C#: Add `BezierInterpolate` method

Adds a `BezierInterpolate` method for floats in `Mathf` and for vectors
in `Vector2` and `Vector3`.

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

@@ -197,6 +197,28 @@ namespace Godot
                             (-pre + 3.0f * from - 3.0f * to + post) * (weight * weight * weight));
         }
 
+        /// <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.
+        /// </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 BezierInterpolate(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 omt3 = omt2 * omt;
+            real_t t2 = t * t;
+            real_t t3 = t2 * t;
+
+            return start * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
+        }
+
         /// <summary>
         /// Converts an angle expressed in degrees to radians.
         /// </summary>

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

@@ -220,6 +220,27 @@ 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.
+        /// </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 vector.</param>
+        /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <returns>The interpolated vector.</returns>
+        public Vector2 BezierInterpolate(Vector2 control1, Vector2 control2, Vector2 end, real_t t)
+        {
+            // Formula from Wikipedia article on Bezier curves
+            real_t omt = 1 - t;
+            real_t omt2 = omt * omt;
+            real_t omt3 = omt2 * omt;
+            real_t t2 = t * t;
+            real_t t3 = t2 * t;
+
+            return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
+        }
+
         /// <summary>
         /// Returns the normalized vector pointing from this vector to <paramref name="to"/>.
         /// </summary>
@@ -522,9 +543,10 @@ namespace Godot
         {
             real_t startLengthSquared = LengthSquared();
             real_t endLengthSquared = to.LengthSquared();
-            if (startLengthSquared == 0.0 || endLengthSquared == 0.0) {
-              // Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
-              return Lerp(to, weight);
+            if (startLengthSquared == 0.0 || endLengthSquared == 0.0)
+            {
+                // Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
+                return Lerp(to, weight);
             }
             real_t startLength = Mathf.Sqrt(startLengthSquared);
             real_t resultLength = Mathf.Lerp(startLength, Mathf.Sqrt(endLengthSquared), weight);

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

@@ -213,6 +213,27 @@ 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.
+        /// </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 vector.</param>
+        /// <param name="t">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <returns>The interpolated vector.</returns>
+        public Vector3 BezierInterpolate(Vector3 control1, Vector3 control2, Vector3 end, real_t t)
+        {
+            // Formula from Wikipedia article on Bezier curves
+            real_t omt = 1 - t;
+            real_t omt2 = omt * omt;
+            real_t omt3 = omt2 * omt;
+            real_t t2 = t * t;
+            real_t t3 = t2 * t;
+
+            return this * omt3 + control1 * omt2 * t * 3 + control2 * omt * t2 * 3 + end * t3;
+        }
+
         /// <summary>
         /// Returns the normalized vector pointing from this vector to <paramref name="to"/>.
         /// </summary>
@@ -562,9 +583,10 @@ namespace Godot
         {
             real_t startLengthSquared = LengthSquared();
             real_t endLengthSquared = to.LengthSquared();
-            if (startLengthSquared == 0.0 || endLengthSquared == 0.0) {
-              // Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
-              return Lerp(to, weight);
+            if (startLengthSquared == 0.0 || endLengthSquared == 0.0)
+            {
+                // Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
+                return Lerp(to, weight);
             }
             real_t startLength = Mathf.Sqrt(startLengthSquared);
             real_t resultLength = Mathf.Lerp(startLength, Mathf.Sqrt(endLengthSquared), weight);