A first experiment to draw a procedural city of cubic building blocks. The city will be different each reload / re-compile. Try out different options by changing the settings at the top of the code.
In a next turtle, I will clean up and optimize the code and add more variety to the buildings.
#city #polygons #3D
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// Forked from "Cubic cityscape #1" by reinder
// https://turtletoy.net/turtle/789cce3829
// Cubic cityscape #1. Created by Reinder Nijhoff 2018
// @reindernijhoff
//
// https://turtletoy.net/turtle/789cce3829
//
// Try different settings here:
const useOrthoGraphicPerspective = Math.random() > .5;
const towerness = .25; // [0, 1)
const topDownView = Math.random() > .5;
const addHatching = Math.random() > .5;
// A lot of ugly code:
const gridSize = 10; //min=1 max=50 step=1
const projectionMargin = 2; //min=0 max=10 step=.1
const segmentCapture = .16; // min=.01 max=1 step=.01
const captureWidth = 200; //min=10 max=200 step=1
// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);
const GRID = { TOP: 1, RIGHT: 2, BOTTOM: 4, LEFT: 8 };
// Global code will be evaluated once.
turtlelib_init();
const turtle = new ObservableTurtle();
const sls = FlyEyeFactory(
turtle,
gridSize,// gridSize,
[projectionMargin-100, projectionMargin-100], //gridTopLeft,
[100-projectionMargin, 100-projectionMargin], //gridBottomRight,
projectionMargin, //gridMargin,
[-captureWidth/2, -captureWidth/2], //sampleTopLeft,
[captureWidth/2, captureWidth/2], //sampleBottomRight,
segmentCapture//sampleTileSizeFraction
);
let viewProjectionMatrix;
let polygonList = [];
const lineSegmentsDrawn = []; // keep track of all line segments. Don't draw duplicates
const width = 30;
const depth = 70;
const camPos = [12,topDownView?13.5:-10.5,-2.3];
const camLookat = [19,topDownView?9.5:-6,-10];
function walk(i) {
if (i == 0) {
setupCamera();
}
for (let j=0; j<width; j++) {
const x = (width - j + (i+1)/2|0) - (width-20);
const z = -(j + i/2|0) + (width-20);
const y = (x-z-40); // 2
drawHome(turtle, [x,y,z], true);
}
return i < depth;
}
function createWall() {
return[createSquare([0,0,0], [1,1,0])]; // wall
}
function createWallDecoration(floorLevel) {
const p = [];
for (let i=0; i<2; i++) {
const x = .2+i*.4;
if (Math.random() > .5) {
p.push(createSquare([x,0.3,0], [x+.2,.7,0])); // window
} else if (floorLevel && Math.random() > .7) {
p.push(createSquare([x,0,0], [x+.2,.7,0])); // door
}
}
return p;
}
function createRoof() {
const p = [];
let flat = false;
if (Math.random() > .5) {
p.push(createSquare([0,1,0], [1,1,-1])); // roof
flat = true;
} else {
p.push(createSquare([0,1,0], [1,1.5,-.5])); // roof
p.push(createSquare([0,1,-1], [1,1.5,-.5]).reverse()); // roof
p.push([[0,1,-1],[0,1.5,-.5],[0,1,0]]);
p.push([[1,1,0],[1,1.5,-.5],[1,1,-1]]);
if (Math.random() > .5) {
return {flatRoof: false, flipped: true, polygons: flipxz(p)};
}
}
return {flatRoof: flat, flipped: false, polygons: p};
}
function drawHome(turtle, loc, floorLevel) {
let p = [];
const occluders = [];
let roof = false;
p = p.concat(center(createWall(), loc));
p = p.concat(center(flipxz(createWall()), loc));
p = p.concat(center(createWallDecoration(floorLevel), loc));
p = p.concat(center(flipxz(createWallDecoration(floorLevel)), loc));
if (Math.random() > 1-towerness) { // extra level
drawHome(turtle, add3(loc,[0,1,0]), false);
} else {
roof = createRoof();
p = p.concat(center(roof.polygons, loc));
}
for (let i=0; i<p.length; i++) {
const polygon = new Polygon();
const vl = p[i];
const vd = useOrthoGraphicPerspective ?
