chore: Unify math types, utils and functions (#8389)

Co-authored-by: dwelle <5153846+dwelle@users.noreply.github.com>

packages/math/ga/ga.test.ts

@@ -0,0 +1,70 @@
+import * as GA from "./ga";
+import { point, toString, direction, offset } from "./ga";
+import * as GAPoint from "./gapoints";
+import * as GALine from "./galines";
+import * as GATransform from "./gatransforms";
+
+describe("geometric algebra", () => {
+  describe("points", () => {
+    it("distanceToLine", () => {
+      const point = GA.point(3, 3);
+      const line = GALine.equation(0, 1, -1);
+      expect(GAPoint.distanceToLine(point, line)).toEqual(2);
+    });
+
+    it("distanceToLine neg", () => {
+      const point = GA.point(-3, -3);
+      const line = GALine.equation(0, 1, -1);
+      expect(GAPoint.distanceToLine(point, line)).toEqual(-4);
+    });
+  });
+  describe("lines", () => {
+    it("through", () => {
+      const a = GA.point(0, 0);
+      const b = GA.point(2, 0);
+      expect(toString(GALine.through(a, b))).toEqual(
+        toString(GALine.equation(0, 2, 0)),
+      );
+    });
+    it("parallel", () => {
+      const point = GA.point(3, 3);
+      const line = GALine.equation(0, 1, -1);
+      const parallel = GALine.parallel(line, 2);
+      expect(GAPoint.distanceToLine(point, parallel)).toEqual(0);
+    });
+  });
+
+  describe("translation", () => {
+    it("points", () => {
+      const start = point(2, 2);
+      const move = GATransform.translation(direction(0, 1));
+      const end = GATransform.apply(move, start);
+      expect(toString(end)).toEqual(toString(point(2, 3)));
+    });
+
+    it("points 2", () => {
+      const start = point(2, 2);
+      const move = GATransform.translation(offset(3, 4));
+      const end = GATransform.apply(move, start);
+      expect(toString(end)).toEqual(toString(point(5, 6)));
+    });
+
+    it("lines", () => {
+      const original = GALine.through(point(2, 2), point(3, 4));
+      const move = GATransform.translation(offset(3, 4));
+      const parallel = GATransform.apply(move, original);
+      expect(toString(parallel)).toEqual(
+        toString(GALine.through(point(5, 6), point(6, 8))),
+      );
+    });
+  });
+  describe("rotation", () => {
+    it("points", () => {
+      const start = point(2, 2);
+      const pivot = point(1, 1);
+      const rotate = GATransform.rotation(pivot, Math.PI / 2);
+      const end = GATransform.apply(rotate, start);
+      expect(toString(end)).toEqual(toString(point(2, 0)));
+    });
+  });
+});