C#: Replace Xform and XformInv with * operator

- In cases where both `Xform`/`XformInv` and the `*` operator were
implemented the `Xform`/`XformInv` methods were removed in favor of the
`*` operator.
- In cases where the `Xform`/`XformInv` existed but not the `*` operator,
the `Xform`/`XformInv` methods were replaced with the `*` operator.
- In cases where no method existed, a new `*` operator has been
implemented to support the same operations that are supported in GDScript.
- Fixes the `Transform.Xform` and `Transform.XformInv` with `Rect2`
implementation to use a zero `Rect2` size to start expanding from
(which is how it's implemented in C++).

modules/mono/editor/script_templates/CharacterBody3D/basic_movement.cs

@@ -26,7 +26,7 @@ public override void _PhysicsProcess(float delta)
         // Get the input direction and handle the movement/deceleration.
         // As good practice, you should replace UI actions with custom gameplay actions.
         Vector2 inputDir = Input.GetVector("ui_left", "ui_right", "ui_up", "ui_down");
-        Vector3 direction = Transform.basis.Xform(new Vector3(inputDir.x, 0, inputDir.y)).Normalized();
+        Vector3 direction = (Transform.basis * new Vector3(inputDir.x, 0, inputDir.y)).Normalized();
         if (direction != Vector3.Zero)
         {
             velocity.x = direction.x * Speed;

modules/mono/glue/GodotSharp/GodotSharp/Core/Basis.cs

@@ -618,41 +618,6 @@ public Basis Transposed()
             return tr;
         }
 
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by the basis matrix.
-        /// </summary>
-        /// <seealso cref="XformInv(Vector3)"/>
-        /// <param name="v">A vector to transform.</param>
-        /// <returns>The transformed vector.</returns>
-        public Vector3 Xform(Vector3 v)
-        {
-            return new Vector3
-            (
-                Row0.Dot(v),
-                Row1.Dot(v),
-                Row2.Dot(v)
-            );
-        }
-
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by the transposed basis matrix.
-        ///
-        /// Note: This results in a multiplication by the inverse of the
-        /// basis matrix only if it represents a rotation-reflection.
-        /// </summary>
-        /// <seealso cref="Xform(Vector3)"/>
-        /// <param name="v">A vector to inversely transform.</param>
-        /// <returns>The inversely transformed vector.</returns>
-        public Vector3 XformInv(Vector3 v)
-        {
-            return new Vector3
-            (
-                Row0[0] * v.x + Row1[0] * v.y + Row2[0] * v.z,
-                Row0[1] * v.x + Row1[1] * v.y + Row2[1] * v.z,
-                Row0[2] * v.x + Row1[2] * v.y + Row2[2] * v.z
-            );
-        }
-
         private static readonly Basis[] _orthoBases = {
             new Basis(1f, 0f, 0f, 0f, 1f, 0f, 0f, 0f, 1f),
             new Basis(0f, -1f, 0f, 1f, 0f, 0f, 0f, 0f, 1f),
@@ -856,6 +821,41 @@ public static Basis FromScale(Vector3 scale)
             );
         }
 
+        /// <summary>
+        /// Returns a Vector3 transformed (multiplied) by the basis matrix.
+        /// </summary>
+        /// <param name="basis">The basis matrix transformation to apply.</param>
+        /// <param name="vector">A Vector3 to transform.</param>
+        /// <returns>The transformed Vector3.</returns>
+        public static Vector3 operator *(Basis basis, Vector3 vector)
+        {
+            return new Vector3
+            (
+                basis.Row0.Dot(vector),
+                basis.Row1.Dot(vector),
+                basis.Row2.Dot(vector)
+            );
+        }
+
+        /// <summary>
+        /// Returns a Vector3 transformed (multiplied) by the transposed basis matrix.
+        ///
+        /// Note: This results in a multiplication by the inverse of the
+        /// basis matrix only if it represents a rotation-reflection.
+        /// </summary>
+        /// <param name="vector">A Vector3 to inversely transform.</param>
+        /// <param name="basis">The basis matrix transformation to apply.</param>
+        /// <returns>The inversely transformed vector.</returns>
+        public static Vector3 operator *(Vector3 vector, Basis basis)
+        {
+            return new Vector3
+            (
+                basis.Row0[0] * vector.x + basis.Row1[0] * vector.y + basis.Row2[0] * vector.z,
+                basis.Row0[1] * vector.x + basis.Row1[1] * vector.y + basis.Row2[1] * vector.z,
+                basis.Row0[2] * vector.x + basis.Row1[2] * vector.y + basis.Row2[2] * vector.z
+            );
+        }
+
         /// <summary>
         /// Returns <see langword="true"/> if the basis matrices are exactly
         /// equal. Note: Due to floating-point precision errors, consider using