sub3(camLookat, camPos) : sub3(scale3(add3(vl[0],vl[2]),.5), camPos);
let normal = cross3(sub3(vl[1],vl[0]),sub3(vl[2],vl[0]));
if (dot3(normal,vd) < 0 ) {
continue;
}
for (let j=0; j<vl.length; j++) {
const v = transform4(vl[j], viewProjectionMatrix);
if (useOrthoGraphicPerspective) {
polygon.cp.push([(v[0]*2.5), -(v[1]*2.5)]);
} else {
polygon.cp.push([(v[0]/v[3]*50), -(v[1]/v[3]*50)]);
}
}
let vis = false;
for (let j=0; j<polygon.cp.length; j++) {
if (Math.abs(polygon.cp[j][0]) < 100 && Math.abs(polygon.cp[j][1]) < 100) {
vis = true;
}
}
if (!vis) {
continue;
}
if (i<2) { // first two are walls
polygon.dp.push(new LineSegment(polygon.cp[0], polygon.cp[1]));
if (roof && !topDownView) {
if (roof.flatRoof || (roof.flipped && i == 1) || (!roof.flipped && i == 0)) {
polygon.dp.push(new LineSegment(polygon.cp[1], polygon.cp[2]));
}
}
polygon.dp.push(new LineSegment(polygon.cp[2], polygon.cp[3]));
} else if (polygon.cp.length === 3) { // roof
polygon.dp.push(new LineSegment(polygon.cp[0], polygon.cp[1]));
polygon.dp.push(new LineSegment(polygon.cp[1], polygon.cp[2]));
} else {
polygon.addOutline();
}
if (addHatching) {
normal = normalize3(normal);
if (normal[2] < 0) {
polygon.addHatching(.85, .75);
}
}
const occluder = drawPolygon(turtle, polygon);
if (i<2) { // first two are walls
occluders.push(polygon);
} else if (occluder) {
occluders.push(occluder);
}
}
polygonList = polygonList.concat(occluders);
}
function drawPolygon(turtle, p) {
for (let j=0; j<polygonList.length; j++) {
if(!p.boolean(polygonList[j])) {
return;
}
}
p.draw(turtle);
return p;
}
function setupCamera() {
viewMatrix = lookAt4m(camPos, camLookat, [0,1,0]);
projectionMatrix = perspective4m(0.4, 1);
viewProjectionMatrix = multiply4m(projectionMatrix, viewMatrix);
}
// helper functions
function flipxz(p) {
for (let i=0; i<p.length; i++) {
const vl = p[i];
for (let j=0; j<vl.length; j++) {
p[i][j] = [-vl[j][2],vl[j][1],vl[j][0]-1];
}
}
return p;
}
function center(p, loc) {
const ret = [];
for (let i=0; i<p.length; i++) {
const vl = p[i], v = [];
for (let j=0; j<vl.length; j++) {
v.push(add3(vl[j], loc));
}
ret.push(v);
}
return ret;
}
function createSquare(lb, rt) {
return [lb,[lb[0],rt[1],rt[2]],rt,[rt[0],lb[1],lb[2]]];
}
// polygon functions
class LineSegment {
constructor(p1, p2) {
this.p1 = p1;
this.p2 = p2;
}
unique() {
for (let i=0, l=lineSegmentsDrawn.length; i<l; i++) {
const ls = lineSegmentsDrawn[i];
if ( (equal2(this.p1, ls.p1) && equal2(this.p2, ls.p2)) ||
(equal2(this.p1, ls.p2) && equal2(this.p2, ls.p1)) ){
return false;
}
}
lineSegmentsDrawn.push(this);
return true;
}
}
class Polygon {
constructor() {
this.cp = []; // clip path: array of [x,y] pairs
this.dp = []; // 2d line to draw: array of linesegments
}
addOutline(s=0) {
for (let i=s, l=this.cp.length; i<l; i++) {
this.dp.push(new LineSegment(this.cp[i], this.cp[(i+1)%l]));
}
}
createPoly(x,y,c,r,a) {
this.cp = [];
for (let i=0; i<c; i++) {
this.cp.push( [x + Math.sin(i*Math.PI*2/c+a) * r, y + Math.cos(i*Math.PI*2/c+a) * r] );
}
}
addHatching(a,d) {
