[wip] cubic hermite

TODO: split to multiple commits TODO: test TODO: cubic hermite quat
mosra · Aug 5, 2018 · 63d3684 · 63d3684
1 parent 1eb4f6a
commit 63d3684
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diff --git a/doc/snippets/MagnumMath.cpp b/doc/snippets/MagnumMath.cpp
@@ -25,6 +25,7 @@
 
 #include "Magnum/Magnum.h"
 #include "Magnum/Math/Color.h"
+#include "Magnum/Math/CubicHermite.h"
 #include "Magnum/Math/DualComplex.h"
 #include "Magnum/Math/DualQuaternion.h"
 #include "Magnum/Math/Half.h"
@@ -593,6 +594,18 @@ static_cast<void>(q1);
 static_cast<void>(q2);
 }
 
+{
+/* [CubicHermitePoint-fromBezier] */
+CubicBezier2D segment;
+auto startPoint = CubicHermitePoint2D::fromBezier(
+    {Vector2{}, Vector2{}, Vector2{}, segment[3]}, segment);
+auto endPoint = CubicHermitePoint2D::fromBezier(segment,
+    {segment[0], Vector2{}, Vector2{}, Vector2{}});
+/* [CubicHermitePoint-fromBezier] */
+static_cast<void>(startPoint);
+static_cast<void>(endPoint);
+}
+
 {
 /* [Deg-usage] */
 using namespace Math::Literals;

diff --git a/src/Magnum/Animation/Interpolation.cpp b/src/Magnum/Animation/Interpolation.cpp
@@ -25,6 +25,7 @@
 
 #include "Interpolation.h"
 
+#include "Magnum/Math/CubicHermite.h"
 #include "Magnum/Math/DualQuaternion.h"
 
 namespace Magnum { namespace Animation {
@@ -36,6 +37,7 @@ Debug& operator<<(Debug& debug, const Interpolation value) {
         #define _c(value) case Interpolation::value: return debug << "Animation::Interpolation::" #value;
         _c(Constant)
         _c(Linear)
+        _c(Spline)
         _c(Custom)
         #undef _c
         /* LCOV_EXCL_STOP */
@@ -66,6 +68,7 @@ template<class T> auto TypeTraits<Math::Quaternion<T>, Math::Quaternion<T>>::int
         case Interpolation::Constant: return Math::select;
         case Interpolation::Linear: return Math::slerp;
 
+        case Interpolation::Spline:
         case Interpolation::Custom: ; /* nope */
     }
 
@@ -77,6 +80,19 @@ template<class T> auto TypeTraits<Math::DualQuaternion<T>, Math::DualQuaternion<
         case Interpolation::Constant: return Math::select;
         case Interpolation::Linear: return Math::sclerp;
 
+        case Interpolation::Spline:
+        case Interpolation::Custom: ; /* nope */
+    }
+
+    CORRADE_ASSERT(false, "Animation::interpolatorFor(): can't deduce interpolator function for" << interpolation, {});
+}
+
+template<UnsignedInt dimensions, class T> auto TypeTraits<Math::CubicHermitePoint<dimensions, T>, Math::Vector<std::size_t(dimensions), T>>::interpolator(Interpolation interpolation) -> Interpolator {
+    switch(interpolation) {
+        case Interpolation::Constant: return Math::select;
+        case Interpolation::Linear: return Math::lerp;
+        case Interpolation::Spline: return Math::splerp;
+
         case Interpolation::Custom: ; /* nope */
     }
 
@@ -85,6 +101,8 @@ template<class T> auto TypeTraits<Math::DualQuaternion<T>, Math::DualQuaternion<
 
 template struct MAGNUM_EXPORT TypeTraits<Math::Quaternion<Float>, Math::Quaternion<Float>>;
 template struct MAGNUM_EXPORT TypeTraits<Math::DualQuaternion<Float>, Math::DualQuaternion<Float>>;
+template struct MAGNUM_EXPORT TypeTraits<Math::CubicHermitePoint<2, Float>, Math::Vector<2, Float>>;
+template struct MAGNUM_EXPORT TypeTraits<Math::CubicHermitePoint<3, Float>, Math::Vector<3, Float>>;
 