modules/mono/glue/GodotSharp/GodotSharp/Core/Projection.cs

@@ -355,7 +355,7 @@ public real_t GetLodMultiplier()
 
         public int GetPixelsPerMeter(int forPixelWidth)
         {
-            Vector3 result = Xform(new Vector3(1, 0, -1));
+            Vector3 result = this * new Vector3(1, 0, -1);
 
             return (int)((result.x * (real_t)0.5 + (real_t)0.5) * forPixelWidth);
         }
@@ -588,21 +588,53 @@ public bool IsOrthogonal()
         }
 
         /// <summary>
-        /// Returns a vector transformed (multiplied) by this projection.
+        /// Returns a Vector4 transformed (multiplied) by the projection.
         /// </summary>
         /// <param name="proj">The projection to apply.</param>
-        /// <param name="v">A vector to transform.</param>
-        /// <returns>The transformed vector.</returns>
-        public static Vector4 operator *(Projection proj, Vector4 v)
+        /// <param name="vector">A Vector4 to transform.</param>
+        /// <returns>The transformed Vector4.</returns>
+        public static Vector4 operator *(Projection proj, Vector4 vector)
         {
             return new Vector4(
-                proj.x.x * v.x + proj.y.x * v.y + proj.z.x * v.z + proj.w.x * v.w,
-                proj.x.y * v.x + proj.y.y * v.y + proj.z.y * v.z + proj.w.y * v.w,
-                proj.x.z * v.x + proj.y.z * v.y + proj.z.z * v.z + proj.w.z * v.w,
-                proj.x.w * v.x + proj.y.w * v.y + proj.z.w * v.z + proj.w.w * v.w
+                proj.x.x * vector.x + proj.y.x * vector.y + proj.z.x * vector.z + proj.w.x * vector.w,
+                proj.x.y * vector.x + proj.y.y * vector.y + proj.z.y * vector.z + proj.w.y * vector.w,
+                proj.x.z * vector.x + proj.y.z * vector.y + proj.z.z * vector.z + proj.w.z * vector.w,
+                proj.x.w * vector.x + proj.y.w * vector.y + proj.z.w * vector.z + proj.w.w * vector.w
             );
         }
 
+        /// <summary>
+        /// Returns a Vector4 transformed (multiplied) by the inverse projection.
+        /// </summary>
+        /// <param name="proj">The projection to apply.</param>
+        /// <param name="vector">A Vector4 to transform.</param>
+        /// <returns>The inversely transformed Vector4.</returns>
+        public static Vector4 operator *(Vector4 vector, Projection proj)
+        {
+            return new Vector4(
+                proj.x.x * vector.x + proj.x.y * vector.y + proj.x.z * vector.z + proj.x.w * vector.w,
+                proj.y.x * vector.x + proj.y.y * vector.y + proj.y.z * vector.z + proj.y.w * vector.w,
+                proj.z.x * vector.x + proj.z.y * vector.y + proj.z.z * vector.z + proj.z.w * vector.w,
+                proj.w.x * vector.x + proj.w.y * vector.y + proj.w.z * vector.z + proj.w.w * vector.w
+            );
+        }
+
+        /// <summary>
+        /// Returns a Vector3 transformed (multiplied) by the projection.
+        /// </summary>
+        /// <param name="proj">The projection to apply.</param>
+        /// <param name="vector">A Vector3 to transform.</param>
+        /// <returns>The transformed Vector3.</returns>
+        public static Vector3 operator *(Projection proj, Vector3 vector)
+        {
+            Vector3 ret = new Vector3(
+                proj.x.x * vector.x + proj.y.x * vector.y + proj.z.x * vector.z + proj.w.x,
+                proj.x.y * vector.x + proj.y.y * vector.y + proj.z.y * vector.z + proj.w.y,
+                proj.x.z * vector.x + proj.y.z * vector.y + proj.z.z * vector.z + proj.w.z
+            );
+            return ret / (proj.x.w * vector.x + proj.y.w * vector.y + proj.z.w * vector.z + proj.w.w);
+        }
+
         /// <summary>
         /// Returns <see langword="true"/> if the projections are exactly equal.
         /// </summary>
@@ -714,21 +746,6 @@ public Vector4 this[int column]
             }
         }
 