// todo, create a tight bounding polygon, for now fill screen
const tp = new Polygon();
tp.createPoly(0,0,4,200,Math.PI*.5);
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 = .5; i<150/d; i++) {
tp.dp.push(new LineSegment([dx*i+cy,dy*i-cx], [dx*i-cy,dy*i+cx]));
tp.dp.push(new LineSegment([-dx*i+cy,-dy*i-cx], [-dx*i-cy,-dy*i+cx]));
}
tp.boolean(this, false);
this.dp = this.dp.concat(tp.dp);
}
draw(t) {
if (this.dp.length ==0) {
return;
}
for (let i=0, l=this.dp.length; i<l; i++) {
const d = this.dp[i];
if (d.unique()) {
if (!equal2(d.p1, t.pos())) {
t.penup();
t.goto(d.p1);
t.pendown();
}
t.goto(d.p2);
}
}
}
inside(p) {
// find number of intersections from p to far away - if even you're outside
const p1 = [0, -1000];
let int = 0;
for (let i=0, l=this.cp.length; i<l; i++) {
if (segment_intersect2(p, p1, this.cp[i], this.cp[(i+1)%l])) {
int ++;
}
}
return int & 1;
}
boolean(p, diff = true) {
// very naive polygon diff algorithm - made this up myself
const ndp = [];
for (let i=0, l=this.dp.length; i<l; i++) {
const ls = this.dp[i];
// find all intersections with clip path
const int = [];
for (let j=0, cl=p.cp.length; j<cl; j++) {
const pint = segment_intersect2(ls.p1,ls.p2,p.cp[j],p.cp[(j+1)%cl]);
if (pint) {
int.push(pint);
}
}
if (int.length == 0) { // 0 intersections, inside or outside?
if (diff != p.inside(ls.p1)) {
ndp.push(ls);
}
} else {
int.push(ls.p1); int.push(ls.p2);
// order intersection points on line ls.p1 to ls.p2
const cmp = sub2(ls.p2,ls.p1);
int.sort((a,b) => dot2(sub2(a,ls.p1),cmp)-dot2(sub2(b,ls.p1),cmp));
for (let j=0; j<int.length-1; j++) {
if (!equal2(int[j], int[j+1]) &&
diff != p.inside(scale2(add2(int[j],int[j+1]),.5))) {
ndp.push(new LineSegment(int[j], int[j+1]));
}
}
}
}
this.dp = ndp;
return this.dp.length > 0;
}
}
// vec2 functions
const equal2=(a,b)=>0.001>dist_sqr2(a,b);
const scale2=(a,b)=>[a[0]*b,a[1]*b];
const add2=(a,b)=>[a[0]+b[0],a[1]+b[1]];
const sub2=(a,b)=>[a[0]-b[0],a[1]-b[1]];
const dot2=(a,b)=>a[0]*b[0]+a[1]*b[1];
const dist_sqr2=(a,b)=>(a[0]-b[0])*(a[0]-b[0])+(a[1]-b[1])*(a[1]-b[1]);
const segment_intersect2=(a,b,d,c)=>{
const e=(c[1]-d[1])*(b[0]-a[0])-(c[0]-d[0])*(b[1]-a[1]);
if(0==e)return false;
c=((c[0]-d[0])*(a[1]-d[1])-(c[1]-d[1])*(a[0]-d[0]))/e;
d=((b[0]-a[0])*(a[1]-d[1])-(b[1]-a[1])*(a[0]-d[0]))/e;
return 0<=c&&1>=c&&0<=d&&1>=d?[a[0]+c*(b[0]-a[0]),a[1]+c*(b[1]-a[1])]:false;
}
// vec3 functions
const scale3=(a,b)=>[a[0]*b,a[1]*b,a[2]*b];
const len3=(a)=>Math.sqrt(dot3(a,a));
const normalize3=(a)=>scale3(a,1/len3(a));
const add3=(a,b)=>[a[0]+b[0],a[1]+b[1],a[2]+b[2]];
const sub3=(a,b)=>[a[0]-b[0],a[1]-b[1],a[2]-b[2]];
const dot3=(a,b)=>a[0]*b[0]+a[1]*b[1]+a[2]*b[2];
const cross3=(a,b)=>[a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]];
// vec4 functions
const transform4=(a,b)=>{
const d=new Float32Array(4);
for(let c=0;4>c;c++)d[c]=b[c]*a[0]+b[c+4]*a[1]+b[c+8]*a[2]+b[c+12];
return d;
}
// mat4 functions
const lookAt4m=(a,b,d)=>{ // pos, lookAt, up
const c=new Float32Array(16);
b=normalize3(sub3(a,b));
d=normalize3(cross3(d,b));
const e=normalize3(cross3(b,d));
