### Squares and Circles

contextfreeart.org/phpbb/viewtopic.php?f=3&t=116
Squares and Circles by signal ยป Thu Jul 07, 2005 7:46 pm

Created by ge1doot on 2019/1/26
106
0

```// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(0.8);

// Global code will be evaluated once.
const turtle = new Turtle();
turtle.penup();
const polygons = Polygons();
//////////////////////////////////////////////////
//
//        /~\
//       C oo
//       _( ^)
//      /   ~\
Array.prototype.rotate = function(v) {
const rad = Math.PI * v / 180;
return [
cos * this[0] + sin * this[2],
cos * this[1] + sin * this[3],
cos * this[2] - sin * this[0],
cos * this[3] - sin * this[1],
this[4],
this[5]
];
};
Array.prototype.translate = function(x, y = 0) {
return [
this[0],
this[1],
this[2],
this[3],
this[4] + x * this[0] + y * this[2],
this[5] + x * this[1] + y * this[3]
];
};
Array.prototype.scale = function(x = 1, y = x) {
return [this[0] * x, this[1] * x, this[2] * y, this[3] * y, this[4], this[5]];
};
Array.prototype.isTooSmall = function(m) {
const x = this[0] * this[0] + this[1] * this[1];
const y = this[2] * this[2] + this[3] * this[3];
return x < m || y < m;
};
////////////////////////////////////////////////
const contextFree = {
init() {
this.box = [100, 100, -100, -100];
this.shapes = [];
},
push(m) {
if (m[4] - 0.5 * m[0] < this.box[0]) this.box[0] = m[4] - 0.5 * m[0];
else if (m[4] + 0.5 * m[0] > this.box[2]) this.box[2] = m[4] + 0.5 * m[0];
if (m[5] + 0.5 * m[3] < this.box[1]) this.box[1] = m[5] + 0.5 * m[3];
else if (m[5] - 0.5 * m[3] > this.box[3]) this.box[3] = m[5] - 0.5 * m[3];
this.shapes.unshift(m);
},
SQUARE(m, a = 0, s = 0, outline = 1) {
m[6] = 0;
m[7] = a;
m[8] = s;
m[9] = outline;
this.push(m);
},
CIRCLE(m, a = 0, s = 0, outline = 1) {
m[6] = 1;
m[7] = a;
m[8] = s;
m[9] = outline;
this.push(m);
},
transform(x, y, m) {
const m0 = m[0] * this.zoom;
const m1 = m[1] * this.zoom;
const m2 = m[2] * this.zoom;
const m3 = m[3] * this.zoom;
const m4 = m[4] * this.zoom - this.ox;
const m5 = m[5] * this.zoom - this.oy;
return [
m0 * x + m2 * y + m4,
m1 * x + m3 * y + m5
];
},
scale(margin = 0.95) {
this.zoom = Math.min(
margin * 200 / (this.box[2] - this.box[0]),
margin * 200 / (this.box[3] - this.box[1])
);
this.ox = (this.box[0] + this.box[2]) * 0.5 * this.zoom;
this.oy = (this.box[3] + this.box[1]) * 0.5 * this.zoom;
},
draw() {
if (!this.shapes.length) return false;
let p;
const m = this.shapes.pop();
switch (m[6]) {
case 0:
// SQUARE
p = polygons.create();
const p0 = this.transform(-0.5, -0.5, m);
const p1 = this.transform(+0.5, -0.5, m);
const p2 = this.transform(+0.5, +0.5, m);
const p3 = this.transform(-0.5, +0.5, m);
if (m[9] === 1) {
p.addSegments(p0, p1, p1, p2, p2, p3, p3, p0);
}
if (m[8] !== 0) p.addHatching(m[7], m[8]);
polygons.draw(turtle, p);
break;
case 1:
// CIRCLE
p = polygons.create();
for (let a = Math.PI / 36; a <= 2 * Math.PI; a += Math.PI / 36) {
p.addPoints(this.transform(Math.cos(a) * 0.5, -Math.sin(a) * 0.5, m));
}
if (m[8] !== 0) p.addHatching(m[7], m[8]);
polygons.draw(turtle, p);
break;
}
return true;
},
////////////////////////// context Free //////////////////////////
SQUARES(m) {
if (m.isTooSmall(0.005)) return;
const r = Math.random() * 1.5;
switch (true) {
case r <= 0.1:
this.SQUARES(
m
.translate(1, 0)
.rotate(45)
.scale(0.5)
);
this.SQUARESORHALT(m);
break;
case r <= 0.2:
this.SQUARES(
m
.translate(1, 0)
.rotate(-90)
.scale(0.9)
);
this.SQUARESORHALT(m);
break;
case r <= 0.5:
this.SQUARES(
m
.translate(1, 0)
.rotate(90)
.scale(0.5)
);
this.SQUARESORHALT(m);
break;
default:
this.SQUARE(m);
this.SQUARE(m.translate(0, 0.2), -Math.PI / 4, 0.5, 0);
return this.SQUARES(m.translate(0.9));
}
},
SQUARESORHALT(m) {
const r = Math.random() * 1.9;
switch (true) {
case r <= 1:
return this.SQUARES(m);
default:
this.CIRCLE(m.translate(0, 0), 0, 0.1, 0);
this.CIRCLE(m.translate(0, 0.15), -Math.PI / 4, 0.5, 0);
}
}
};
/////////////////////////////////////////////////////////////////////////////
const m = [1, 0, 0, 1, 0, 0];
do {
contextFree.init();
contextFree.SQUARES(m);
} while (contextFree.shapes.length < 500);
contextFree.scale();

// The walk function will be called until it returns false.
