C#: Implement BezierDerivative

Adds `BezierDerivative` method to Mathf, Vector2 and Vector3 (already exposed in Core).

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

@@ -282,7 +282,7 @@ namespace Godot
 
         /// <summary>
         /// Returns the point at the given <paramref name="t"/> on a one-dimensional Bezier curve defined by
-        /// the given <paramref name="control1"/>, <paramref name="control2"/> and <paramref name="end"/> points.
+        /// the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
         /// </summary>
         /// <param name="start">The start value for the interpolation.</param>
         /// <param name="control1">Control point that defines the bezier curve.</param>
@@ -302,6 +302,27 @@ namespace Godot
             return start * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
         }
 
+        /// <summary>
+        /// Returns the derivative at the given <paramref name="t"/> on a one dimensional Bezier curve defined by
+        /// the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
+        /// </summary>
+        /// <param name="start">The start value for the interpolation.</param>
+        /// <param name="control1">Control point that defines the bezier curve.</param>
+        /// <param name="control2">Control point that defines the bezier curve.</param>
+        /// <param name="end">The destination value for the interpolation.</param>
+        /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <returns>The resulting value of the interpolation.</returns>
+        public static real_t BezierDerivative(real_t start, real_t control1, real_t control2, real_t end, real_t t)
+        {
+            // Formula from Wikipedia article on Bezier curves
+            real_t omt = 1 - t;
+            real_t omt2 = omt * omt;
+            real_t t2 = t * t;
+
+            real_t d = (control1 - start) * 3 * omt2 + (control2 - control1) * 6 * omt * t + (end - control2) * 3 * t2;
+            return d;
+        }
+
         /// <summary>
         /// Converts an angle expressed in degrees to radians.
         /// </summary>

modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs

@@ -240,7 +240,7 @@ namespace Godot
 
         /// <summary>
         /// Returns the point at the given <paramref name="t"/> on a one-dimensional Bezier curve defined by this vector
-        /// and the given <paramref name="control1"/>, <paramref name="control2"/> and <paramref name="end"/> points.
+        /// and the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
         /// </summary>
         /// <param name="control1">Control point that defines the bezier curve.</param>
         /// <param name="control2">Control point that defines the bezier curve.</param>
@@ -259,6 +259,23 @@ namespace Godot
             return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
         }
 
+        /// <summary>
+        /// Returns the derivative at the given <paramref name="t"/> on the Bezier curve defined by this vector
+        /// and the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
+        /// </summary>
+        /// <param name="control1">Control point that defines the bezier curve.</param>
+        /// <param name="control2">Control point that defines the bezier curve.</param>
+        /// <param name="end">The destination value for the interpolation.</param>
+        /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <returns>The resulting value of the interpolation.</returns>
+        public readonly Vector2 BezierDerivative(Vector2 control1, Vector2 control2, Vector2 end, real_t t)
+        {
+            return new Vector2(
+                Mathf.BezierDerivative(x, control1.x, control2.x, end.x, t),
+                Mathf.BezierDerivative(y, control1.y, control2.y, end.y, t)
+            );
+        }
+
         /// <summary>
         /// Returns the normalized vector pointing from this vector to <paramref name="to"/>.
         /// </summary>

modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs

@@ -234,7 +234,7 @@ namespace Godot
 
         /// <summary>
         /// Returns the point at the given <paramref name="t"/> on a one-dimensional Bezier curve defined by this vector
-        /// and the given <paramref name="control1"/>, <paramref name="control2"/> and <paramref name="end"/> points.
+        /// and the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
         /// </summary>
         /// <param name="control1">Control point that defines the bezier curve.</param>
         /// <param name="control2">Control point that defines the bezier curve.</param>
@@ -253,6 +253,24 @@ namespace Godot
             return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
         }
 
+        /// <summary>
+        /// Returns the derivative at the given <paramref name="t"/> on the Bezier curve defined by this vector
+        /// and the given <paramref name="control1"/>, <paramref name="control2"/>, and <paramref name="end"/> points.
+        /// </summary>
+        /// <param name="control1">Control point that defines the bezier curve.</param>
+        /// <param name="control2">Control point that defines the bezier curve.</param>
+        /// <param name="end">The destination value for the interpolation.</param>
+        /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <returns>The resulting value of the interpolation.</returns>
+        public readonly Vector3 BezierDerivative(Vector3 control1, Vector3 control2, Vector3 end, real_t t)
+        {
+            return new Vector3(
+                Mathf.BezierDerivative(x, control1.x, control2.x, end.x, t),
+                Mathf.BezierDerivative(y, control1.y, control2.y, end.y, t),
+                Mathf.BezierDerivative(z, control1.z, control2.z, end.y, t)
+            );
+        }
+
         /// <summary>
         /// Returns the normalized vector pointing from this vector to <paramref name="to"/>.
         /// </summary>