c[0]=d[0];c[1]=e[0];c[2]=b[0];c[3]=0;
c[4]=d[1];c[5]=e[1];c[6]=b[1];c[7]=0;
c[8]=d[2];c[9]=e[2];c[10]=b[2];c[11]=0;
c[12]=-(d[0]*a[0]+d[1]*a[1]+d[2]*a[2]);
c[13]=-(e[0]*a[0]+e[1]*a[1]+e[2]*a[2]);
c[14]=-(b[0]*a[0]+b[1]*a[1]+b[2]*a[2]);
c[15]=1;
return c;
}
const multiply4m=(a,b)=>{
const d=new Float32Array(16);
for(let c=0;16>c;c+=4)
for(let e=0;4>e;e++)
d[c+e]=b[c+0]*a[0+e]+b[c+1]*a[4+e]+b[c+2]*a[8+e]+b[c+3]*a[12+e];
return d;
}
const perspective4m=(a,b)=>{ // fovy, aspect
const c=(new Float32Array(16)).fill(0,0);
c[5]=1/Math.tan(a/2);
c[0]=c[5]/b;
c[10]=c[11]=-1;
return c;
}
function FlyEyeFactory(turtle, gridSize, gridTopLeft, gridBottomRight, gridMargin, sampleTopLeft, sampleBottomRight, sampleTileSizeFraction) {
const sampleWidth = sampleBottomRight[0] - sampleTopLeft[0];
const sampleHeight = sampleBottomRight[1] - sampleTopLeft[1];
const tileWidth = sampleWidth * sampleTileSizeFraction;
const tileHeight = sampleHeight * sampleTileSizeFraction;
const sampleCenterTopLeft = V.add(sampleTopLeft, [tileWidth/2, tileHeight/2]);
const columnIncrement = gridSize == 1? 0: (sampleWidth - tileWidth) / (gridSize - 1);
const rowIncrement = gridSize == 1? 0: (sampleHeight - tileHeight) / (gridSize - 1);
const gridWidth = gridBottomRight[0] - gridTopLeft[0];
const gridHeight = gridBottomRight[1] - gridTopLeft[1];
const gridTileWidth = (gridWidth - gridMargin * Math.max(1, gridSize - 1)) / gridSize;
const gridTileHeight = (gridHeight - gridMargin * Math.max(1, gridSize - 1)) / gridSize;
const flyEyeSegments = [];
for(let c = 0; c < gridSize; c++) {
for(let r = 0; r < gridSize; r++) {
flyEyeSegments.push(
new SquareLens(
turtle, [
V.add(sampleTopLeft, [columnIncrement * c, rowIncrement * r]),
V.add(
V.add(sampleTopLeft, [columnIncrement * c, rowIncrement * r]),
[tileWidth, tileHeight]
)
], [
V.add(gridTopLeft, [c * (gridTileWidth + gridMargin), r * (gridTileHeight + gridMargin)]),
V.add(
V.add(gridTopLeft, [c * (gridTileWidth + gridMargin), r * (gridTileHeight + gridMargin)]),
[gridTileWidth, gridTileHeight]
)
],
(c == 0? GRID.LEFT: 0) | (r == 0? GRID.TOP: 0) |
(c == gridSize - 1? GRID.RIGHT: 0) | (r == gridSize - 1? GRID.BOTTOM: 0)
)
);
}
}
return flyEyeSegments;
}
function ObservableTurtle(x, y) {
class ObservableTurtle extends Turtle {
constructor(x, y) {
super(x, y);
this.observers = [];
}
goto(x, y) {
const isDown = this.isdown();
const from = this.pos();
this.up();
super.goto(x, y);
if(isDown) {
this.notifyObservers(from, this.pos());
this.down();
}
}
registerObserver(o) {
return this.observers.push(o) - 1;
}
notifyObservers(...data) {
this.observers.forEach(o => o.update(...data))
}
}
return new ObservableTurtle(x, y);
}
function SquareLens(turtleToObserve, lookAt, projectTo, edge = 0, projector = null) {
class SquareLens {
constructor(turtleToObserve, lookAt, projectTo, bottomOrRight, projector) {
this.turtleToObserve = turtleToObserve;
this.turtleToObserve.registerObserver(this);
this.edge = edge;
this.projector = projector == null? new Turtle(): projector;
this.lookAt = lookAt;
this.projectTo = projectTo;
