A path, a goose & a bicycle
A tortoise (see: Transforms) with a 'path transform' is used to draw houses, bicycles, and geese.
#tortoise #path
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// A tortoise, a goose & a bicycle. Created by Reinder Nijhoff 2019
// @reindernijhoff
//
// https://turtletoy.net/turtle/d93671dfa0
//
const pathInput = `M57,61C-72,51 -23,-84 36,-67`; // type=path, Click here to redraw the path
const path = Path(pathInput);
function Translate(x,y) { return p => [p[0]+x, p[1]+y]; }
function Scale(s) { return p => [p[0]*s, p[1]*s]; }
function Circle(r) { return p => { let ry = r - p[1]; a = p[0]/r;
return [ry*Math.cos(a), ry*Math.sin(a)]; } }
function PathTransform(path) {
return p => {
const l = path.length();
if (p[0] > l) return path.p(1);
const x = p[0] / l;
const y = p[1];
const t = path.p(x);
const n = [-t[3], t[2]];
const nl = Math.hypot(...n);
return [t[0] - y * t[3] / nl, t[1] + y * t[2] / nl];
}
}
const scale = 0.5;
const numHouses = 400;
const turtle = new Tortoise();
turtle.addTransform(PathTransform(path));
for (let i=0; i<1000; i++) {
turtle.forward(numHouses*25 / 1000);
turtle.forward(numHouses*25 / 1000);
}
function walk(i) {
if (Math.random() > .67) {
const h = new Tortoise();
h.addTransform(Scale(.3));
h.addTransform(Translate(i * 20 + 10, 0));
h.addTransform(PathTransform(path));
drawHouse(h);
} else if (Math.random() > .5) {
const h = new Tortoise();
h.addTransform(Scale(.18));
h.addTransform(Translate(i * 20 + 10, 0));
h.addTransform(PathTransform(path));
drawBicycle(h, 0, 0)
} else {
const h = new Tortoise();
h.addTransform(Scale(.15));
h.addTransform(Translate(i * 20 + 10, -3.5));
h.addTransform(PathTransform(path));
goose(h);
}
return i < numHouses - 1;
}
// House
function drawHouse(t) {
square(t, [-10,-20], [30,0]);
square(t, [-5,-15], [2,-8]);
square(t, [7,0], [14,-15]);
square(t, [19,-15], [25,-8]);
square(t, [-25,-15], [-15,-8]);
for (let i=-20; i<=20; i+=4) {
t.jmp(i,-30); t.goto(i+10,-20);
}
t.jmp(-20,-30); t.goto(20,-30);
t.jmp(-20,-30); t.goto(-30,-20);
t.jmp(-30,-20); t.goto(-30,0);
t.jmp(-30,0); t.goto(-10,0);
}
function square(t, lt, rb) {
t.jmp(lt); t.goto(lt[0], rb[1]); t.goto(rb), t.goto(rb[0], lt[1]); t.goto(lt);
}
function drawBicycle(t, x, y) {
t = t.addTransform(Translate(x, y));
t.jmp(-15,-20); t.circle(10);
t.jmp( 15,-20); t.circle(10);
t.jmp(-15, -10);
t.goto(0, -10); t.goto(10, -25);
t.goto(-5, -25); t.goto(-15, -10);
t.jmp( 0, -10); t.goto(-6, -28); t.goto(-8, -28); t.goto(-2, -28);
t.jmp( 15, -10); t.goto( 9, -28); t.goto( 14, -28); t.circle(2, 180);
}
////////////////////////////////////////////////////////////////
// Path utility code. Created by Reinder Nijhoff 2023
// Parses a single SVG path (only M, C and L statements are
// supported). The p-method will return
// [...position, ...derivative] for a normalized point t.
