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