// Hexagon Truchet. Created by Reinder Nijhoff 2019 - @reindernijhoff
//
// https://turtletoy.net/turtle/e5df5b10e0
//
const turtle = new Turtle();
const scale = 5;
const lineWidth = .4; // min=0.1, max=0.4, step=0.01
const showHexagons = false;
const h0 = Math.sqrt(3)/2;
const h1 = 1/2;
function drawHexagon(t, x, y) {
if (Math.abs(scale*x) > 100+scale ||
Math.abs(scale*y) > 100+scale) return; // early discard
const a = ((Math.random()*3)|0)*Math.PI/3; // random angle
const poly = new Polygons();
// 2 transform functions: translate-scale (for background hatching), and rotate-translate-scale
const ts = p => [scale*(p[0]+x),scale*(p[1]+y)];
const rts = p => ts([Math.cos(a)*p[0]+Math.sin(a)*p[1], Math.cos(a)*p[1]-Math.sin(a)*p[0]]);
// vec2 helper functions
const add = (a, b) => [a[0]+b[0], a[1]+b[1]];
const sub = (a, b) => [a[0]-b[0], a[1]-b[1]];
const scl = (a, b) => [a[0]*b, a[1]*b];
// 2 methods to create lines in a tile
const line = (s, e, d) => { // line from s to e and width d
const p = poly.create();
p.addPoints(rts(add(s,d)), rts(add(e,d)), rts(sub(e,d)), rts(sub(s,d)));
p.addSegments(rts(add(s,d)), rts(add(e,d)), rts(sub(e,d)), rts(sub(s,d)));
return p;
}
const circle = (c, r, s, e) => { // circle around c, from angle s to e with radius r
const p = poly.create(), c0 =[], c1 = [], f=10;
for (let i=0; i<=f; i++) {
c0.push(rts(add(c, [Math.cos(s+(e-s)*i/f)*(r+lineWidth), Math.sin(s+(e-s)*i/f)*(r+lineWidth)])));
c1.push(rts(add(c, [Math.cos(e-(e-s)*i/f)*(r-lineWidth), Math.sin(e-(e-s)*i/f)*(r-lineWidth)])));
}
p.addPoints(...c0,...c1);
for (let i=0; i<f; i++) p.addSegments(c0[i], c0[i+1]);
for (let i=0; i<f; i++) p.addSegments(c1[i], c1[i+1]);
return p;
}
// six corners of hexagon
const c = [];
for (let i=0; i<6; i++) {
c.push([Math.cos(i*Math.PI/3), Math.sin(i*Math.PI/3)]);
}
// generate lines in tile
const l = [], tileType = (Math.random()*5)|0; // 5 different tile types
switch (tileType) {
case 0: l.push(line([0,h0], [0,-h0], [lineWidth, 0])); // 3 straight lines
l.push(line([1-h1/2,h0/2], [-1+h1/2,-h0/2], scl([Math.cos(Math.PI/3), -Math.sin(Math.PI/3)], lineWidth)));
l.push(line([1-h1/2,-h0/2], [-1+h1/2,h0/2], scl([Math.cos(-Math.PI/3), -Math.sin(-Math.PI/3)], lineWidth)));
break;
case 1: l.push(line([0,h0], [0,-h0], [lineWidth, 0])); // straight line + 2 arcs #1
l.push(circle(c[0], h1, Math.PI-Math.PI/3, Math.PI+Math.PI/3));
l.push(circle(c[3], h1, -Math.PI/3, +Math.PI/3));
break;
case 2: l.push(line([0,h0], [0,-h0], [lineWidth, 0])); // straight line + 2 arcs #2
l.push(circle([0,2*h0], 1+h1, -Math.PI/2-Math.PI/6, -Math.PI/2+Math.PI/6));
l.push(circle([0,-2*h0], 1+h1, Math.PI/2-Math.PI/6, Math.PI/2+Math.PI/6));
break;
case 3: l.push(circle(c[0], h1, Math.PI-Math.PI/3, Math.PI+Math.PI/3)); // 3 arcs #1
l.push(circle(c[2], h1, -2*Math.PI/3, 0));
l.push(circle(c[4], h1, 0, 2*Math.PI/3));
break;
default: l.push(circle([0,2*h0], 1+h1, -Math.PI/2-Math.PI/6, -Math.PI/2+Math.PI/6)); // 3 arcs #2
l.push(circle([-1-h1, h0], 1+h1, 0, -Math.PI/3));
l.push(circle(c[5], h1, Math.PI/3, Math.PI));
break;
}
// shuffle lines and draw
l.sort((a,b) => Math.random()-.5);
l.map(p => poly.draw(t, p));
// background
const p0 = poly.create();
p0.addPoints(...c.map(p => ts(p)));
if (showHexagons) p0.addOutline();
if (lineWidth < 0.35) p0.addHatching(Math.PI/4, 1);
poly.draw(t, p0);
}
function walk(i) {
const s = (100/scale|0)+10;
const y = Math.floor(i/(s*2))-s;
const x = (i % (s*2)) - s;
drawHexagon(turtle, x*3 + ((y % 2 == 0)?1.5:0), y*h0);
return i < s*s*4;
}
////////////////////////////////////////////////////////////////
// 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);
}
};
}