this.midLookAt = V.add(this.lookAt[0], V.scale(V.sub(...this.lookAt.map(l => l).reverse()), .5));
this.midProjectTo = V.add(this.projectTo[0], V.scale(V.sub(...this.projectTo.map(l => l).reverse()), .5));
this.lookAtBox = [[0, 0], [1, 0], [1, 1], [0, 1]].map(e => e.map((w, i) => this.lookAt[e[i]][i]));
this.lookAtBoxEdges = this.lookAtBox.map((e, i, a) => [e, V.sub(a[(i+1)%a.length], e)]);
this.ratios = lookAt[0].map((e, i, a) => (projectTo[1][i] - projectTo[0][i])/(lookAt[1][i] - lookAt[0][i]));
}
update(...data) {
let from = data[0];
let to = data[1];
const intersections = this.lookAtBoxEdges.map(edge => Intersection.info(...edge, data[0], V.sub(to, from))).filter(int => int !== false && (0 <= int[1] && int[1] < 1 && 0 <= int[2] && int[2] <= 1));
const insiders = data.map(pt => Intersection.inside(this.lookAtBox, pt));
const collinear = (() => {
//check if segment from-to overlaps with border (collinear)
if(from[0] == to[0]) { //vertical line
//make the line go bottom
let fromY = Math.min(from[1], to[1]);
let toY = Math.max(from[1], to[1]);
if(fromY < this.lookAt[0][1] && toY < this.lookAt[0][1] ||
fromY > this.lookAt[1][1] && toY > this.lookAt[1][1]) {
return false;
}
if(from[0] != this.lookAt[0][0] && from[0] != this.lookAt[1][0]) {
return false;
}
if(from[0] == this.lookAt[1][0] &&//right lookat
(this.edge & GRID.RIGHT) == 0) { //if it's not the right lens
return false; //skip collinear
}
if(fromY <= this.lookAt[0][1]) {
from = [from[0], this.lookAt[0][1]];
}
if(lookAt[1][1] <= toY) {
to = [from[0], this.lookAt[1][1]];
}
return true;
} else if (from[1] == to[1]) { //horizontal line
//make the line go right
let fromX = Math.min(from[0], to[0]);
let toX = Math.max(from[0], to[0]);
if(fromX < this.lookAt[0][0] && toX < this.lookAt[0][0] ||
fromX > this.lookAt[1][0] && toX > this.lookAt[1][0]) {
return false;
}
if(from[1] != this.lookAt[0][1] && from[1] != this.lookAt[1][1]) {
return false;
}
if(from[1] == this.lookAt[1][1] &&//bottom lookat
(this.edge & GRID.BOTTOM) == 0) { //if it's not the bottom lens
return false; //skip collinear
}
if(fromX <= this.lookAt[0][0]) {
from = [this.lookAt[0][0], from[1]];
}
if(lookAt[1][0] <= toX) {
to = [this.lookAt[1][0], from[1]];
}
return true;
}
return false;
})();
if(!collinear && !insiders.every(i => i)) { //if not both inside
if(intersections.length == 0) { //and not intersections
return; //bail
}
intersections.sort((a, b) => a[2] < b[2]? -1: 1);
if(insiders.every(i => !i)) { //both outside
from = intersections[0][0];
to = intersections[intersections.length - 1][0];
} else { //one inside
if(insiders[0]) {
to = intersections[intersections.length - 1][0];
} else {
from = intersections[0][0];
}
}
}
this.projector.jump(V.add(V.mul(V.sub(from, this.midLookAt), this.ratios), this.midProjectTo));
this.projector.goto(V.add(V.mul(V.sub(to, this.midLookAt), this.ratios), this.midProjectTo));
}
}
return new SquareLens(turtleToObserve, lookAt, projectTo, edge, projector);
}
// Below is automatically maintained by Turtlelib 1.0
// Changes below this comment might interfere with its correct functioning.
