// Forked from "Stars" by reinder
// https://turtletoy.net/turtle/a5befa1f8d
// Transforms. Created by Reinder Nijhoff 2019 - @reindernijhoff
// The MIT License
//
// I have cleaned up the code of my 'polygon clipping algorithm', as used in a lot
// of my turtles. The algorithm is pretty naive and far from perfect, but it will
// work most of the time :)
//
// You can use this utility to draw polygons. The lines of a polygon (this can be
// the outline, but you're free to add extra segments of hatching to the polygon), will
// be clipped with all polygons that are already drawn.
//
// https://turtletoy.net/turtle/a5befa1f8d
//
const turtle = new Turtle();
const polygons = new Polygons();
const total = 250;
function walk(i) {
drawThing(turtle, i, total);
return i < total - 1;
}
const hatchAngle = Math.PI*2*Math.random();
const sizes = [1.0, 0.33, 0.45, 0.66];
function drawThing(turtle,ii,total) {
const p1 = polygons.create(), p2 = polygons.create();
let x = 200*Math.random()-100, y = 200*Math.random()-100,
a = Math.random() * Math.PI/2, b = 2+Math.random()*5|0, c = 1+Math.random()*3|0, s = 10 + 10 * Math.random();
if (ii == 0) {
x = 0, y=0, s=35;
const cp = []; // create clip points that define the shape of the polygon
a = Math.PI/2;
var heart = [0.7, 0.6, 0.6, 0.6, 0.7, 0.8, 0.9, 0.9, 0.62];
for (let i=0; i<heart.length*2; i++) {
const l = s * heart[(i > 8) ? 16-i : i];
cp.push( [x+Math.cos(a+i/8*Math.PI)*l, y+Math.sin(a+i/8*Math.PI)*l]);
}
p1.addPoints(...cp);
p2.addPoints(...cp.map(p => [p[0]+2, p[1]+6])); // shadow offset
const hatchiness = 2 + Math.random() * 7.5;
if (Math.random() > 0.5) p1.addHatching(hatchAngle, hatchiness);
if (Math.random() > 0.5) p1.addHatching(hatchAngle + Math.PI/2, hatchiness);
p1.addOutline(); // polygon 1, star with outline
p2.addHatching(-Math.PI*.25, 0.75); // polygon 2, star shadow
polygons.draw(turtle, p1, true);
polygons.draw(turtle, p2, false);
} else if (Math.sqrt(x * x + y * y) > 65) {
const sizes = [1, .45, .66];
const cp = []; // create clip points that define the shape of the polygon
var sides = Math.random() * 6 | 0 + 4;
for (let i=0; i<sides*2; i++) {
//const l = s * sizes[Math.random()* sizes.length | 0];
const l = s * (i % 4 ? 1 : (i % 2 ? .33 : .66) );
cp.push( [x+Math.cos(a+i/sides*Math.PI)*l, y+Math.sin(a+i/sides*Math.PI)*l]);
}
p1.addPoints(...cp);
p2.addPoints(...cp.map(p => [p[0]+3, p[1]+3])); // shadow offset
p1.addOutline(); // polygon 1, star with outline
p2.addHatching(hatchAngle, 1); // polygon 2, star shadow
if (ii > total*2/3) p2.addHatching(hatchAngle + Math.PI/2, 1); // polygon 2, star shadow
if (ii < total/2) {
polygons.draw(turtle, p1, true);
polygons.draw(turtle, p2, false);
} else {
polygons.draw(turtle, p2, false);
polygons.draw(turtle, p1, true);
}
}
}
////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////
function Polygons() {
const polygonList = [];
const Polygon = class {
constructor() {
this.cp = []; // clip path: array of [x,y] pairs
this.dp = []; // 2d lines [x0,y0],[x1,y1] to draw
this.aabb = []; // AABB bounding box
}
addPoints(...points) {
// add point to clip path and update bounding box
let xmin = 1e5, xmax = -1e5, ymin = 1e5, ymax = -1e5;
(this.cp = [...this.cp, ...points]).forEach( p => {
xmin = Math.min(xmin, p[0]), xmax = Math.max(xmax, p[0]);
ymin = Math.min(ymin, p[1]), ymax = Math.max(ymax, p[1]);
});
this.aabb = [(xmin+xmax)/2, (ymin+ymax)/2, (xmax-xmin)/2, (ymax-ymin)/2];
}
addSegments(...points) {
// add segments (each a pair of points)
points.forEach(p => this.dp.push(p));
}
addOutline() {
for (let i = 0, l = this.cp.length; i < l; i++) {
this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
}
}
draw(t) {
for (let i = 0, l = this.dp.length; i < l; i+=2) {
t.jump(this.dp[i]), t.goto(this.dp[i + 1]);
}
}
addHatching(a, d) {
const tp = new Polygon();
tp.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);
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);
this.dp = [...this.dp, ...tp.dp];
}
inside(p) {
let int = 0; // find number of i ntersection points from p to far away
for (let i = 0, l = this.cp.length; i < l; i++) {
if (this.segment_intersect(p, [0.1, -1000], this.cp[i], this.cp[(i + 1) % l])) {
int++;
}
}
return int & 1; // if even your outside
}
boolean(p, diff = true) {
// bouding box optimization by ge1doot.
if (Math.abs(this.aabb[0] - p.aabb[0]) - (p.aabb[2] + this.aabb[2]) >= 0 &&
Math.abs(this.aabb[1] - p.aabb[1]) - (p.aabb[3] + this.aabb[3]) >= 0) return this.dp.length > 0;
// 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.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];
int.sort( (a,b) => (a[0] - ls0[0]) * cmpx + (a[1] - ls0[1]) * cmpy -
(b[0] - ls0[0]) * cmpx - (b[1] - ls0[1]) * cmpy);
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 >= 0.001) {
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]);
}
}
}
}
}
return (this.dp = ndp).length > 0;
}
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
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 {
list: () => polygonList,
create: () => new Polygon(),
draw: (turtle, p, addToVisList=true) => {
for (let j = 0; j < polygonList.length && p.boolean(polygonList[j]); j++);
p.draw(turtle);
if (addToVisList) polygonList.push(p);
}
};
}
