### Starfish

Raymarching + Contour of a simple "scene".
Takes a while to start.

```// LL 2021

const turtle = new Turtle();

//Canvas.setpenopacity(-1);

const density = 71;       // min=1, max=301, step=2
const precision = 1.0;     // min=0.1, max=3, step=0.1
const passes = 1;          /// min=1, max=3, step=1 (X, XY, XYZ)
const cam_dist = 2.0;      /// min=0.1, max=10.5, step=0.01
const cam_angle = 0;       /// min=-3.14159, max=3.15159, step=0.01

const MAX_STEPS = 100;
const MAX_DIST = 100;
const SURF_DIST = .001;

const range = [ -.15, 0.4 ];

function length2(v2) { return Math.sqrt(v2[0]*v2[0] + v2[1]*v2[1]); }
function length3(v3) { return Math.sqrt(v3[0]*v3[0] + v3[1]*v3[1] + v3[2]*v3[2]); }
function normalize3(v3) { var l = length3(v3); if (l<0.00001) l=1; return [v3[0]/l, v3[1]/l, v3[2]/l]; }
function mul2(a2, f) { return [a2[0]*f, a2[1]*f]; }
function mul3(a3, f) { return [a3[0]*f, a3[1]*f, a3[2]*f]; }
function add3(a3, b3) { return [a3[0]+b3[0], a3[1]+b3[1], a3[2]+b3[2]]; }
function sub3(a3, b3) { return [a3[0]-b3[0], a3[1]-b3[1], a3[2]-b3[2]]; }
function cross3(a3, b3) { return [ a3[1] * b3[2] - a3[2] * b3[1], a3[2] * b3[0] - a3[0] * b3[2], a3[0] * b3[1] - a3[1] * b3[0] ]; }
function fract3(v3) { return [ v3[0]-Math.floor(v3[0]), v3[1]-Math.floor(v3[1]), v3[2]-Math.floor(v3[2]) ]; }
function floor3(v3) { return [ Math.floor(v3[0]), Math.floor(v3[1]), Math.floor(v3[2]) ]; }
function abs3(v3) { return [ Math.abs(v3[0]), Math.abs(v3[1]), Math.abs(v3[2]) ]; }
function dot3(a3, b3) { return a3[0] * b3[0] + a3[1] * b3[1] + a3[2] * b3[2]; }
function mul_mat2(v2, m22) { return [ v2[0] * m22[0] + v2[1] * m22[1], v2[0] * m22[2] + v2[1] * m22[3] ]; }
function clamp(x, min, max) { return Math.min(max, Math.max(min, x)); }
function smoothstep(edge0, edge1, x) { x = clamp((x - edge0) / (edge1 - edge0), 0.0, 1.0); return x * x * (3 - 2 * x); }
function tri3(x3) { return abs3(sub3(fract3(x3), .5)); }
function mix(x, y, a) { return x * (1-a) + y * a; }
function mix3(a3, b3, f) { return [ mix(a3[0], b3[0], f), mix(a3[1], b3[1], f), mix(a3[2], b3[2], f) ]; }
function smin(a, b , s) { var h = clamp( 0.5 + 0.5*(b-a)/s, 0. , 1.); return mix(b, a, h) - h*(1.0-h)*s; }

function rotation_mat22(a)
{
var s = Math.sin(a);
var c = Math.cos(a);
return [c, -s, s, c];
}

function GetRayDir(uv2, p3, l3, z)
{
var f3 = normalize3(sub3(l3, p3));
var r3 = normalize3(cross3([0,1,0], f3));
var u3 = cross3(f3, r3);
var c3 = mul3(f3, z);
var d3 = normalize3(i3);
return d3;
}

// Box
function sdBox(p3, s3)
{
p3 = sub3(abs3(p3), s3);
var r = Math.min(Math.max(p3[0], Math.max(p3[1], p3[2])), 0);
var q3 = [Math.max(p3[0], 0), Math.max(p3[1], 0), Math.max(p3[2], 0)];
return length3(q3);
}

// Torus
function sdTorus(p3, r1, r2)
{
var cp2 = [ length2([p3[0], p3[2]]) - r1, p3[1] ];
var d = length2(cp2) - r2;

return d;
}

// Knot
function sdKnot(p3, r1, r2, twist, split)
{
