496 lines
13 KiB
TypeScript
496 lines
13 KiB
TypeScript
import { Heap } from 'ts-heap'
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import { HalfEdge, Face, Vertex } from './dcel';
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interface WithPriority {
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get_priority(): number;
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}
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export class Point {
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x: number;
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y: number;
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face?: Face;
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constructor(x: number, y: number, face? :Face) {
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this.x = x;
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this.y = y;
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this.face = face;
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}
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equals(other: Point): boolean {
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return Math.abs(this.x - other.x) + Math.abs(this.y - other.y) < 0.00001;
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}
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toString(): string {
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return `{x: ${this.x}, y: ${this.y}}`;
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}
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}
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class CircleEvent implements WithPriority {
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y: number;
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alive: boolean = true;
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center: Vertex;
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leaf: Leaf;
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from: Point[];
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static
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from_sites(s1: Point, s2: Point, s3: Point, leaf: Leaf): CircleEvent {
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const a = s1.x * (s2.y - s3.y) - s1.y*(s2.x - s3.x) + s2.x*s3.y - s3.x * s2.y;
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const b = (s1.x ** 2 + s1.y ** 2) * (s3.y - s2.y) + (s2.x ** 2 + s2.y ** 2)*(s1.y - s3.y) + (s3.x ** 2 + s3.y ** 2) * (s2.y - s1.y);
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const c = (s1.x ** 2 + s1.y ** 2) * (s2.x - s3.x) + (s2.x ** 2 + s2.y ** 2)*(s3.x - s1.x) + (s3.x ** 2 + s3.y ** 2) * (s1.x - s2.x);
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const d = (s1.x ** 2 + s1.y ** 2) * (s3.x*s2.y - s2.x*s3.y) + (s2.x ** 2 + s2.y ** 2)*(s1.x*s3.y - s3.x*s1.y) + (s3.x ** 2 + s3.y ** 2) * (s2.x*s1.y - s1.x*s2.y);
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const center = new Vertex(-b / (2. * a), -c / (2. * a));
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const r = Math.sqrt((b ** 2 + c ** 2 - 4. * a * d) / (4. * a ** 2));
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const y = center.coords[1] - r;
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const out = new CircleEvent();
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out.y = y;
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out.center = center;
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out.leaf = leaf;
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out.from = [s1, s2, s3];
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return out;
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}
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get_priority(): number {
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return this.y;
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}
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print() {
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console.log(`Circle event at ${this.y} ${JSON.stringify(this.center)}, ${this.leaf.point.toString()} from ${JSON.stringify(this.from.map((e) => e.toString()))}`);
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}
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}
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class SiteEvent implements WithPriority{
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face: Face;
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point: Point;
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constructor(point: Point) {
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this.face = new Face(point);
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this.point = point;
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this.point.face = this.face;
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}
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get_priority(): number {
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return this.point.y;
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}
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print() {
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console.log(`Site event ${this.point.toString()}`);
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}
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}
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function calc_x(left: Point, right: Point, y: number): number {
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const [a1, b1, c1] = from_focus_vertex(left, y);
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const [a2, b2, c2] = from_focus_vertex(right, y);
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if (Math.abs(a1 - a2) < 0.0001) {
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return (left.x + right.x) / 2.;
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}
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const da = a1 - a2;
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const db = b1 - b2;
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const dc = c1 - c2;
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const d = db * db - 4. * da * dc;
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if (d <= 0.) {
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throw new Error(`D is less then 0 ${d}`);
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}
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const dd = Math.sqrt(d);
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const x = (-db + dd) / (2. * da);
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return x;
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}
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function from_focus_vertex(focus: Point, y: number): number[] {
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const a = (focus.y - y) / 2;
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const h = focus.x;
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const k = focus.y - a;
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return [1 / (4. * a), -h / (2 * a), (h ** 2 / (4 * a)) + k]
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}
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function cmp_event(e1: WithPriority, e2: WithPriority) {
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return e2.get_priority() - e1.get_priority();
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}
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type Queue = Heap<WithPriority>;
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type Node = Leaf | Breakpoint;
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type Parent = Breakpoint | State;
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class Leaf {
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point: Point;
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event: CircleEvent | undefined;
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left: Leaf | undefined;
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right: Leaf | undefined;
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parent: Parent;
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half_edge: HalfEdge;
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constructor(point: Point, parent: Parent) {
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this.point = point;
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this.parent = parent;
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this.half_edge = new HalfEdge(undefined, undefined);
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}
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false_alarm() {
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if(this.event) {
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console.log(`False alarm ${JSON.stringify(this.event.center)} ${this.event.y}`);
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this.event.alive = false;
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}
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}
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update_left(leaf: Leaf) {
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if (this.left) {
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this.left.right = leaf;
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}
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leaf.left = this.left;
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}
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update_right(leaf: Leaf) {
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if (this.right) {
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this.right.left = leaf;
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}
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leaf.right = this.right;
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}
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split(point: Point, events: Queue) {
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this.false_alarm();
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if (this.point.y == point.y) {
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const middle = new Leaf(point, undefined);
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const parent = this.parent;
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if (this.point.x > point.x) {
