C#: Add `CubicInterpolateInTime`

5 files changed, 170 insertions, 1 deletions

diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs
index 00e775e6ad..124410a1c2 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs
@@ -175,7 +175,8 @@ namespace Godot
         }
 
         /// <summary>
-        /// Cubic interpolates between two values by a normalized value with pre and post values.
+        /// Cubic interpolates between two values by the factor defined in <paramref name="weight"/>
+        /// with pre and post values.
         /// </summary>
         /// <param name="from">The start value for interpolation.</param>
         /// <param name="to">The destination value for interpolation.</param>
@@ -193,6 +194,33 @@ namespace Godot
         }
 
         /// <summary>
+        /// Cubic interpolates between two values by the factor defined in <paramref name="weight"/>
+        /// with pre and post values.
+        /// It can perform smoother interpolation than <see cref="CubicInterpolate"/>
+        /// by the time values.
+        /// </summary>
+        /// <param name="from">The start value for interpolation.</param>
+        /// <param name="to">The destination value for interpolation.</param>
+        /// <param name="pre">The value which before "from" value for interpolation.</param>
+        /// <param name="post">The value which after "to" value for interpolation.</param>
+        /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <param name="toT"></param>
+        /// <param name="preT"></param>
+        /// <param name="postT"></param>
+        /// <returns>The resulting value of the interpolation.</returns>
+        public static real_t CubicInterpolateInTime(real_t from, real_t to, real_t pre, real_t post, real_t weight, real_t toT, real_t preT, real_t postT)
+        {
+            /* Barry-Goldman method */
+            real_t t = Lerp(0.0f, toT, weight);
+            real_t a1 = Lerp(pre, from, preT == 0 ? 0.0f : (t - preT) / -preT);
+            real_t a2 = Lerp(from, to, toT == 0 ? 0.5f : t / toT);
+            real_t a3 = Lerp(to, post, postT - toT == 0 ? 1.0f : (t - toT) / (postT - toT));
+            real_t b1 = Lerp(a1, a2, toT - preT == 0 ? 0.0f : (t - preT) / (toT - preT));
+            real_t b2 = Lerp(a2, a3, postT == 0 ? 1.0f : t / postT);
+            return Lerp(b1, b2, toT == 0 ? 0.5f : t / toT);
+        }
+
+        /// <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>
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
index 8568ecf299..5cc478ca71 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
@@ -196,6 +196,75 @@ namespace Godot
         }
 
         /// <summary>
+        /// Performs a spherical cubic interpolation between quaternions <paramref name="preA"/>, this quaternion,
+        /// <paramref name="b"/>, and <paramref name="postB"/>, by the given amount <paramref name="weight"/>.
+        /// It can perform smoother interpolation than <see cref="SphericalCubicInterpolate"/>
+        /// by the time values.
+        /// </summary>
+        /// <param name="b">The destination quaternion.</param>
+        /// <param name="preA">A quaternion before this quaternion.</param>
+        /// <param name="postB">A quaternion after <paramref name="b"/>.</param>
+        /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <param name="bT"></param>
+        /// <param name="preAT"></param>
+        /// <param name="postBT"></param>
+        /// <returns>The interpolated quaternion.</returns>
+        public Quaternion SphericalCubicInterpolateInTime(Quaternion b, Quaternion preA, Quaternion postB, real_t weight, real_t bT, real_t preAT, real_t postBT)
+        {
+#if DEBUG
+            if (!IsNormalized())
+            {
+                throw new InvalidOperationException("Quaternion is not normalized");
+            }
+            if (!b.IsNormalized())
+            {
+                throw new ArgumentException("Argument is not normalized", nameof(b));
+            }
+#endif
+
+            // Align flip phases.
+            Quaternion fromQ = new Basis(this).GetRotationQuaternion();
+            Quaternion preQ = new Basis(preA).GetRotationQuaternion();
+            Quaternion toQ = new Basis(b).GetRotationQuaternion();
+            Quaternion postQ = new Basis(postB).GetRotationQuaternion();
+
+            // Flip quaternions to shortest path if necessary.
+            bool flip1 = Math.Sign(fromQ.Dot(preQ)) < 0;
+            preQ = flip1 ? -preQ : preQ;
+            bool flip2 = Math.Sign(fromQ.Dot(toQ)) < 0;
+            toQ = flip2 ? -toQ : toQ;
+            bool flip3 = flip2 ? toQ.Dot(postQ) <= 0 : Math.Sign(toQ.Dot(postQ)) < 0;
+            postQ = flip3 ? -postQ : postQ;
+
+            // Calc by Expmap in fromQ space.
+            Quaternion lnFrom = new Quaternion(0, 0, 0, 0);
+            Quaternion lnTo = (fromQ.Inverse() * toQ).Log();
+            Quaternion lnPre = (fromQ.Inverse() * preQ).Log();
+            Quaternion lnPost = (fromQ.Inverse() * postQ).Log();
+            Quaternion ln = new Quaternion(
+                Mathf.CubicInterpolateInTime(lnFrom.x, lnTo.x, lnPre.x, lnPost.x, weight, bT, preAT, postBT),
+                Mathf.CubicInterpolateInTime(lnFrom.y, lnTo.y, lnPre.y, lnPost.y, weight, bT, preAT, postBT),
+                Mathf.CubicInterpolateInTime(lnFrom.z, lnTo.z, lnPre.z, lnPost.z, weight, bT, preAT, postBT),
+                0);
+            Quaternion q1 = fromQ * ln.Exp();
+
+            // Calc by Expmap in toQ space.
+            lnFrom = (toQ.Inverse() * fromQ).Log();
+            lnTo = new Quaternion(0, 0, 0, 0);
+            lnPre = (toQ.Inverse() * preQ).Log();
+            lnPost = (toQ.Inverse() * postQ).Log();
+            ln = new Quaternion(
+                Mathf.CubicInterpolateInTime(lnFrom.x, lnTo.x, lnPre.x, lnPost.x, weight, bT, preAT, postBT),
+                Mathf.CubicInterpolateInTime(lnFrom.y, lnTo.y, lnPre.y, lnPost.y, weight, bT, preAT, postBT),
+                Mathf.CubicInterpolateInTime(lnFrom.z, lnTo.z, lnPre.z, lnPost.z, weight, bT, preAT, postBT),
+                0);
+            Quaternion q2 = toQ * ln.Exp();
+
+            // To cancel error made by Expmap ambiguity, do blends.
+            return q1.Slerp(q2, weight);
+        }
+
+        /// <summary>
         /// Returns the dot product of two quaternions.
         /// </summary>
         /// <param name="b">The other quaternion.</param>
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
index 03ee12884b..b2964db8cd 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
@@ -216,6 +216,29 @@ namespace Godot
         }
 
