Convert vectors correctly in nonorthogonal bases

pymunk/tests/test_vec2d.py

@@ -28,3 +28,31 @@ def testComparison(self) -> None:
         self.assertTrue(int_vec != (0, 0))
         self.assertTrue(int_vec != 5)  # type: ignore
         self.assertTrue(int_vec != (3, -2, -5))  # type: ignore
+
+    def testNonorthogonalBasis(self) -> None:
+        bases = [
+            ((32, 16), (-32, 16)),
+            ((2, 1), (1, 3)),
+            ((1, 3), (2, 1)),
+            ((-2, -1), (1, 3)),
+        ]
+        for x_axis, y_axis in bases:
+            for expected in [(1, 0), (0, 1), (3, -2), (-0.5, 1.5)]:
+                with self.subTest(basis=(x_axis, y_axis), expected=expected):
+                    world = Vec2d(*x_axis) * expected[0] + Vec2d(*y_axis) * expected[1]
+                    actual = world.convert_to_basis(x_axis, y_axis)
+                    self.assertAlmostEqual(actual.x, expected[0])
+                    self.assertAlmostEqual(actual.y, expected[1])
+
+    def testOrthogonalBasis(self) -> None:
+        for x_axis, y_axis in [((5, 0), (0, 0.5)), ((3, 4), (-4, 3))]:
+            with self.subTest(basis=(x_axis, y_axis)):
+                expected = Vec2d(2, -3)
+                world = Vec2d(*x_axis) * expected.x + Vec2d(*y_axis) * expected.y
+                self.assertEqual(world.convert_to_basis(x_axis, y_axis), expected)
+
+    def testDependentBasis(self) -> None:
+        for x_axis, y_axis in [((0, 0), (0, 1)), ((1, 2), (2, 4))]:
+            with self.subTest(basis=(x_axis, y_axis)):
+                with self.assertRaises(ZeroDivisionError):
+                    Vec2d(3, 4).convert_to_basis(x_axis, y_axis)

pymunk/vec2d.py

@@ -571,13 +571,21 @@ def convert_to_basis(
     ) -> "Vec2d":
         """Convert the vector to a new basis defined by the given x and y vectors.
 
+        The basis vectors must be linearly independent, but need not be
+        perpendicular.
+
         >>> Vec2d(10, 1).convert_to_basis((5, 0), (0, 0.5))
         Vec2d(2.0, 2.0)
+        >>> Vec2d(32, 16).convert_to_basis((32, 16), (-32, 16))
+        Vec2d(1.0, 0.0)
+
+        :raises ZeroDivisionError: If the basis vectors are linearly dependent.
         """
         assert len(x_vector) == 2
         assert len(y_vector) == 2
-        x = self.dot(x_vector) / Vec2d(*x_vector).length_squared
-        y = self.dot(y_vector) / Vec2d(*y_vector).length_squared
+        determinant = x_vector[0] * y_vector[1] - x_vector[1] * y_vector[0]
+        x = (self.x * y_vector[1] - self.y * y_vector[0]) / determinant
+        y = (x_vector[0] * self.y - x_vector[1] * self.x) / determinant
         return Vec2d(x, y)
 
     @property