var cp2 = [ length2([p3[0], p3[2]]) - r1, p3[1] ];

var a = Math.atan2(p3[2], p3[0]); // polar angle between -pi and pi
cp2 = mul_mat2(cp2, rotation_mat22(a * twist));
cp2[1] = Math.abs(cp2[1]) - split;

var d = length2(cp2) - r2;

return d * .8;
}

// Sphere
function sdSphere(p3, r)
{
var d = length3(p3) - r;
return d;
}

function warp3(p3)
{
const f = 0.1;
const t = 1 * p3[1] + 1 * p3[2] + 10.0 * 1;
return [p3[0] + Math.sin(t) * f, p3[1], p3[2] + Math.cos(t) * f];
}

function displacement(p3)
{
return Math.sin(71*p3[0])*Math.sin(21*p3[1])*Math.sin(21*p3[2]);
}

var scene_objects = [];

function recurse(min_radius, p3, r, angle_start, angle_inc)
{

scene_objects.push([p3, r]);

const rr = r * 0.95;
const mov = r + rr * -0.4;
for (var angle=0; angle<Math.PI*2; angle+=Math.PI*2/1)
{
var q3 = [ 0,  Math.cos(angle_start+angle), Math.sin(angle_start+angle)];
q3 = mul3(q3, mov);
recurse(min_radius, q3, rr, angle_start + angle_inc, angle_inc);
}
}

function init_scene()
{
for (var angle=0; angle<Math.PI*2; angle+=Math.PI*2/5)
{
const angle_inc = 0.12;
recurse(0.01, [0, 0, 0], 0.28, angle, angle_inc);
}
console.log(`Scene has \${scene_objects.length} items`);
}

init_scene();

function map(p3)
{
var d = MAX_DIST;

p3 = warp3(p3);

var count = scene_objects.length;
for (var i=0; i<count; i++)
{
const obj = scene_objects[i];
d = smin(d, sdSphere(add3(p3, obj[0]), obj[1]), 0.01);
//d = Math.min(d, sdSphere(add3(p3, obj[0]), obj[1]));
//d = Math.min(d, sdSphere(add3(warp3(p3), obj[0]), obj[1]));
}

d -= displacement(warp3(p3)) * 0.05;

return d;
}

function RayMarch(ro3, rd3)
{
var dO = 0;

for (var i = 0; i < MAX_STEPS; i++)
{
var p3 = add3(ro3, mul3(rd3, dO));
var dS = map(p3);
dO += dS;
if (dO > MAX_DIST) return MAX_DIST;
if (Math.abs(dS)<SURF_DIST) break;
}

return dO;
}

var pass = -1;

function cache_key(p2) { return p2[0] * 10000 + p2[1] * 10; }

var cache = {};
var cache_tests = 0;
var cache_misses = 0;

//function floor2(x) { return x; }
function floor2(x) { const precision = 0.5; return Math.round(x / precision) * precision; }

function floor_p2(p2)
{
return [ floor2(p2[0]), floor2(p2[1]) ];
}

// p: 2D point in -100 to 100 range
function zFunc(p2)
{
p2 = floor_p2(p2);

// Ray origin
var ro3 = [ cam_dist * Math.cos(cam_angle), -0.1, cam_dist * Math.sin(cam_angle) ];

// Look at
var l3 = [ 0, 0, 0 ];

// Convert to -1 to 1
var uv2 = [ p2[0] / 100, p2[1] / 100 ];

// Ray direction
var rd3 = GetRayDir(uv2, ro3, l3, 1.);

var key_p2 = cache_key(p2);

var dist = MAX_DIST;

cache_tests++;
if (key_p2 in cache)
{
dist = cache[key_p2];
}
else
{
cache_misses++;
// Get distance to intersection
dist = RayMarch(ro3, rd3);
cache[key_p2] = dist;
}

if (dist < MAX_DIST)
{
// Get intersection point
var p3 = add3(ro3, mul3(rd3, dist));
dist = (p3[pass]-range[0]) / (range[1]-range[0]) * density;
}

return dist;
}

//function floor(x) { const precision = 0.25; return Math.round(x / precision) * precision; }
