diff --git a/tests/core/math/test_transform_2d.h b/tests/core/math/test_transform_2d.h
index 36d27ce7a9d..6d3c80e5cab 100644
--- a/tests/core/math/test_transform_2d.h
+++ b/tests/core/math/test_transform_2d.h
@@ -45,48 +45,132 @@ Transform2D identity() {
 	return Transform2D();
 }
 
+TEST_CASE("[Transform2D] Default constructor") {
+	Transform2D default_constructor = Transform2D();
+	CHECK(default_constructor == Transform2D(Vector2(1, 0), Vector2(0, 1), Vector2(0, 0)));
+}
+
+TEST_CASE("[Transform2D] Copy constructor") {
+	Transform2D T = create_dummy_transform();
+	Transform2D copy_constructor = Transform2D(T);
+	CHECK(T == copy_constructor);
+}
+
+TEST_CASE("[Transform2D] Constructor from angle and position") {
+	constexpr float ROTATION = Math_PI / 4;
+	const Vector2 TRANSLATION = Vector2(20, -20);
+
+	const Transform2D test = Transform2D(ROTATION, TRANSLATION);
+	const Transform2D expected = Transform2D().rotated(ROTATION).translated(TRANSLATION);
+	CHECK(test == expected);
+}
+
+TEST_CASE("[Transform2D] Constructor from angle, scale, skew and position") {
+	constexpr float ROTATION = Math_PI / 2;
+	const Vector2 SCALE = Vector2(2, 0.5);
+	constexpr float SKEW = Math_PI / 4;
+	const Vector2 TRANSLATION = Vector2(30, 0);
+
+	const Transform2D test = Transform2D(ROTATION, SCALE, SKEW, TRANSLATION);
+	Transform2D expected = Transform2D().scaled(SCALE).rotated(ROTATION).translated(TRANSLATION);
+	expected.set_skew(SKEW);
+
+	CHECK(test.is_equal_approx(expected));
+}
+
+TEST_CASE("[Transform2D] Constructor from raw values") {
+	const Transform2D test = Transform2D(1, 2, 3, 4, 5, 6);
+	const Transform2D expected = Transform2D(Vector2(1, 2), Vector2(3, 4), Vector2(5, 6));
+	CHECK(test == expected);
+}
+
+TEST_CASE("[Transform2D] xform") {
+	const Vector2 v = Vector2(2, 3);
+	const Transform2D T = Transform2D(Vector2(1, 2), Vector2(3, 4), Vector2(5, 6));
+	const Vector2 expected = Vector2(1 * 2 + 3 * 3 + 5 * 1, 2 * 2 + 4 * 3 + 6 * 1);
+	CHECK(T.xform(v) == expected);
+}
+
+TEST_CASE("[Transform2D] Basis xform") {
+	const Vector2 v = Vector2(2, 2);
+	const Transform2D T1 = Transform2D(Vector2(1, 2), Vector2(3, 4), Vector2(0, 0));
+
+	// Both versions should be the same when the origin is (0,0).
+	CHECK(T1.basis_xform(v) == T1.xform(v));
+
+	const Transform2D T2 = Transform2D(Vector2(1, 2), Vector2(3, 4), Vector2(5, 6));
+
+	// Each version should be different when the origin is not (0,0).
+	CHECK_FALSE(T2.basis_xform(v) == T2.xform(v));
+}
+
+TEST_CASE("[Transform2D] Affine inverse") {
+	const Transform2D orig = create_dummy_transform();
+	const Transform2D affine_inverted = orig.affine_inverse();
+	const Transform2D affine_inverted_again = affine_inverted.affine_inverse();
+	CHECK(affine_inverted_again == orig);
+}
+
+TEST_CASE("[Transform2D] Orthonormalized") {
+	const Transform2D T = create_dummy_transform();
+	const Transform2D orthonormalized_T = T.orthonormalized();
+
+	// Check each basis has length 1.
+	CHECK(Math::is_equal_approx(orthonormalized_T[0].length_squared(), 1));
+	CHECK(Math::is_equal_approx(orthonormalized_T[1].length_squared(), 1));
+
+	const Vector2 vx = Vector2(orthonormalized_T[0].x, orthonormalized_T[1].x);
+	const Vector2 vy = Vector2(orthonormalized_T[0].y, orthonormalized_T[1].y);
+
+	// Check the basis are orthogonal.
+	CHECK(Math::is_equal_approx(orthonormalized_T.tdotx(vx), 1));
+	CHECK(Math::is_equal_approx(orthonormalized_T.tdotx(vy), 0));
+	CHECK(Math::is_equal_approx(orthonormalized_T.tdoty(vx), 0));
+	CHECK(Math::is_equal_approx(orthonormalized_T.tdoty(vy), 1));
+}
+
 TEST_CASE("[Transform2D] translation") {
-	Vector2 offset = Vector2(1, 2);
+	const Vector2 offset = Vector2(1, 2);
 