         /// <summary>
+        /// Performs a cubic interpolation between vectors <paramref name="preA"/>, this vector,
+        /// <paramref name="b"/>, and <paramref name="postB"/>, by the given amount <paramref name="weight"/>.
+        /// It can perform smoother interpolation than <see cref="CubicInterpolate"/>
+        /// by the time values.
+        /// </summary>
+        /// <param name="b">The destination vector.</param>
+        /// <param name="preA">A vector before this vector.</param>
+        /// <param name="postB">A vector after <paramref name="b"/>.</param>
+        /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <param name="t"></param>
+        /// <param name="preAT"></param>
+        /// <param name="postBT"></param>
+        /// <returns>The interpolated vector.</returns>
+        public Vector2 CubicInterpolateInTime(Vector2 b, Vector2 preA, Vector2 postB, real_t weight, real_t t, real_t preAT, real_t postBT)
+        {
+            return new Vector2
+            (
+                Mathf.CubicInterpolateInTime(x, b.x, preA.x, postB.x, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(y, b.y, preA.y, postB.y, weight, t, preAT, postBT)
+            );
+        }
+
+        /// <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>
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs
index cdba06c089..b53ca5e45a 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs
@@ -209,6 +209,30 @@ namespace Godot
         }
 
         /// <summary>
+        /// Performs a cubic interpolation between vectors <paramref name="preA"/>, this vector,
+        /// <paramref name="b"/>, and <paramref name="postB"/>, by the given amount <paramref name="weight"/>.
+        /// It can perform smoother interpolation than <see cref="CubicInterpolate"/>
+        /// by the time values.
+        /// </summary>
+        /// <param name="b">The destination vector.</param>
+        /// <param name="preA">A vector before this vector.</param>
+        /// <param name="postB">A vector after <paramref name="b"/>.</param>
+        /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <param name="t"></param>
+        /// <param name="preAT"></param>
+        /// <param name="postBT"></param>
+        /// <returns>The interpolated vector.</returns>
+        public Vector3 CubicInterpolateInTime(Vector3 b, Vector3 preA, Vector3 postB, real_t weight, real_t t, real_t preAT, real_t postBT)
+        {
+            return new Vector3
+            (
+                Mathf.CubicInterpolateInTime(x, b.x, preA.x, postB.x, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(y, b.y, preA.y, postB.y, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(z, b.z, preA.z, postB.z, weight, t, preAT, postBT)
+            );
+        }
+
+        /// <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>
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector4.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector4.cs
index 705da04692..b6f243dfb4 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector4.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector4.cs
@@ -193,6 +193,31 @@ namespace Godot
         }
 
         /// <summary>
+        /// Performs a cubic interpolation between vectors <paramref name="preA"/>, this vector,
+        /// <paramref name="b"/>, and <paramref name="postB"/>, by the given amount <paramref name="weight"/>.
+        /// It can perform smoother interpolation than <see cref="CubicInterpolate"/>
+        /// by the time values.
+        /// </summary>
+        /// <param name="b">The destination vector.</param>
+        /// <param name="preA">A vector before this vector.</param>
+        /// <param name="postB">A vector after <paramref name="b"/>.</param>
+        /// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
+        /// <param name="t"></param>
+        /// <param name="preAT"></param>
+        /// <param name="postBT"></param>
+        /// <returns>The interpolated vector.</returns>
+        public Vector4 CubicInterpolateInTime(Vector4 b, Vector4 preA, Vector4 postB, real_t weight, real_t t, real_t preAT, real_t postBT)
+        {
+            return new Vector4
+            (
+                Mathf.CubicInterpolateInTime(x, b.x, preA.x, postB.x, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(y, b.y, preA.y, postB.y, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(y, b.z, preA.z, postB.z, weight, t, preAT, postBT),
+                Mathf.CubicInterpolateInTime(w, b.w, preA.w, postB.w, weight, t, preAT, postBT)
+            );
+        }
+
+        /// <summary>
         /// Returns the normalized vector pointing from this vector to <paramref name="to"/>.
         /// </summary>
         /// <param name="to">The other vector to point towards.</param>