feat(geom): initial import ComplexPolygon & impls (#464)

- add complexPolygon() factory fn
- add bounds() & centroid() impls

packages/geom/src/api/complex-polygon.ts

@@ -0,0 +1,51 @@
+import { ensureArray } from "@thi.ng/arrays/ensure-array";
+import type { Attribs, IHiccupShape } from "@thi.ng/geom-api";
+import { __copyAttribs } from "../internal/copy.js";
+import { Polygon } from "./polygon.js";
+
+export class ComplexPolygon implements IHiccupShape {
+	children: Polygon[];
+
+	constructor(
+		public boundary: Polygon = new Polygon(),
+		children?: Iterable<Polygon>,
+		public attribs?: Attribs
+	) {
+		this.children = children ? ensureArray(children) : [];
+	}
+
+	get type() {
+		return "complexpoly";
+	}
+
+	addChild(poly: Polygon) {
+		this.children.push(poly);
+	}
+
+	copy(): ComplexPolygon {
+		return new ComplexPolygon(
+			this.boundary.copy(),
+			this.children.map((h) => h.copy()),
+			__copyAttribs(this)
+		);
+	}
+
+	withAttribs(attribs: Attribs): ComplexPolygon {
+		return new ComplexPolygon(this.boundary, this.children, attribs);
+	}
+
+	toHiccup() {
+		const segments: any[] = [];
+		const $hiccupSegments = ({ points }: Polygon) => {
+			if (!points.length) return;
+			segments.push(["M", points[0]]);
+			for (let i = 1, n = points.length; i < n; i++) {
+				segments.push(["L", points[i]]);
+			}
+			segments.push(["Z"]);
+		};
+		$hiccupSegments(this.boundary);
+		for (let c of this.children) $hiccupSegments(c);
+		return ["path", this.attribs, segments];
+	}
+}

packages/geom/src/bounds.ts

@@ -20,6 +20,7 @@ import { subN2 } from "@thi.ng/vectors/subn";
 import { aabbFromMinMaxWithMargin } from "./aabb.js";
 import type { Arc } from "./api/arc.js";
 import type { Circle } from "./api/circle.js";
+import type { ComplexPolygon } from "./api/complex-polygon.js";
 import type { Cubic } from "./api/cubic.js";
 import type { Ellipse } from "./api/ellipse.js";
 import type { Group } from "./api/group.js";
@@ -87,6 +88,11 @@ export const bounds: MultiFn1O<IShape, number, Maybe<AABBLike>> = defmulti<
 				mulN2(null, [2, 2], $.r + margin)
 			),
 
+		complexpoly: ($: ComplexPolygon, margin = 0) => {
+			const res = __collBounds([$.boundary, ...$.children], bounds);
+			return res ? new Rect(...res).offset(margin) : undefined;
+		},
+
 		cubic: ({ points }: Cubic, margin = 0) =>
 			rectFromMinMaxWithMargin(
 				...cubicBounds(points[0], points[1], points[2], points[3]),

packages/geom/src/centroid.ts

@@ -7,16 +7,20 @@ import { centroid as _centroid } from "@thi.ng/geom-poly-utils/centroid";
 import type { Vec } from "@thi.ng/vectors";
 import { add } from "@thi.ng/vectors/add";
 import { addmN } from "@thi.ng/vectors/addmn";
-import { maddN } from "@thi.ng/vectors/maddn";
+import { divN2 } from "@thi.ng/vectors/divn";
+import { maddN, maddN2 } from "@thi.ng/vectors/maddn";
 import { mixN } from "@thi.ng/vectors/mixn";
+import { msubN2 } from "@thi.ng/vectors/msubn";
 import { mulN } from "@thi.ng/vectors/muln";
 import { set } from "@thi.ng/vectors/set";
 import type { Circle } from "./api/circle.js";
+import type { ComplexPolygon } from "./api/complex-polygon.js";
 import type { Group } from "./api/group.js";
 import type { Line } from "./api/line.js";
 import type { Plane } from "./api/plane.js";
 import type { Polygon } from "./api/polygon.js";
 import type { Triangle } from "./api/triangle.js";
+import { area } from "./area.js";
 import { bounds } from "./bounds.js";
 import { __dispatch } from "./internal/dispatch.js";
 
@@ -69,6 +73,29 @@ export const centroid: MultiFn1O<IShape, Vec, Maybe<Vec>> = defmulti<
 	{
 		circle: ($: Circle, out?) => set(out || [], $.pos),
 
+		// https://math.stackexchange.com/a/623849
+		// ((Aout * Cout) - (Ain * Cin)) / (Aout - Ain)
+		complexpoly: ($: ComplexPolygon, out?) => {
+			const outerArea = Math.abs(area($.boundary));
+			let innerArea = 0;
+			let innerCentroid = [0, 0];
+			for (let child of $.children) {
+				const a = Math.abs(area(child));
+				innerArea += a;
+				maddN2(innerCentroid, centroid(child)!, a, innerCentroid);
+			}
+			return divN2(
+				null,
+				msubN2(
+					out || [],
+					centroid($.boundary)!,
+					outerArea,
+					innerCentroid
+				),
+				outerArea - innerArea
+			);
+		},
+
 		group: ($: Group, out?) => {
 			const b = bounds($);
 			return b ? centroid(b, out) : undefined;

packages/geom/src/complex-polygon.ts

@@ -0,0 +1,9 @@
+import type { Attribs } from "@thi.ng/geom-api";
+import { ComplexPolygon } from "./api/complex-polygon.js";
+import { Polygon } from "./api/polygon.js";
+
+export const complexPolygon = (
+	boundary?: Polygon,
+	children?: Iterable<Polygon>,
+	attribs?: Attribs
+) => new ComplexPolygon(boundary, children, attribs);

packages/geom/src/index.ts

@@ -3,6 +3,7 @@ export * from "./api/apc.js";
 export * from "./api/arc.js";
 export * from "./api/bpatch.js";
 export * from "./api/circle.js";
+export * from "./api/complex-polygon.js";
 export * from "./api/cubic.js";
 export * from "./api/ellipse.js";
 export * from "./api/group.js";
@@ -25,6 +26,7 @@ export * from "./aabb.js";
 export * from "./arc.js";
 export * from "./bpatch.js";
 export * from "./circle.js";
+export * from "./complex-polygon.js";
 export * from "./cubic.js";
 export * from "./ellipse.js";
 export * from "./group.js";