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by this projection.
-        /// </summary>
-        /// <param name="v">A vector to transform.</param>
-        /// <returns>The transformed vector.</returns>
-        private Vector3 Xform(Vector3 v)
-        {
-            Vector3 ret = new Vector3(
-                x.x * v.x + y.x * v.y + z.x * v.z + w.x,
-                x.y * v.x + y.y * v.y + z.y * v.z + w.y,
-                x.z * v.x + y.z * v.y + z.z * v.z + w.z
-            );
-            return ret / (x.w * v.x + y.w * v.y + z.w * v.z + w.w);
-        }
-
         // Constants
         private static readonly Projection _zero = new Projection(
             new Vector4(0, 0, 0, 0),

modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs

@@ -313,24 +313,6 @@ public Quaternion Slerpni(Quaternion to, real_t weight)
             );
         }
 
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by this quaternion.
-        /// </summary>
-        /// <param name="v">A vector to transform.</param>
-        /// <returns>The transformed vector.</returns>
-        public Vector3 Xform(Vector3 v)
-        {
-#if DEBUG
-            if (!IsNormalized())
-            {
-                throw new InvalidOperationException("Quaternion is not normalized");
-            }
-#endif
-            var u = new Vector3(x, y, z);
-            Vector3 uv = u.Cross(v);
-            return v + (((uv * w) + u.Cross(uv)) * 2);
-        }
-
         // Constants
         private static readonly Quaternion _identity = new Quaternion(0, 0, 0, 1);
 
@@ -460,6 +442,36 @@ public Quaternion(Vector3 axis, real_t angle)
             );
         }
 
+        /// <summary>
+        /// Returns a Vector3 rotated (multiplied) by the quaternion.
+        /// </summary>
+        /// <param name="quaternion">The quaternion to rotate by.</param>
+        /// <param name="vector">A Vector3 to transform.</param>
+        /// <returns>The rotated Vector3.</returns>
+        public static Vector3 operator *(Quaternion quaternion, Vector3 vector)
+        {
+#if DEBUG
+            if (!quaternion.IsNormalized())
+            {
+                throw new InvalidOperationException("Quaternion is not normalized");
+            }
+#endif
+            var u = new Vector3(quaternion.x, quaternion.y, quaternion.z);
+            Vector3 uv = u.Cross(vector);
+            return vector + (((uv * quaternion.w) + u.Cross(uv)) * 2);
+        }
+
+        /// <summary>
+        /// Returns a Vector3 rotated (multiplied) by the inverse quaternion.
+        /// </summary>
+        /// <param name="vector">A Vector3 to inversely rotate.</param>
+        /// <param name="quaternion">The quaternion to rotate by.</param>
+        /// <returns>The inversely rotated Vector3.</returns>
+        public static Vector3 operator *(Vector3 vector, Quaternion quaternion)
+        {
+            return quaternion.Inverse() * vector;
+        }
+
         /// <summary>
         /// Adds each component of the left <see cref="Quaternion"/>
         /// to the right <see cref="Quaternion"/>. This operation is not
@@ -502,38 +514,6 @@ public Quaternion(Vector3 axis, real_t angle)
             return new Quaternion(-quat.x, -quat.y, -quat.z, -quat.w);
         }
 
-        /// <summary>
-        /// Rotates (multiplies) the <see cref="Vector3"/>
-        /// by the given <see cref="Quaternion"/>.
-        /// </summary>
-        /// <param name="quat">The quaternion to rotate by.</param>
-        /// <param name="vec">The vector to rotate.</param>
-        /// <returns>The rotated vector.</returns>
-        public static Vector3 operator *(Quaternion quat, Vector3 vec)
-        {
-#if DEBUG
-            if (!quat.IsNormalized())
-            {
-                throw new InvalidOperationException("Quaternion is not normalized.");
-            }
-#endif
-            var u = new Vector3(quat.x, quat.y, quat.z);
-            Vector3 uv = u.Cross(vec);
-            return vec + (((uv * quat.w) + u.Cross(uv)) * 2);
-        }
-
-        /// <summary>
-        /// Inversely rotates (multiplies) the <see cref="Vector3"/>
-        /// by the given <see cref="Quaternion"/>.
-        /// </summary>
-        /// <param name="vec">The vector to rotate.</param>
-        /// <param name="quat">The quaternion to rotate by.</param>
-        /// <returns>The inversely rotated vector.</returns>
-        public static Vector3 operator *(Vector3 vec, Quaternion quat)
-        {
-            return quat.Inverse() * vec;
-        }
-
         /// <summary>
         /// Multiplies each component of the <see cref="Quaternion"/>
         /// by the given <see cref="real_t"/>. This operation is not