function turtlelib_init() {
turtlelib_ns_c6665b0e9b_Jurgen_Vector_Math();
turtlelib_ns_c5f8fa95ed_Jurgen_Intersection();
}
// Turtlelib Jurgen Vector Math v 4 - start - {"id":"c6665b0e9b","package":"Jurgen","name":"Vector Math","version":"4"}
function turtlelib_ns_c6665b0e9b_Jurgen_Vector_Math() {
/////////////////////////////////////////////////////////
// Vector functions - Created by Jurgen Westerhof 2024 //
/////////////////////////////////////////////////////////
class Vector {
static add (a,b) { return a.map((v,i)=>v+b[i]); }
static sub (a,b) { return a.map((v,i)=>v-b[i]); }
static mul (a,b) { return a.map((v,i)=>v*b[i]); }
static div (a,b) { return a.map((v,i)=>v/b[i]); }
static scale(a,s) { return a.map(v=>v*s); }
static det(m) { return m.length == 1? m[0][0]: m.length == 2 ? m[0][0]*m[1][1]-m[0][1]*m[1][0]: m[0].reduce((r,e,i) => r+(-1)**(i+2)*e*this.det(m.slice(1).map(c => c.filter((_,j) => i != j))),0); }
static angle(a) { return Math.PI - Math.atan2(a[1], -a[0]); } //compatible with turtletoy heading
static rot2d(angle) { return [[Math.cos(angle), -Math.sin(angle)], [Math.sin(angle), Math.cos(angle)]]; }
static rot3d(yaw,pitch,roll) { return [[Math.cos(yaw)*Math.cos(pitch), Math.cos(yaw)*Math.sin(pitch)*Math.sin(roll)-Math.sin(yaw)*Math.cos(roll), Math.cos(yaw)*Math.sin(pitch)*Math.cos(roll)+Math.sin(yaw)*Math.sin(roll)],[Math.sin(yaw)*Math.cos(pitch), Math.sin(yaw)*Math.sin(pitch)*Math.sin(roll)+Math.cos(yaw)*Math.cos(roll), Math.sin(yaw)*Math.sin(pitch)*Math.cos(roll)-Math.cos(yaw)*Math.sin(roll)],[-Math.sin(pitch), Math.cos(pitch)*Math.sin(roll), Math.cos(pitch)*Math.cos(roll)]]; }
static trans(matrix,a) { return a.map((v,i) => a.reduce((acc, cur, ci) => acc + cur * matrix[ci][i], 0)); }
//Mirror vector a in a ray through [0,0] with direction mirror
static mirror2d(a,mirror) { return [Math.atan2(...mirror)].map(angle => this.trans(this.rot2d(angle), this.mul([-1,1], this.trans(this.rot2d(-angle), a)))).pop(); }
static equals(a,b) { return !a.some((e, i) => e != b[i]); }
static approx(a,b,p) { return this.len(this.sub(a,b)) < (p === undefined? .001: p); }
static norm (a) { return this.scale(a,1/this.len(a)); }
static len (a) { return Math.hypot(...a); }
static lenSq (a) { return a.reduce((a,c)=>a+c**2,0); }
static lerp (a,b,t) { return a.map((v, i) => v*(1-t) + b[i]*t); }
static dist (a,b) { return Math.hypot(...this.sub(a,b)); }
static dot (a,b) { return a.reduce((a,c,i) => a+c*b[i], 0); }
static cross(...ab) { return ab[0].map((e, i) => ab.map(v => v.filter((ee, ii) => ii != i))).map((m,i) => (i%2==0?-1:1)*this.det(m)); }
static clamp(a,min,max) { return a.map((e,i) => Math.min(Math.max(e, min[i]), max[i])) };
static rotateClamp(a,min,max) { return a.map((e,i) => {const d = max[i]-min[i];if(d == 0) return min[i];while(e < min[i]) { e+=d; }while(e > max[i]) { e-=d; }return e;});
}
}
this.V = Vector;
}
// Turtlelib Jurgen Vector Math v 4 - end