function floor(x) { return x; }

function line_key(line)
{
return Math.min(line[0][0], line[1][0]) * 1000000000 + Math.min(line[0][1], line[1][1]) * 1000000 + Math.max(line[0][0], line[1][0]) * 1000 + Math.max(line[0][1], line[1][1]);
}

var line_cache = {};
function is_unique(line)
{
const key = line_key(line);
if (key in line_cache) return false
line_cache[key] = 1;
return true;
}

function floor_line(line)
{
return [ [ floor(line[0][0]), floor(line[0][1]) ], [ floor(line[1][0]), floor(line[1][1]) ] ];
}

var unique_line_count = 0;
var total_line_count = 0;
var start_time = performance.now();

function walk(i) {
pass = Math.floor(i / (density+1));
if (pass >= passes)
{
console.log(`Scene has \${scene_objects.length} items`);
const elapsed = ((performance.now() - start_time) / 1000).toFixed(1);
const percent1 = (unique_line_count * 100 / total_line_count).toFixed(1);
const percent2 = (cache_misses * 100 / cache_tests).toFixed(1);
console.log(`Time: \${elapsed} s | Unique lines: \${unique_line_count} of \${total_line_count} (\${percent1}%) | Cache misses: \${cache_misses} of \${cache_tests} (\${percent2}%)`)

return false;
}

const lines = ContourLines(i%density, 1/precision, zFunc);
//const lines = ContourLines(i%density, 1/precision, zFunc);
var last_end = [0, 0];
lines.forEach(line => {
total_line_count++;

// TODO: lines are in the wrong order. Find continous paths.
var line2 = floor_line(line);
if (is_unique(line2))
{
if (last_end[0] == line[1][0] && last_end[1] == line[1][1])
{
turtle.goto(line2[1]);
turtle.goto(line2[0]);
last_end = line[0];
}
else if (last_end[0] == line[0][0] && last_end[1] == line[0][1])
{
turtle.goto(line2[0]);
turtle.goto(line2[1]);
last_end = line[1];
}
else
{
turtle.jump(line2[1]);
turtle.goto(line2[0]);
last_end = line[0];
}

unique_line_count++;
}
});

return true;
}

// Metaball Contour Lines. Created by Reinder Nijhoff 2020 - @reindernijhoff
// https://turtletoy.net/turtle/104c4775c5
function ContourLines(z, step, zFunc) {
const intersectSegmentZ = (z, v1, v2) => {
if (v1[2] === v2[2]) return false;
const t = (z - v1[2]) / (v2[2] - v1[2]);
if (t <= 0 || t > 1) return false;
return [v1[0]+(v2[0]-v1[0])*t, v1[1]+(v2[1]-v1[1])*t];
}
const intersectTriangleZ = (z, p1, p2, p3) => {
const p = [];
const v1 = intersectSegmentZ(z, p1, p2);
const v2 = intersectSegmentZ(z, p2, p3);
const v3 = intersectSegmentZ(z, p3, p1);
if (v1 && v2) p.push([v1, v2]);
if (v1 && v3) p.push([v1, v3]);
if (v2 && v3) p.push([v2, v3]);
return p;
}
const result = [];
for (let x = -100; x <= 100; x += step) {
for (let y = -100; y <= 100; y += step) {
const corners = [[x, y], [x+step, y], [x+step, y+step], [x, y+step]];
corners.forEach( c => c[2] = zFunc(c) );
const c3 = [x+step/2, y+step/2, zFunc([x+step/2, y+step/2])];
for (let i=0; i<4; i++) {
result.push(...intersectTriangleZ(z, corners[i], corners[(i+1) & 3], c3));
}
}
}
return result;
}

```