Add Slerp methods on Vectors

#3682

Source/Engine/Core/Math/Vector2.cs

@@ -954,6 +954,33 @@ namespace FlaxEngine
             return result;
         }
 
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        /// <param name="result">>When the method completes, contains the linear interpolation of the two vectors.</param>
+        public static void Slerp(ref Vector2 start, ref Vector2 end, float amount, out Vector2 result)
+        {
+            var dot = Mathr.Clamp(Dot(start, end), -1.0f, 1.0f);
+            var theta = Mathr.Acos(dot) * amount;
+            Vector2 relativeVector = (end - start * dot).Normalized;
+            result = ((start * Mathr.Cos(theta)) + (relativeVector * Mathr.Sin(theta)));
+        }
+
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        public static Vector2 Slerp(Vector2 start, Vector2 end, float amount)
+        {
+            Slerp(ref start, ref end, amount, out Vector2 result);
+            return result;
+        }
+
         /// <summary>
         /// Performs a gradual change of a vector towards a specified target over time
         /// </summary>

Source/Engine/Core/Math/Vector2.h

@@ -558,6 +558,24 @@ public:
         return result;
     }
 
+    // Performs a spherical linear interpolation between two vectors.
+    static void Slerp(const Vector2Base& start, const Vector2Base& end, T amount, Vector2Base& result) 
+    {
+        T dot = Math::Clamp(Dot(start, end), -1.0f, 1.0f);
+        T theta = Math::Acos(dot) * amount;
+        Vector2Base relativeVector = end - start * dot;
+        relativeVector.Normalize();
+        result = ((start * Math::Cos(theta)) + (relativeVector * Math::Sin(theta)));
+    }
+
+    // Performs a spherical linear interpolation between two vectors.
+    static Vector2Base Slerp(const Vector2Base& start, const Vector2Base& end, T amount) 
+    {
+        Vector2Base result;
+        Slerp(start, end, amount, result);
+        return result;
+    }
+
 public:
     /// <summary>
     /// Calculates the area of the triangle.

Source/Engine/Core/Math/Vector3.cs

@@ -1043,6 +1043,33 @@ namespace FlaxEngine
             return result;
         }
 
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        /// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
+        public static void Slerp(ref Vector3 start, ref Vector3 end, float amount, out Vector3 result)
+        {
+            var dot = Mathr.Clamp(Dot(start, end), -1.0f, 1.0f);
+            var theta = Mathr.Acos(dot) * amount;
+            Vector3 relativeVector = (end - start * dot).Normalized;
+            result = ((start * Mathr.Cos(theta)) + (relativeVector * Mathr.Sin(theta)));
+        }
+
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        public static Vector3 Slerp(Vector3 start, Vector3 end, float amount)
+        {
+            Slerp(ref start, ref end, amount, out var result);
+            return result;
+        }
+
         /// <summary>
         /// Performs a gradual change of a vector towards a specified target over time
         /// </summary>

Source/Engine/Core/Math/Vector3.h

@@ -686,6 +686,24 @@ public:
         return result;
     }
 
+    // Performs a spherical linear interpolation between two vectors.
+    static void Slerp(const Vector3Base& start, const Vector3Base& end, T amount, Vector3Base& result) 
+    {
+        T dot = Math::Clamp(Dot(start, end), -1.0f, 1.0f);
+        T theta = Math::Acos(dot) * amount;
+        Vector3Base relativeVector = end - start * dot;
+        relativeVector.Normalize();
+        result = ((start * Math::Cos(theta)) + (relativeVector * Math::Sin(theta)));
+    }
+
+    // Performs a spherical linear interpolation between two vectors.
+    static Vector3Base Slerp(const Vector3Base& start, const Vector3Base& end, T amount)
+    {
+        Vector3Base result;
+        Slerp(start, end, amount, result);
+        return result;
+    }
+
     // Performs a cubic interpolation between two vectors.
     static void SmoothStep(const Vector3Base& start, const Vector3Base& end, T amount, Vector3Base& result)
     {

Source/Engine/Core/Math/Vector4.cs

@@ -891,6 +891,33 @@ namespace FlaxEngine
             return result;
         }
 
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        /// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
+        public static void Slerp(ref Vector4 start, ref Vector4 end, Real amount, out Vector4 result)
+        {
+            var dot = Mathr.Clamp(Dot(start, end), -1.0f, 1.0f);
+            var theta = Mathr.Acos(dot) * amount;
+            Vector4 relativeVector = (end - start * dot).Normalized;
+            result = ((start * Mathr.Cos(theta)) + (relativeVector * Mathr.Sin(theta)));
+        }
+
+        /// <summary>
+        /// Performs a spherical linear interpolation between two vectors.
+        /// </summary>
+        /// <param name="start">Start vector.</param>
+        /// <param name="end">End vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end" />.</param>
+        public static Vector4 Slerp(Vector4 start, Vector4 end, Real amount)
+        {
+            Slerp(ref start, ref end, amount, out var result);
+            return result;
+        }
+
         /// <summary>
         /// Performs a cubic interpolation between two vectors.
         /// </summary>

Source/Engine/Core/Math/Vector4.h

@@ -566,6 +566,24 @@ public:
         return result;
     }
 
+    // Performs a spherical linear interpolation between two vectors.
+    static void Slerp(const Vector4Base& start, const Vector4Base& end, T amount, Vector4Base& result) 
+    {
+        T dot = Math::Clamp(Dot(start, end), -1.0f, 1.0f);
+        T theta = Math::Acos(dot) * amount;
+        Vector4Base relativeVector = end - start * dot;
+        relativeVector.Normalize();
+        result = ((start * Math::Cos(theta)) + (relativeVector * Math::Sin(theta)));
+    }
+
+    // Performs a spherical linear interpolation between two vectors.
+    static Vector4Base Slerp(const Vector4Base& start, const Vector4Base& end, T amount)
+    {
+        Vector4Base result;
+        Slerp(start, end, amount, result);
+        return result;
+    }
+
     FLAXENGINE_API static Vector4Base Transform(const Vector4Base& v, const Matrix& m);
 };