refactor(geom): update centroid() for complexpoly

- re-use migrated fn from thi.ng/geom-poly-utils

packages/geom/src/centroid.ts

@@ -2,15 +2,16 @@ import type { Maybe } from "@thi.ng/api";
 import type { MultiFn1O } from "@thi.ng/defmulti";
 import { defmulti } from "@thi.ng/defmulti/defmulti";
 import type { AABBLike, IShape, PCLike } from "@thi.ng/geom-api";
-import { centerOfWeight2 } from "@thi.ng/geom-poly-utils/center-of-weight";
+import {
+	centerOfWeight2,
+	complexCenterOfWeight2,
+} from "@thi.ng/geom-poly-utils/center-of-weight";
 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 { divN2 } from "@thi.ng/vectors/divn";
-import { maddN, maddN2 } from "@thi.ng/vectors/maddn";
+import { maddN } 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";
@@ -20,7 +21,6 @@ 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";
 
@@ -75,28 +75,12 @@ 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
-			);
-		},
+		complexpoly: ($: ComplexPolygon, out?) =>
+			complexCenterOfWeight2(
+				$.boundary.points,
+				$.children.map((c) => c.points),
+				out
+			),
 
 		group: ($: Group, out?) => {
 			const b = bounds($);