diff --git a/Source/Engine/Animations/AnimationUtils.h b/Source/Engine/Animations/AnimationUtils.h index a7f85f124..c90afcea3 100644 --- a/Source/Engine/Animations/AnimationUtils.h +++ b/Source/Engine/Animations/AnimationUtils.h @@ -84,21 +84,21 @@ namespace AnimationUtils } template - FORCE_INLINE static void Interpolate(const T& a, const T& b, float alpha, T& result) + FORCE_INLINE static void Interpolate(const T& a, const T& b, float t, T& result) { - result = (T)(a + alpha * (b - a)); + result = (T)(a + t * (b - a)); } template<> - FORCE_INLINE void Interpolate(const Vector3& a, const Vector3& b, float alpha, Vector3& result) + FORCE_INLINE void Interpolate(const Vector3& a, const Vector3& b, float t, Vector3& result) { - Vector3::Lerp(a, b, alpha, result); + Vector3::Lerp(a, b, t, result); } template<> - FORCE_INLINE void Interpolate(const Quaternion& a, const Quaternion& b, float alpha, Quaternion& result) + FORCE_INLINE void Interpolate(const Quaternion& a, const Quaternion& b, float t, Quaternion& result) { - Quaternion::Slerp(a, b, alpha, result); + Quaternion::Slerp(a, b, t, result); } static void WrapTime(float& time, float start, float end, bool loop) @@ -134,98 +134,111 @@ namespace AnimationUtils /// Evaluates a cubic Hermite curve at a specific point. /// /// The time parameter that at which to evaluate the curve, in range [0, 1]. - /// The starting point (at t=0). - /// The ending point (at t=1). - /// The starting tangent (at t=0). - /// The ending tangent (at t = 1). + /// The starting point (at t=0). + /// The ending point (at t=1). + /// The starting tangent (at t=0). + /// The ending tangent (at t = 1). /// The evaluated value. template - static void CubicHermite(const float t, const T& pointA, const T& pointB, const T& tangentA, const T& tangentB, T* result) + static void CubicHermite(const T& p0, const T& p1, const T& t0, const T& t1, float t, T& result) { - const float t2 = t * t; - const float t3 = t2 * t; - - float a = 2 * t3 - 3 * t2 + 1; - float b = t3 - 2 * t2 + t; - float c = -2 * t3 + 3 * t2; - float d = t3 - t2; - - *result = a * pointA + b * tangentA + c * pointB + d * tangentB; + const float tt = t * t; + const float ttt = tt * t; + result = (2 * ttt - 3 * tt + 1) * p0 + (ttt - 2 * tt + t) * t0 + (-2 * ttt + 3 * tt) * p1 + (ttt - tt) * t1; } /// /// Evaluates the first derivative of a cubic Hermite curve at a specific point. /// /// The time parameter that at which to evaluate the curve, in range [0, 1]. - /// The starting point (at t=0). - /// The ending point (at t=1). - /// The starting tangent (at t=0). - /// The ending tangent (at t = 1). + /// The starting point (at t=0). + /// The ending point (at t=1). + /// The starting tangent (at t=0). + /// The ending tangent (at t=1). /// The evaluated value. template - static void CubicHermiteD1(const float t, const T& pointA, const T& pointB, const T& tangentA, const T& tangentB, T* result) + static void CubicHermiteFirstDerivative(const T& p0, const T& p1, const T& t0, const T& t1, float t, T& result) { - const float t2 = t * t; - - float a = 6 * t2 - 6 * t; - float b = 3 * t2 - 4 * t + 1; - float c = -6 * t2 + 6 * t; - float d = 3 * t2 - 2 * t; - - *result = a * pointA + b * tangentA + c * pointB + d * tangentB; + const float tt = t * t; + result = (6 * tt - 6 * t) * p0 + (3 * tt - 4 * t + 1) * t0 + (-6 * tt + 6 * t) * p1 + (3 * tt - 2 * t) * t1; } template - static void Bezier(const T& p0, const T& p1, const T& p2, const T& p3, float alpha, T& result) + static void Bezier(const T& p0, const T& p1, const T& p2, const T& p3, float t, T& result) { T p01, p12, p23, p012, p123; - Interpolate(p0, p1, alpha, p01); - Interpolate(p1, p2, alpha, p12); - Interpolate(p2, p3, alpha, p23); - Interpolate(p01, p12, alpha, p012); - Interpolate(p12, p23, alpha, p123); - Interpolate(p012, p123, alpha, result); + Interpolate(p0, p1, t, p01); + Interpolate(p1, p2, t, p12); + Interpolate(p2, p3, t, p23); + Interpolate(p01, p12, t, p012); + Interpolate(p12, p23, t, p123); + Interpolate(p012, p123, t, result); } template<> - void Bezier(const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3, float alpha, Vector2& result) + void Bezier(const Vector2& p0, const Vector2& p1, const Vector2& p2, const