modules/mono/glue/GodotSharp/GodotSharp/Core/Transform2D.cs

@@ -384,31 +384,6 @@ public Transform2D TranslatedLocal(Vector2 offset)
             return copy;
         }
 
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by this transformation matrix.
-        /// </summary>
-        /// <seealso cref="XformInv(Vector2)"/>
-        /// <param name="v">A vector to transform.</param>
-        /// <returns>The transformed vector.</returns>
-        [Obsolete("Xform is deprecated. Use the multiplication operator (Transform2D * Vector2) instead.")]
-        public Vector2 Xform(Vector2 v)
-        {
-            return new Vector2(Tdotx(v), Tdoty(v)) + origin;
-        }
-
-        /// <summary>
-        /// Returns a vector transformed (multiplied) by the inverse transformation matrix.
-        /// </summary>
-        /// <seealso cref="Xform(Vector2)"/>
-        /// <param name="v">A vector to inversely transform.</param>
-        /// <returns>The inversely transformed vector.</returns>
-        [Obsolete("XformInv is deprecated. Use the multiplication operator (Vector2 * Transform2D) instead.")]
-        public Vector2 XformInv(Vector2 v)
-        {
-            Vector2 vInv = v - origin;
-            return new Vector2(x.Dot(vInv), y.Dot(vInv));
-        }
-
         // Constants
         private static readonly Transform2D _identity = new Transform2D(1, 0, 0, 1, 0, 0);
         private static readonly Transform2D _flipX = new Transform2D(-1, 0, 0, 1, 0, 0);
@@ -502,7 +477,7 @@ public Transform2D(real_t rotation, Vector2 origin)
         }
 
         /// <summary>
-        /// Returns a Vector2 transformed (multiplied) by transformation matrix.
+        /// Returns a Vector2 transformed (multiplied) by the transformation matrix.
         /// </summary>
         /// <param name="transform">The transformation to apply.</param>
         /// <param name="vector">A Vector2 to transform.</param>
@@ -525,7 +500,7 @@ public Transform2D(real_t rotation, Vector2 origin)
         }
 
         /// <summary>
-        /// Returns a Rect2 transformed (multiplied) by transformation matrix.
+        /// Returns a Rect2 transformed (multiplied) by the transformation matrix.
         /// </summary>
         /// <param name="transform">The transformation to apply.</param>
         /// <param name="rect">A Rect2 to transform.</param>
@@ -536,7 +511,7 @@ public Transform2D(real_t rotation, Vector2 origin)
             Vector2 toX = transform.x * rect.Size.x;
             Vector2 toY = transform.y * rect.Size.y;
 
-            return new Rect2(pos, rect.Size).Expand(pos + toX).Expand(pos + toY).Expand(pos + toX + toY);
+            return new Rect2(pos, new Vector2()).Expand(pos + toX).Expand(pos + toY).Expand(pos + toX + toY);
         }
 
         /// <summary>
@@ -552,11 +527,11 @@ public Transform2D(real_t rotation, Vector2 origin)
             Vector2 to2 = new Vector2(rect.Position.x + rect.Size.x, rect.Position.y + rect.Size.y) * transform;
             Vector2 to3 = new Vector2(rect.Position.x + rect.Size.x, rect.Position.y) * transform;
 
-            return new Rect2(pos, rect.Size).Expand(to1).Expand(to2).Expand(to3);
+            return new Rect2(pos, new Vector2()).Expand(to1).Expand(to2).Expand(to3);
         }
 
         /// <summary>
-        /// Returns a copy of the given Vector2[] transformed (multiplied) by transformation matrix.
+        /// Returns a copy of the given Vector2[] transformed (multiplied) by the transformation matrix.
         /// </summary>
         /// <param name="transform">The transformation to apply.</param>
         /// <param name="array">A Vector2[] to transform.</param>