function walk(i) {
return contextFree.draw();
}

////////////////////////////////////////////////////////////////
// reinder's occlusion code parts from "Cubic space division #2"
// Optimizations and code clean-up by ge1doot
////////////////////////////////////////////////////////////////

function Polygons() {
const polygonList = [];
const Polygon = class {
constructor() {
this.cp = [];       // clip path: array of [x,y] pairs
this.dp = [];       // 2d line to draw
this.aabb = [];     // AABB bounding box
}
for (let i = 0; i < points.length; i++) this.cp.push(points[i]);
this.aabb = this.AABB();
}
for (let i = 0; i < points.length; i++) this.dp.push(points[i]);
}
for (let i = s, l = this.cp.length; i < l; i++) {
this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
}
}
draw(t) {
if (this.dp.length === 0) return;
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const d0 = this.dp[i];
const d1 = this.dp[i + 1];
t.penup();
t.goto(d0);
t.pendown();
t.goto(d1);
}
}
AABB() {
let xmin = 2000;
let xmax = -2000;
let ymin = 2000;
let ymax = -2000;
for (let i = 0, l = this.cp.length; i < l; i++) {
const x = this.cp[i][0];
const y = this.cp[i][1];
if (x < xmin) xmin = x;
if (x > xmax) xmax = x;
if (y < ymin) ymin = y;
if (y > ymax) ymax = y;
}
// Bounding box: center x, center y, half w, half h
return [
(xmin + xmax) * 0.5,
(ymin + ymax) * 0.5,
(xmax - xmin) * 0.5,
(ymax - ymin) * 0.5
];
}
const tp = new Polygon();
tp.cp.push(
[this.aabb[0] - this.aabb[2], this.aabb[1] - this.aabb[3]],
[this.aabb[0] + this.aabb[2], this.aabb[1] - this.aabb[3]],
[this.aabb[0] + this.aabb[2], this.aabb[1] + this.aabb[3]],
[this.aabb[0] - this.aabb[2], this.aabb[1] + this.aabb[3]]
);
const dx = Math.sin(a) * d, dy = Math.cos(a) * d;
const cx = Math.sin(a) * 200, cy = Math.cos(a) * 200;
for (let i = 0.5; i < 150 / d; i++) {
tp.dp.push([dx * i + cy, dy * i - cx], [dx * i - cy, dy * i + cx]);
tp.dp.push([-dx * i + cy, -dy * i - cx], [-dx * i - cy, -dy * i + cx]);
}
tp.boolean(this, false);
for (let i = 0, l = tp.dp.length; i < l; i++) this.dp.push(tp.dp[i]);
}
inside(p) {
// find number of i ntersection points from p to far away
const p1 = [0.1, -1000];
let int = 0;
for (let i = 0, l = this.cp.length; i < l; i++) {
if (
this.vec2_find_segment_intersect(
p,
p1,
this.cp[i],
this.cp[(i + 1) % l]
) !== false
) {
int++;
}
}
return int & 1;
}
boolean(p, diff = true) {
// polygon diff algorithm (narrow phase)
const ndp = [];
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const ls0 = this.dp[i];
const ls1 = this.dp[i + 1];
// find all intersections with clip path
const int = [];
for (let j = 0, cl = p.cp.length; j < cl; j++) {
const pint = this.vec2_find_segment_intersect(
ls0,
ls1,
p.cp[j],
p.cp[(j + 1) % cl]
);
if (pint !== false) {
int.push(pint);
}
}
if (int.length === 0) {
// 0 intersections, inside or outside?
if (diff === !p.inside(ls0)) {
ndp.push(ls0, ls1);
}
} else {
int.push(ls0, ls1);
// order intersection points on line ls.p1 to ls.p2
const cmpx = ls1[0] - ls0[0];
const cmpy = ls1[1] - ls0[1];
for (let i = 0, len = int.length; i < len; i++) {
let j = i;
const item = int[j];
for (
const db = (item[0] - ls0[0]) * cmpx + (item[1] - ls0[1]) * cmpy;
j > 0 && (int[j - 1][0] - ls0[0]) * cmpx + (int[j - 1][1] - ls0[1]) * cmpy < db;
j--
) int[j] = int[j - 1];
int[j] = item;
}
for (let j = 0; j < int.length - 1; j++) {
if (
(int[j][0] - int[j + 1][0]) ** 2 + (int[j][1] - int[j + 1][1]) ** 2 >= 0.01
) {
if (
diff ===
!p.inside([
(int[j][0] + int[j + 1][0]) / 2,
(int[j][1] + int[j + 1][1]) / 2
])
) {
ndp.push(int[j], int[j + 1]);
}
}
}
}
}
this.dp = ndp;
return this.dp.length > 0;
}
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
vec2_find_segment_intersect(l1p1, l1p2, l2p1, l2p2) {
const d =
(l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) -
(l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]);
if (d === 0) return false;
const n_a =
(l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) -
(l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]);
const n_b =
(l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) -
(l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]);
const ua = n_a / d;
const ub = n_b / d;
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
return [
l1p1[0] + ua * (l1p2[0] - l1p1[0]),
l1p1[1] + ua * (l1p2[1] - l1p1[1])
];
}
return false;
}
};
return {
create() {
return new Polygon();
},
draw(turtle, p) {
let vis = true;
for (let j = 0; j < polygonList.length; j++) {
const p1 = polygonList[j];
// AABB overlapping test - still O(N2) but very fast
if (
Math.abs(p1.aabb[0] - p.aabb[0]) - (p.aabb[2] + p1.aabb[2]) < 0 &&
Math.abs(p1.aabb[1] - p.aabb[1]) - (p.aabb[3] + p1.aabb[3]) < 0
) {
if (p.boolean(p1) === false) {
vis = false;
break;
}
}
}
if (vis) {
p.draw(turtle);
polygonList.push(p);
}
}
};
}```