Vector2& p3, float t, Vector2& result) { - const float u = 1.0f - alpha; - const float tt = alpha * alpha; + const float u = 1.0f - t; + const float tt = t * t; const float uu = u * u; const float uuu = uu * u; - const float ttt = tt * alpha; - result = uuu * p0 + 3 * uu * alpha * p1 + 3 * u * tt * p2 + ttt * p3; + const float ttt = tt * t; + result = uuu * p0 + 3 * uu * t * p1 + 3 * u * tt * p2 + ttt * p3; } template<> - void Bezier(const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3, float alpha, Vector3& result) + void Bezier(const Vector3& p0, const Vector3& p1, const Vector3& p2, const Vector3& p3, float t, Vector3& result) { - const float u = 1.0f - alpha; - const float tt = alpha * alpha; + const float u = 1.0f - t; + const float tt = t * t; const float uu = u * u; const float uuu = uu * u; - const float ttt = tt * alpha; - result = uuu * p0 + 3 * uu * alpha * p1 + 3 * u * tt * p2 + ttt * p3; + const float ttt = tt * t; + result = uuu * p0 + 3 * uu * t * p1 + 3 * u * tt * p2 + ttt * p3; } template<> - void Bezier(const Quaternion& p0, const Quaternion& p1, const Quaternion& p2, const Quaternion& p3, float alpha, Quaternion& result) + void Bezier(const Quaternion& p0, const Quaternion& p1, const Quaternion& p2, const Quaternion& p3, float t, Quaternion& result) { Quaternion p01, p12, p23, p012, p123; - Quaternion::Slerp(p0, p1, alpha, p01); - Quaternion::Slerp(p1, p2, alpha, p12); - Quaternion::Slerp(p2, p3, alpha, p23); - Quaternion::Slerp(p01, p12, alpha, p012); - Quaternion::Slerp(p12, p23, alpha, p123); - Quaternion::Slerp(p012, p123, alpha, result); + Quaternion::Slerp(p0, p1, t, p01); + Quaternion::Slerp(p1, p2, t, p12); + Quaternion::Slerp(p2, p3, t, p23); + Quaternion::Slerp(p01, p12, t, p012); + Quaternion::Slerp(p12, p23, t, p123); + Quaternion::Slerp(p012, p123, t, result); } template<> - void Bezier(const Transform& p0, const Transform& p1, const Transform& p2, const Transform& p3, float alpha, Transform& result) + void Bezier(const Transform& p0, const Transform& p1, const Transform& p2, const Transform& p3, float t, Transform& result) { - Bezier(p0.Translation, p1.Translation, p2.Translation, p3.Translation, alpha, result.Translation); - Bezier(p0.Orientation, p1.Orientation, p2.Orientation, p3.Orientation, alpha, result.Orientation); - Bezier(p0.Scale, p1.Scale, p2.Scale, p3.Scale, alpha, result.Scale); + Bezier(p0.Translation, p1.Translation, p2.Translation, p3.Translation, t, result.Translation); + Bezier(p0.Orientation, p1.Orientation, p2.Orientation, p3.Orientation, t, result.Orientation); + Bezier(p0.Scale, p1.Scale, p2.Scale, p3.Scale, t, result.Scale); + } + + template + static void BezierFirstDerivative(const T& p0, const T& p1, const T& p2, const T& p3, float t, T& result) + { + const float u = 1.0f - t; + const float tt = t * t; + const float uu = u * u; + result = 3.0f * uu * (p1 - p0) + 6.0f * u * t * (p2 - p1) + 3.0f * tt * (p3 - p2); + } + + template<> + static void BezierFirstDerivative(const Quaternion& p0, const Quaternion& p1, const Quaternion& p2, const Quaternion& p3, float t, Quaternion& result) + { + Vector3 euler; + BezierFirstDerivative(p0.GetEuler(), p1.GetEuler(), p2.GetEuler(), p3.GetEuler(), t, euler); + result = Quaternion::Euler(euler); + } + + template<> + static void BezierFirstDerivative(const Transform& p0, const Transform& p1, const Transform& p2, const Transform& p3, float t, Transform& result) + { + BezierFirstDerivative(p0.Translation, p1.Translation, p2.Translation, p3.Translation, t, result.Translation); + BezierFirstDerivative(p0.Orientation, p1.Orientation, p2.Orientation, p3.Orientation, t, result.Orientation); + BezierFirstDerivative(p0.Scale, p1.Scale, p2.Scale, p3.Scale, t, result.Scale); } } diff --git a/Source/Engine/Animations/Curve.h b/Source/Engine/Animations/Curve.h index 618e0ee0c..24dcd87a8 100644 --- a/Source/Engine/Animations/Curve.h +++ b/Source/Engine/Animations/Curve.h @@ -48,6 +48,11 @@ public: result = a.Value; } + FORCE_INLINE static void InterpolateFirstDerivative(const StepCurveKeyframe& a, const StepCurveKeyframe& b, float alpha, float length, T& result) + { + result = AnimationUtils::GetZero(); + } + FORCE_INLINE static void InterpolateKey(const StepCurveKeyframe& a, const