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const br = new Breakpoint([point, middle], [this.point, this], this.parent);
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if (this.left) this.left.right = middle;
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this.left = middle;
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middle.right = this;
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if (parent instanceof Breakpoint) {
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parent.set_me(this, br);
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} else {
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parent.root = br;
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}
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const maybe_left = middle.check_circles(point.y, events);
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if (maybe_left && maybe_left.center.coords[0] < middle.point.x) {
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console.log(`Adding circle`);
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maybe_left.print();
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middle.event = maybe_left;
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events.add(maybe_left);
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}
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const maybe_right = this.check_circles(point.y, events);
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if (maybe_right && maybe_right.center.coords[0] >= middle.point.x) {
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console.log(`Adding circle`);
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maybe_right.print();
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this.event = maybe_right;
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events.add(maybe_right);
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}
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} else {
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const br = new Breakpoint([this.point, this], [point, middle], this.parent);
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if (this.right) this.right.left = middle;
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this.right = middle;
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middle.left = this;
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if (parent instanceof Breakpoint) {
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parent.set_me(this, br);
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} else {
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parent.root = br;
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}
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const maybe_left = this.check_circles(point.y, events);
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if (maybe_left && maybe_left.center.coords[0] < middle.point.x) {
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console.log(`Adding circle`);
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maybe_left.print();
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this.event = maybe_left;
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events.add(maybe_left);
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}
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const maybe_right = middle.check_circles(point.y, events);
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if (maybe_right && maybe_right.center.coords[0] >= middle.point.x) {
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console.log(`Adding circle`);
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maybe_right.print();
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middle.event = maybe_right;
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events.add(maybe_right);
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}
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}
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return;
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}
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const left = new Leaf(this.point, undefined);
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left.left = this.left;
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if (this.left) this.left.right = left;
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const right = new Leaf(this.point, undefined);
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right.right = this.right;
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if (this.right) this.right.left = right;
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const middle = new Leaf(point, undefined);
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middle.left = left;
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middle.right = right;
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right.left = middle;
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left.right = middle;
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const br1 = new Breakpoint([this.point, left], [point, middle], undefined);
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const br2 = new Breakpoint([point, br1], [this.point, right], this.parent);
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br1.parent = br2;
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if (this.parent instanceof Breakpoint) {
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this.parent.set_me(this, br2);
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} else {
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this.parent.root = br2;
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}
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const maybe_left = left.check_circles(point.y, events);
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if (maybe_left && maybe_left.center.coords[0] < middle.point.x) {
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console.log(`Adding circle`);
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maybe_left.print();
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left.event = maybe_left;
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events.add(maybe_left);
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}
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const maybe_right = right.check_circles(point.y, events);
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if (maybe_right && maybe_right.center.coords[0] >= middle.point.x) {
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console.log(`Adding circle`);
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maybe_right.print();
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right.event = maybe_right;
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events.add(maybe_right);
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}
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}
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check_circles(y: number, events: Queue): CircleEvent | undefined {
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const left = this.left;
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const right = this.right;
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if (left && right) {
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const circle = CircleEvent.from_sites(left.point, this.point, right.point, this);
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console.log(`${circle.y} < ${y}`);
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if (circle.y < y ) {
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return circle;
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}
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}
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}
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delete(vertex: Vertex) {
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if (this.parent instanceof Breakpoint) {
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this.parent.remove_me(this.point, vertex);
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} else {
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console.error("Shouldnt be here");
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}
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}
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print(indent: string) {
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console.log(`${indent}Leaf from ${this.point.toString()} vertex: ${this.half_edge.to_string()}`);
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}
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}
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class Breakpoint {
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left: [Point, Node];
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right: [Point, Node];
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parent: Parent;
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half_edge: HalfEdge;
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constructor(left: [Point, Node], right: [Point, Node], parent: Parent) {
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this.left = left;
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this.right = right;
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this.left[1].parent = this;
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this.right[1].parent = this;
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this.parent = parent;
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this.half_edge = new HalfEdge(undefined, left[0].face, right[0].face);
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}
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remove_me(point: Point, vertex: Vertex) {
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const edge = this.half_edge.insert(vertex);
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const other = this.get_other(point);
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if (this.parent instanceof Breakpoint) {
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this.parent.set_me(this, other);
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this.parent.set_edge(edge);
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} else {
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this.parent.root = other;
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}