 }
 

diff --git a/src/Magnum/Animation/Interpolation.h b/src/Magnum/Animation/Interpolation.h
@@ -60,6 +60,13 @@ enum class Interpolation: UnsignedByte {
      */
     Linear,
 
+    /**
+     * Spline interpolation.
+     *
+     * @see @ref Math::splerp()
+     */
+    Spline,
+
     /**
      * Custom interpolation. An user-supplied interpolation function should be
      * used.
@@ -96,12 +103,15 @@ faster but less precise results.
 Interpolation type  | Value type        | Result type   | Interpolator
 ------------------- | ----------------- | ------------- | ------------
 @ref Interpolation::Constant | any `V`  | `V`           | @ref Math::select()
+@ref Interpolation::Constant | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::select(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::select()"
 @ref Interpolation::Linear | @cpp bool @ce <b></b> | @cpp bool @ce <b></b> | @ref Math::select()
 @ref Interpolation::Linear | @ref Math::BoolVector | @ref Math::BoolVector | @ref Math::select()
 @ref Interpolation::Linear | any scalar `V` | `V`       | @ref Math::lerp()
 @ref Interpolation::Linear | any vector `V` | `V`       | @ref Math::lerp()
 @ref Interpolation::Linear | @ref Math::Quaternion | @ref Math::Quaternion | @ref Math::slerp(const Quaternion<T>&, const Quaternion<T>&, T) "Math::slerp()"
 @ref Interpolation::Linear | @ref Math::DualQuaternion | @ref Math::DualQuaternion | @ref Math::sclerp(const DualQuaternion<T>&, const DualQuaternion<T>&, T) "Math::sclerp()"
+@ref Interpolation::Linear | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::lerp(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::lerp()"
+@ref Interpolation::Spline | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::splerp(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::splerp()"
 
 @see @ref interpolate(), @ref interpolateStrict()
 @experimental
@@ -222,6 +232,7 @@ template<class V> auto TypeTraits<V, V>::interpolator(Interpolation interpolatio
         case Interpolation::Constant: return Math::select;
         case Interpolation::Linear: return Math::lerp;
 
+        case Interpolation::Spline:
         case Interpolation::Custom: ; /* nope */
     }
 
@@ -239,6 +250,7 @@ template<class T> auto TypeTraitsBool<T>::interpolator(Interpolation interpolati
         case Interpolation::Constant:
         case Interpolation::Linear: return Math::select;
 
+        case Interpolation::Spline:
         case Interpolation::Custom: ; /* nope */
     }
 
@@ -259,6 +271,14 @@ template<class T> struct MAGNUM_EXPORT TypeTraits<Math::DualQuaternion<T>, Math:
     static Interpolator interpolator(Interpolation interpolation);
 };
 
+/* Cubic Hermite spline point has a different result type */
+/** @todo get rid of the std::size_t() cast (all math types should have UInt) */
+template<UnsignedInt dimensions, class T> struct MAGNUM_EXPORT TypeTraits<Math::CubicHermitePoint<dimensions, T>, Math::Vector<std::size_t(dimensions), T>> {
+    typedef Math::Vector<std::size_t(dimensions), T>(*Interpolator)(const Math::CubicHermitePoint<dimensions, T>&, const Math::CubicHermitePoint<dimensions, T>&, Float);
+
+    static Interpolator interpolator(Interpolation interpolation);
+};
+
 }
 
 /* Needs to be defined later so it can pick up the TypeTraits definitions */

diff --git a/src/Magnum/Animation/Test/PlayerTest.cpp b/src/Magnum/Animation/Test/PlayerTest.cpp
@@ -833,6 +833,10 @@ void PlayerTest::runFor100YearsFloat() {
 
