feat(geom): add inscribedSquare*() fns

packages/geom/src/ctors/rect.ts

@@ -1,6 +1,14 @@
 import { Attribs } from "@thi.ng/geom-api";
-import { sub2, Vec } from "@thi.ng/vectors";
-import { Rect } from "../api";
+import { centroid } from "@thi.ng/geom-poly-utils";
+import { SQRT2_2, SQRT3 } from "@thi.ng/math";
+import {
+    dist,
+    ReadonlyVec,
+    sub2,
+    subN2,
+    Vec
+} from "@thi.ng/vectors";
+import { Circle, Polygon, Rect } from "../api";
 import { argsVV } from "../internal/args";
 
 export function rect(pos: Vec, size: number | Vec, attribs?: Attribs): Rect;
@@ -12,3 +20,45 @@ export function rect(...args: any[]) {
 
 export const rectFromMinMax = (min: Vec, max: Vec, attribs?: Attribs) =>
     new Rect(min, sub2([], max, min), attribs);
+
+/**
+ * Returns square inscribed in given circle instance. The circle can also be
+ * given as centroid & radius.
+ *
+ * @param circle
+ */
+export function inscribedSquare(circle: Circle): Rect;
+export function inscribedSquare(pos: ReadonlyVec, r: number): Rect;
+export function inscribedSquare(...args: any[]) {
+    let pos: ReadonlyVec, r: number;
+    if (args.length === 1) {
+        const c: Circle = args[0];
+        pos = c.pos;
+        r = c.r;
+    } else {
+        [pos, r] = args;
+    }
+    r *= SQRT2_2;
+    return rect(subN2([], pos, r), r * 2);
+}
+
+/**
+ * Returns square inscribed in given (unrotated) hexagon. The hexagon
+ * can be given as `Polygon` or centroid and edge length.
+ *
+ * @param hex
+ */
+export function inscribedSquareHex(hex: Polygon): Rect;
+export function inscribedSquareHex(pos: ReadonlyVec, len: number): Rect;
+export function inscribedSquareHex(...args: any[]) {
+    let pos: ReadonlyVec, l: number;
+    if (args.length === 1) {
+        const pts = (<Polygon>args[0]).points;
+        pos = centroid(pts);
+        l = dist(pts[0], pts[1]);
+    } else {
+        [pos, l] = args;
+    }
+    l *= 3 - SQRT3;
+    return rect(subN2([], pos, l / 2), l);
+}