4 files changed, 54 insertions, 18 deletions

diff --git a/core/math/transform_2d.cpp b/core/math/transform_2d.cpp
index bb8bf9f569..226076029b 100644
--- a/core/math/transform_2d.cpp
+++ b/core/math/transform_2d.cpp
@@ -217,34 +217,48 @@ Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
 	return t;
 }
 
-Transform2D Transform2D::scaled(const Size2 &p_scale) const {
+Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
 	Transform2D copy = *this;
-	copy.scale(p_scale);
+	copy.scale_basis(p_scale);
 	return copy;
 }
 
-Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
+Transform2D Transform2D::scaled(const Size2 &p_scale) const {
+	// Equivalent to left multiplication
 	Transform2D copy = *this;
-	copy.scale_basis(p_scale);
+	copy.scale(p_scale);
 	return copy;
 }
 
+Transform2D Transform2D::scaled_local(const Size2 &p_scale) const {
+	// Equivalent to right multiplication
+	return Transform2D(columns[0] * p_scale.x, columns[1] * p_scale.y, columns[2]);
+}
+
 Transform2D Transform2D::untranslated() const {
 	Transform2D copy = *this;
 	copy.columns[2] = Vector2();
 	return copy;
 }
 
+Transform2D Transform2D::translated(const Vector2 &p_offset) const {
+	// Equivalent to left multiplication
+	return Transform2D(columns[0], columns[1], columns[2] + p_offset);
+}
+
 Transform2D Transform2D::translated_local(const Vector2 &p_offset) const {
-	Transform2D copy = *this;
-	copy.translate_local(p_offset);
-	return copy;
+	// Equivalent to right multiplication
+	return Transform2D(columns[0], columns[1], columns[2] + basis_xform(p_offset));
 }
 
 Transform2D Transform2D::rotated(const real_t p_angle) const {
-	Transform2D copy = *this;
-	copy.rotate(p_angle);
-	return copy;
+	// Equivalent to left multiplication
+	return Transform2D(p_angle, Vector2()) * (*this);
+}
+
+Transform2D Transform2D::rotated_local(const real_t p_angle) const {
+	// Equivalent to right multiplication
+	return (*this) * Transform2D(p_angle, Vector2()); // Could be optimized, because origin transform can be skipped.
 }
 
 real_t Transform2D::basis_determinant() const {
diff --git a/core/math/transform_2d.h b/core/math/transform_2d.h
index e64d050f0c..f23f32867a 100644
--- a/core/math/transform_2d.h
+++ b/core/math/transform_2d.h
@@ -85,10 +85,13 @@ struct _NO_DISCARD_ Transform2D {
 	_FORCE_INLINE_ const Vector2 &get_origin() const { return columns[2]; }
 	_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
 
-	Transform2D scaled(const Size2 &p_scale) const;
 	Transform2D basis_scaled(const Size2 &p_scale) const;
+	Transform2D scaled(const Size2 &p_scale) const;
+	Transform2D scaled_local(const Size2 &p_scale) const;
+	Transform2D translated(const Vector2 &p_offset) const;
 	Transform2D translated_local(const Vector2 &p_offset) const;
 	Transform2D rotated(const real_t p_angle) const;
+	Transform2D rotated_local(const real_t p_angle) const;
 
 	Transform2D untranslated() const;
 
diff --git a/core/math/transform_3d.cpp b/core/math/transform_3d.cpp
index c497a276f3..a634faca9a 100644
--- a/core/math/transform_3d.cpp
+++ b/core/math/transform_3d.cpp
@@ -62,7 +62,15 @@ void Transform3D::rotate(const Vector3 &p_axis, real_t p_angle) {
 }
 
 Transform3D Transform3D::rotated(const Vector3 &p_axis, real_t p_angle) const {
-	return Transform3D(Basis(p_axis, p_angle), Vector3()) * (*this);
+	// Equivalent to left multiplication
+	Basis p_basis(p_axis, p_angle);
+	return Transform3D(p_basis * basis, p_basis.xform(origin));
+}
+
+Transform3D Transform3D::rotated_local(const Vector3 &p_axis, real_t p_angle) const {
+	// Equivalent to right multiplication
+	Basis p_basis(p_axis, p_angle);
+	return Transform3D(basis * p_basis, origin);
 }
 
 void Transform3D::rotate_basis(const Vector3 &p_axis, real_t p_angle) {
@@ -120,9 +128,13 @@ void Transform3D::scale(const Vector3 &p_scale) {
 }
 
 Transform3D Transform3D::scaled(const Vector3 &p_scale) const {
-	Transform3D t = *this;
-	t.scale(p_scale);
-	return t;
+	// Equivalent to left multiplication
+	return Transform3D(basis.scaled(p_scale), origin * p_scale);
+}
+
+Transform3D Transform3D::scaled_local(const Vector3 &p_scale) const {
+	// Equivalent to right multiplication
+	return Transform3D(basis.scaled_local(p_scale), origin);
 }
 
 void Transform3D::scale_basis(const Vector3 &p_scale) {
@@ -139,10 +151,14 @@ void Transform3D::translate_local(const Vector3 &p_translation) {
 	}
 }
 
+Transform3D Transform3D::translated(const Vector3 &p_translation) const {
+	// Equivalent to left multiplication
+	return Transform3D(basis, origin + p_translation);
+}
+
 Transform3D Transform3D::translated_local(const Vector3 &p_translation) const {
-	Transform3D t = *this;
-	t.translate_local(p_translation);
-	return t;
+	// Equivalent to right multiplication
+	return Transform3D(basis, origin + basis.xform(p_translation));
 }
 
 void Transform3D::orthonormalize() {
diff --git a/core/math/transform_3d.h b/core/math/transform_3d.h
index 1f8026043f..b572e90859 100644
--- a/core/math/transform_3d.h
+++ b/core/math/transform_3d.h
@@ -46,6 +46,7 @@ struct _NO_DISCARD_ Transform3D {
 	Transform3D affine_inverse() const;
 
 	Transform3D rotated(const Vector3 &p_axis, real_t p_angle) const;
+	Transform3D rotated_local(const Vector3 &p_axis, real_t p_angle) const;
 
 	void rotate(const Vector3 &p_axis, real_t p_angle);
 	void rotate_basis(const Vector3 &p_axis, real_t p_angle);
@@ -55,9 +56,11 @@ struct _NO_DISCARD_ Transform3D {
 
 	void scale(const Vector3 &p_scale);
 	Transform3D scaled(const Vector3 &p_scale) const;
+	Transform3D scaled_local(const Vector3 &p_scale) const;
 	void scale_basis(const Vector3 &p_scale);
 	void translate_local(real_t p_tx, real_t p_ty, real_t p_tz);
 	void translate_local(const Vector3 &p_translation);
+	Transform3D translated(const Vector3 &p_translation) const;
 	Transform3D translated_local(const Vector3 &p_translation) const;
 
 	const Basis &get_basis() const { return basis; }