     CORRADE_COMPARE(player.state(), State::Playing);
     {
+        /* Asm.js uses doubles for all floating-point calculations, so we don't
+           lose any precision and thus even the "run for 100 years" test passes
+           there. Unfortunately it's not possible to detect if this is asm.js
+           so the XFAIL is done like this. */
         #ifndef CORRADE_TARGET_EMSCRIPTEN
         CORRADE_EXPECT_FAIL_IF(data.failsFuzzyFloat, "Imprecision larger than 2.5e-4f.");
         #else

diff --git a/src/Magnum/Animation/Track.h b/src/Magnum/Animation/Track.h
@@ -63,13 +63,16 @@ are common combinations:
 Interpolation type  | Value type        | Result type   | Interpolator
 ------------------- | ----------------- | ------------- | ------------
 Constant            | any `V`           | `V`           | @ref Math::select()
+Constant | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::select(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::select()"
 Linear  | @cpp bool @ce <b></b> | @cpp bool @ce <b></b> | @ref Math::select()
 Linear  | @ref Math::BoolVector | @ref Math::BoolVector | @ref Math::select()
 Linear              | any scalar `V`    | `V`           | @ref Math::lerp()
 Linear              | any vector `V`    | `V`           | @ref Math::lerp()
 Linear              | @ref Math::Quaternion | @ref Math::Quaternion | @ref Math::lerp(const Quaternion<T>&, const Quaternion<T>&, T) "Math::lerp()"
+Linear | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::lerp(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::lerp()"
 Spherical linear    | @ref Math::Quaternion | @ref Math::Quaternion | @ref Math::slerp(const Quaternion<T>&, const Quaternion<T>&, T) "Math::slerp()"
 Screw linear        | @ref Math::DualQuaternion | @ref Math::DualQuaternion | @ref Math::sclerp(const DualQuaternion<T>&, const DualQuaternion<T>&, T) "Math::sclerp()"
+Spline | @ref Math::CubicHermitePoint | @ref Math::Vector | @ref Math::splerp(const CubicHermitePoint<dimensions, T>&, const CubicHermitePoint<dimensions, T>&, T) "Math::splerp()"
 
 It's also possible to supply a generic interpolation behavior by passing the
 @ref Interpolation enum to the constructor. In case the interpolator function

diff --git a/src/Magnum/Magnum.h b/src/Magnum/Magnum.h
@@ -456,6 +456,12 @@ typedef Math::CubicBezier2D<Float> CubicBezier2D;
 /** @brief Float three-dimensional cubic Bézier curve */
 typedef Math::CubicBezier3D<Float> CubicBezier3D;
 
+/** @brief Float two-dimensional cubic Hermite spline point */
+typedef Math::CubicHermitePoint2D<Float> CubicHermitePoint2D;
+
+/** @brief Float three-dimensional cubic Hermite spline point */
+typedef Math::CubicHermitePoint3D<Float> CubicHermitePoint3D;
+
 /** @brief Float complex number */
 typedef Math::Complex<Float> Complex;
 
@@ -641,6 +647,12 @@ typedef Math::CubicBezier2D<Float> CubicBezier2Dd;
 /** @brief Double three-dimensional cubic Bézier curve */
 typedef Math::CubicBezier3D<Float> CubicBezier3Dd;
 
+/** @brief Double two-dimensional cubic Hermite spline point */
+typedef Math::CubicHermitePoint2D<Double> CubicHermitePoint2Dd;
+
+/** @brief Double three-dimensional cubic Hermite spline point */
+typedef Math::CubicHermitePoint3D<Double> CubicHermitePoint3Dd;
+
 /** @brief Double complex number */
 typedef Math::Complex<Double> Complexd;
 

diff --git a/src/Magnum/Math/CMakeLists.txt b/src/Magnum/Math/CMakeLists.txt
@@ -30,6 +30,7 @@ set(MagnumMath_HEADERS
     Color.h
     Complex.h
     Constants.h
+    CubicHermite.h
     Distance.h
     Dual.h
     DualComplex.h