// Turtlelib Jurgen Intersection v 4 - start - {"id":"c5f8fa95ed","package":"Jurgen","name":"Intersection","version":"4"}
function turtlelib_ns_c5f8fa95ed_Jurgen_Intersection() {
///////////////////////////////////////////////////////////////
// Intersection functions - Created by Jurgen Westerhof 2024 //
///////////////////////////////////////////////////////////////
class Intersection {
//a-start, a-direction, b-start, b-direction
//returns false on no intersection or [[intersection:x,y], scalar a-direction, scalar b-direction
static info(as, ad, bs, bd) { const d = V.sub(bs, as), det = -V.det([bd, ad]); if(det === 0) return false; const res = [V.det([d, bd]) / det, V.det([d, ad]) / det]; return [V.add(as, V.scale(ad, res[0])), ...res]; }
static ray(a, b, c, d) { return this.info(a, b, c, d); }
static segment(a,b,c,d, inclusiveStart = true, inclusiveEnd = true) { const i = this.info(a, V.sub(b, a), c, V.sub(d, c)); return i === false? false: ( (inclusiveStart? 0<=i[1] && 0<=i[2]: 0<i[1] && 0<i[2]) && (inclusiveEnd? i[1]<=1 && i[2]<=1: i[1]<1 && i[2]<1) )?i[0]:false;}
static tour(tour, segmentStart, segmentDirection) { return tour.map((e, i, a) => [i, this.info(e, V.sub(a[(i+1)%a.length], e), segmentStart, segmentDirection)]).filter(e => e[1] !== false && 0 <= e[1][1] && e[1][1] <= 1).filter(e => 0 <= e[1][2]).map(e => ({position: e[1][0],tourIndex: e[0],tourSegmentPortion: e[1][1],segmentPortion: e[1][2],}));}
static inside(tour, pt) { return tour.map((e,i,a) => this.segment(e, a[(i+1)%a.length], pt, [Number.MAX_SAFE_INTEGER, 0], true, false)).filter(e => e !== false).length % 2 == 1; }
static circles(centerA, radiusA, centerB, radiusB) {const result = {intersect_count: 0,intersect_occurs: true,one_is_in_other: false,are_equal: false,point_1: [null, null],point_2: [null, null],};const dx = centerB[0] - centerA[0];const dy = centerB[1] - centerA[1];const dist = Math.hypot(dy, dx);if (dist > radiusA + radiusB) {result.intersect_occurs = false;}if (dist < Math.abs(radiusA - radiusB) && !N.approx(dist, Math.abs(radiusA - radiusB))) {result.intersect_occurs = false;result.one_is_in_other = true;}if (V.approx(centerA, centerB) && radiusA === radiusB) {result.are_equal = true;}if (result.intersect_occurs) {const centroid = (radiusA**2 - radiusB**2 + dist * dist) / (2.0 * dist);const x2 = centerA[0] + (dx * centroid) / dist;const y2 = centerA[1] + (dy * centroid) / dist;const prec = 10000;const h = (Math.round(radiusA**2 * prec)/prec - Math.round(centroid**2 * prec)/prec)**.5;const rx = -dy * (h / dist);const ry = dx * (h / dist);result.point_1 = [x2 + rx, y2 + ry];result.point_2 = [x2 - rx, y2 - ry];if (result.are_equal) {result.intersect_count = Infinity;} else if (V.equals(result.point_1, result.point_2)) {result.intersect_count = 1;} else {result.intersect_count = 2;}}return result;}
}
this.Intersection = Intersection;
}
// Turtlelib Jurgen Intersection v 4 - end