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C#: Add `CubicInterpolateInTime`

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Raul Santos 2022-08-24 12:30:14 +02:00
parent 4c5cefe4fe
commit 623f4a52ca
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5 changed files with 170 additions and 1 deletions
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30
modules/mono/glue/GodotSharp/GodotSharp/Core/Mathf.cs
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@ -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>
@ -192,6 +193,33 @@ namespace Godot
(-pre + 3.0f * from - 3.0f * to + post) * (weight * weight * weight));
}
/// <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.

69
modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
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@ -195,6 +195,75 @@ namespace Godot
return q1.Slerp(q2, weight);
}
/// <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>

23
modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
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@ -215,6 +215,29 @@ 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.

24
modules/mono/glue/GodotSharp/GodotSharp/Core/Vector3.cs
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@ -208,6 +208,30 @@ 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.

25
modules/mono/glue/GodotSharp/GodotSharp/Core/Vector4.cs
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@ -192,6 +192,31 @@ 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>