image[y*200+x] = get_pixel(x-100,y-100);
}
}

// our list of active quads
var allNodes = [];
var finishedNodes = [];
// initialized with the root quad

// draw the outside quad
turtle.pendown();
turtle.jump(-100,-100);
turtle.goto(-100, 100);
turtle.goto( 100, 100);
turtle.goto( 100,-100);
turtle.goto(-100,-100);
//drawOriginal();

function drawOriginal() {
// display the raytraced image
for(var py=0;py<200;++py) {
for(var px=0;px<200;++px) {
if(image[py*200+px]<0.65) {
turtle.jump(px-100,py-100);
turtle.seth(45);
turtle.forward(1);
}
if(image[py*200+px]<0.15) {
turtle.jump(px-100,py-100);
turtle.seth(45+90);
turtle.forward(1);
}
}
}
}

function walk(i) {
// find the quadtree node with the biggest error
var worst=0;
for(var j=1;j<allNodes.length;++j) {
if(allNodes[worst][5] < allNodes[j][5]) {
worst=j;
}
}
// split the quad node and draw the split
// remember the error (maybe quit when error small enough?)
var err=allNodes[worst][5];
// take the worst off the list
allNodes.splice(worst,1);

if(i==iterations) {
drawAllRemainingNodes();
return false;
}
return true;
}

function drawAllRemainingNodes() {
brightest=0;
for(var j=0;j<allNodes.length;++j) {
if(brightest<allNodes[j][4]) {
brightest=allNodes[j][4];
}
}
for(var j=0;j<finishedNodes.length;++j) {
if(brightest<finishedNodes[j][4]) {
brightest=finishedNodes[j][4];
}
}
for(var j=0;j<allNodes.length;++j) {