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}
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set_edge(edge: HalfEdge) {
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this.left[1].half_edge = edge;
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this.right[1].half_edge = edge.split(edge.origin);
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}
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set_me(old_me: Node, new_me: Node) {
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if (this.left[1] == old_me) {
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this.left[1] = new_me;
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} else {
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this.right[1] = new_me;
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}
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}
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get(point: Point): Leaf {
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const { x, y } = point;
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const test_x = calc_x(this.left[0], this.right[0], y);
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if (test_x >= x) {
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if (this.left[1] instanceof Leaf) {
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return this.left[1];
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} else {
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return this.left[1].get(point);
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}
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} else {
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if (this.right[1] instanceof Leaf) {
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return this.right[1];
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} else {
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return this.right[1].get(point);
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}
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}
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}
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get_other(point: Point): Node {
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if (this.left[0].equals(point)) {
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return this.right[1];
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} else {
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return this.left[1];
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}
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}
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print(indent: string) {
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console.log(`${indent}vertex: ${this.half_edge.to_string()}`);
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console.log(`${indent}left`);
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this.left[1].print(indent + ' ');
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console.log(`${indent}right`);
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this.right[1].print(indent + ' ');
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}
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}
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function get_from_node(root: Node, point: Point): Leaf {
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if (root instanceof Leaf) {
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return root;
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} else {
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return root.get(point);
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}
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}
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class State {
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root: Node | undefined;
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print() {
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if (this.root) {
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this.root.print('');
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} else {
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console.log("No root no tree");
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}
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}
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}
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export function voronoi(points: Point[]): Point[] {
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const out = [];
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const state = new State;
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const queue = new Heap<WithPriority>(cmp_event);
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for (let point of points) {
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queue.add(new SiteEvent(point));
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}
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let event;
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while (event = queue.pop()){
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console.log('---------------------------');
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event.print();
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if (event instanceof SiteEvent) {
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handle_site_event(event, queue, state, out);
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} else {
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if (!event.alive) {
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console.log("Dead");
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continue;
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}
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handle_circle_event(event, queue, state, out);
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}
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state.print();
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console.log(queue);
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print_leaves(get_from_node(state.root, new Point(0, 0)));
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}
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return out;
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}
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function handle_site_event(event: SiteEvent, queue: Queue, state: State, out: Point[]) {
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if (state.root) {
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const leaf = get_from_node(state.root, event.point);
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leaf.split(event.point, queue);
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} else {
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state.root = new Leaf(event.point, state);
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}
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}
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function handle_circle_event(event: CircleEvent, queue: Queue, state: State, out: [number, number][]) {
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if (!event.alive) return;
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event.leaf.delete(event.center);
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const right = event.leaf.right;
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const left = event.leaf.left;
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if (right) {
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right.false_alarm();
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// if (right.right) right.right.false_alarm();
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right.left = left;
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const maybe_right = right.check_circles(event.y, queue);
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if (maybe_right){
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console.log(`Adding circle event`);
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maybe_right.print();
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right.event = maybe_right;
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queue.add(maybe_right);
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}
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}
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if (left) {
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left.false_alarm();
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// if (left.left) left.left.false_alarm();
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left.right = right;
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const maybe_left = left.check_circles(event.y, queue);
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if (maybe_left){
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console.log(`Adding circle event`);
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maybe_left.print();
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left.event = maybe_left;
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queue.add(maybe_left);
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}
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}
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out.push(event.center.coords);
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}
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function print_leaves(start: Leaf) {
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let current = start;
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while (current.left) {
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current = current.left;
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}
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const points = [current.point];
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while (current.right) {
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current = current.right;
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points.push(current.point);
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}
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console.log(JSON.stringify(points.map((p) => p.toString())));
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}
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