 	// Both versions should give the same result applied to identity.
 	CHECK(identity().translated(offset) == identity().translated_local(offset));
 
 	// Check both versions against left and right multiplications.
-	Transform2D orig = create_dummy_transform();
-	Transform2D T = identity().translated(offset);
+	const Transform2D orig = create_dummy_transform();
+	const Transform2D T = identity().translated(offset);
 	CHECK(orig.translated(offset) == T * orig);
 	CHECK(orig.translated_local(offset) == orig * T);
 }
 
 TEST_CASE("[Transform2D] scaling") {
-	Vector2 scaling = Vector2(1, 2);
+	const Vector2 scaling = Vector2(1, 2);
 
 	// Both versions should give the same result applied to identity.
 	CHECK(identity().scaled(scaling) == identity().scaled_local(scaling));
 
 	// Check both versions against left and right multiplications.
-	Transform2D orig = create_dummy_transform();
-	Transform2D S = identity().scaled(scaling);
+	const Transform2D orig = create_dummy_transform();
+	const Transform2D S = identity().scaled(scaling);
 	CHECK(orig.scaled(scaling) == S * orig);
 	CHECK(orig.scaled_local(scaling) == orig * S);
 }
 
 TEST_CASE("[Transform2D] rotation") {
-	real_t phi = 1.0;
+	constexpr real_t phi = 1.0;
 
 	// Both versions should give the same result applied to identity.
 	CHECK(identity().rotated(phi) == identity().rotated_local(phi));
 
 	// Check both versions against left and right multiplications.
-	Transform2D orig = create_dummy_transform();
-	Transform2D R = identity().rotated(phi);
+	const Transform2D orig = create_dummy_transform();
+	const Transform2D R = identity().rotated(phi);
 	CHECK(orig.rotated(phi) == R * orig);
 	CHECK(orig.rotated_local(phi) == orig * R);
 }
 
 TEST_CASE("[Transform2D] Interpolation") {
-	Transform2D rotate_scale_skew_pos = Transform2D(Math::deg_to_rad(170.0), Vector2(3.6, 8.0), Math::deg_to_rad(20.0), Vector2(2.4, 6.8));
-	Transform2D rotate_scale_skew_pos_halfway = Transform2D(Math::deg_to_rad(85.0), Vector2(2.3, 4.5), Math::deg_to_rad(10.0), Vector2(1.2, 3.4));
+	const Transform2D rotate_scale_skew_pos = Transform2D(Math::deg_to_rad(170.0), Vector2(3.6, 8.0), Math::deg_to_rad(20.0), Vector2(2.4, 6.8));
+	const Transform2D rotate_scale_skew_pos_halfway = Transform2D(Math::deg_to_rad(85.0), Vector2(2.3, 4.5), Math::deg_to_rad(10.0), Vector2(1.2, 3.4));
 	Transform2D interpolated = Transform2D().interpolate_with(rotate_scale_skew_pos, 0.5);
 	CHECK(interpolated.get_origin().is_equal_approx(rotate_scale_skew_pos_halfway.get_origin()));
 	CHECK(interpolated.get_rotation() == doctest::Approx(rotate_scale_skew_pos_halfway.get_rotation()));
@@ -98,8 +182,8 @@ TEST_CASE("[Transform2D] Interpolation") {
 }
 
 TEST_CASE("[Transform2D] Finite number checks") {
-	const Vector2 x(0, 1);
-	const Vector2 infinite(NAN, NAN);
+	const Vector2 x = Vector2(0, 1);
+	const Vector2 infinite = Vector2(NAN, NAN);
 
 	CHECK_MESSAGE(
 			Transform2D(x, x, x).is_finite(),