//
// https://turtletoy.net/turtle/46adb0ad70
////////////////////////////////////////////////////////////////
function Path(svg) {
class MoveTo {
constructor(p) { this.p0 = p; }
p(t, s) { return [...this.p0, 1, 0]; }
length() { return 0; }
}
class LineTo {
constructor(p0, p1) { this.p0 = p0, this.p1 = p1; }
p(t, s = 1) {
const nt = 1 - t, p0 = this.p0, p1 = this.p1;
return [
nt*p0[0] + t*p1[0],
nt*p0[1] + t*p1[1],
(p1[0] - p0[0]) * s,
(p1[1] - p0[1]) * s,
];
}
length() {
const p0 = this.p0, p1 = this.p1;
return Math.hypot(p0[0]-p1[0], p0[1]-p1[1]);
}
}
class BezierTo {
constructor(p0, c0, c1, p1) { this.p0 = p0, this.c0 = c0, this.c1 = c1, this.p1 = p1; }
p(t, s = 1) {
const nt = 1 - t, p0 = this.p0, c0 = this.c0, c1 = this.c1, p1 = this.p1;
return [
nt*nt*nt*p0[0] + 3*t*nt*nt*c0[0] + 3*t*t*nt*c1[0] + t*t*t*p1[0],
nt*nt*nt*p0[1] + 3*t*nt*nt*c0[1] + 3*t*t*nt*c1[1] + t*t*t*p1[1],
(3*nt*nt*(c0[0]-p0[0]) + 6*t*nt*(c1[0]-c0[0]) + 3*t*t*(p1[0]-c1[0])) * s,
(3*nt*nt*(c0[1]-p0[1]) + 6*t*nt*(c1[1]-c0[1]) + 3*t*t*(p1[1]-c1[1])) * s,
];
}
length() {
return this._length || (
this._length = Array.from({length:25}, (x, i) => this.p(i/25)).reduce(
(a,c,i,v) => i > 0 ? a + Math.hypot(c[0]-v[i-1][0], c[1]-v[i-1][1]) : a, 0));
}
}
class Path {
constructor(svg) {
this.segments = [];
this.parsePath(svg);
}
parsePath(svg) {
const t = svg.match(/([0-9.-]+|[MLC])/g);
for (let s, i=0; i<t.length;) {
switch (t[i++]) {
case 'M': this.add(new MoveTo(s=[t[i++],t[i++]]));
break;
case 'L': this.add(new LineTo(s, s=[t[i++],t[i++]]));
break;
case 'C': this.add(new BezierTo(s, [t[i++],t[i++]], [t[i++],t[i++]], s=[t[i++],t[i++]]));
break;
default: i++;
}
}
}
add(segment) {
this.segments.push(segment);
this._length = 0;
}
length() {
return this._length || (this._length = this.segments.reduce((a,c) => a + c.length(), 0));
}
p(t) {
t = Math.max(Math.min(t, 1), 0) * this.length();
for (let l=0, i=0, sl=0; i<this.segments.length; i++, l+=sl) {
sl = this.segments[i].length();
if (t > l && t <= l + sl) {
return this.segments[i].p((t-l)/sl, sl/this.length());
}
}
return this.segments[Math.min(1, this.segments.length-1)].p(0);
}
}
return new Path(svg);
}
////////////////////////////////////////////////////////////////
// Tortoise utility code. Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/102cbd7c4d
////////////////////////////////////////////////////////////////
function Tortoise(x, y) {
class Tortoise extends Turtle {
constructor(x, y) {
super(x, y);
this.ps = Array.isArray(x) ? [...x] : [x || 0, y || 0];
this.transforms = [];
}
addTransform(t) {
this.transforms.push(t);
this.jump(this.ps);
return this;
}
applyTransforms(p) {
if (!this.transforms) return p;
let pt = [...p];
this.transforms.map(t => { pt = t(pt); });
return pt;
}
goto(x, y, rec = 0) {
const p = Array.isArray(x) ? [...x] : [x, y];
if (rec > 5) return p;
const pt = this.applyTransforms(p);
if (this.isdown() && (this.pt[0]-pt[0])**2 + (this.pt[1]-pt[1])**2 > 8) {
this.goto((this.ps[0]+p[0])/2, (this.ps[1]+p[1])/2, rec+1);
this.goto(p[0], p[1], rec+1);
} else {
super.goto(pt);
this.ps = p;
this.pt = pt;
}
}
position() { return this.ps; }
}
return new Tortoise(x,y);
}
// Goose by imakerobots: https://turtletoy.net/turtle/a6b25da0df
//
const a=[-128.964, -86.085,
-129.279, -87.079,
-129.776, -88.158,
-130.277, -89.07,
-130.848, -90.015,
-131.467, -90.985,
-132.115, -91.968,
-132.769, -92.957];
const b = [
-128.964, -86.085,
-128.823, -85.093,
-128.771, -83.98,
-128.776, -82.857,
-128.815, -81.799,
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