StepCurveKeyframe& b, float alpha, float length, StepCurveKeyframe& result) { result = a; @@ -97,6 +102,11 @@ public: AnimationUtils::Interpolate(a.Value, b.Value, alpha, result); } + FORCE_INLINE static void InterpolateFirstDerivative(const LinearCurveKeyframe& a, const LinearCurveKeyframe& b, float alpha, float length, T& result) + { + result = b.Value - a.Value; + } + FORCE_INLINE static void InterpolateKey(const LinearCurveKeyframe& a, const LinearCurveKeyframe& b, float alpha, float length, LinearCurveKeyframe& result) { result.Time = a.Time + (b.Time - a.Time) * alpha; @@ -157,20 +167,23 @@ public: { T leftTangent = a.Value + a.TangentOut * length; T rightTangent = b.Value + b.TangentIn * length; + AnimationUtils::CubicHermite( a.Value, b.Value, leftTangent, rightTangent, alpha, result); + } - AnimationUtils::CubicHermite(alpha, a.Value, b.Value, leftTangent, rightTangent, result); + static void InterpolateFirstDerivative(const HermiteCurveKeyframe& a, const HermiteCurveKeyframe& b, float alpha, float length, T& result) + { + T leftTangent = a.Value + a.TangentOut * length; + T rightTangent = b.Value + b.TangentIn * length; + AnimationUtils::CubicHermiteFirstDerivative( a.Value, b.Value, leftTangent, rightTangent, alpha, result); } static void InterpolateKey(const HermiteCurveKeyframe& a, const HermiteCurveKeyframe& b, float alpha, float length, HermiteCurveKeyframe& result) { result.Time = a.Time + length * alpha; - T leftTangent = a.Value + a.TangentOut * length; T rightTangent = b.Value + b.TangentIn * length; - - AnimationUtils::CubicHermite(alpha, a.Value, b.Value, leftTangent, rightTangent, result.Value); - AnimationUtils::CubicHermiteD1(alpha, a.Value, b.Value, leftTangent, rightTangent, result.TangentIn); - + AnimationUtils::CubicHermite(a.Value, b.Value, leftTangent, rightTangent, alpha, result.Value); + AnimationUtils::CubicHermiteFirstDerivative(a.Value, b.Value, leftTangent, rightTangent, alpha, result.TangentIn); result.TangentIn /= length; result.TangentOut = result.TangentIn; } @@ -238,20 +251,24 @@ public: T leftTangent, rightTangent; AnimationUtils::GetTangent(a.Value, a.TangentOut, length, leftTangent); AnimationUtils::GetTangent(b.Value, b.TangentIn, length, rightTangent); - AnimationUtils::Bezier(a.Value, leftTangent, rightTangent, b.Value, alpha, result); } + static void InterpolateFirstDerivative(const BezierCurveKeyframe& a, const BezierCurveKeyframe& b, float alpha, float length, T& result) + { + T leftTangent, rightTangent; + AnimationUtils::GetTangent(a.Value, a.TangentOut, length, leftTangent); + AnimationUtils::GetTangent(b.Value, b.TangentIn, length, rightTangent); + AnimationUtils::BezierFirstDerivative(a.Value, leftTangent, rightTangent, b.Value, alpha, result); + } + static void InterpolateKey(const BezierCurveKeyframe& a, const BezierCurveKeyframe& b, float alpha, float length, BezierCurveKeyframe& result) { result.Time = a.Time + length * alpha; - T leftTangent, rightTangent; AnimationUtils::GetTangent(a.Value, a.TangentOut, length, leftTangent); AnimationUtils::GetTangent(b.Value, b.TangentIn, length, rightTangent); - AnimationUtils::Bezier(a.Value, leftTangent, rightTangent, b.Value, alpha, result.Value); - result.TangentIn = a.TangentOut; result.TangentOut = b.TangentIn; } @@ -366,6 +383,48 @@ public: KeyFrame::Interpolate(leftKey, rightKey, t, length, result); } + /// + /// Evaluates the first derivative of the animation curve at the specified time (aka velocity). + /// + /// The keyframes data container. + /// The calculated first derivative from the curve at provided time. + /// The time to evaluate the curve at. + /// If true the curve will loop when it goes past the end or beginning. Otherwise the curve value will be clamped. + void EvaluateFirstDerivative(const KeyFrameData& data, T& result, float time, bool loop = true) const + { + const int32 count = data.Length(); + if (count == 0) + { + result = _default; + return; + } + + const float start = 0; + const float end = data[count - 1].Time; + AnimationUtils::WrapTime(time, start, end, loop); + + int32 leftKeyIdx; + int32 rightKeyIdx; + FindKeys(data, time, leftKeyIdx, rightKeyIdx); + + const KeyFrame& leftKey = data[leftKeyIdx]; + const KeyFrame& rightKey = data[rightKeyIdx]; + + if (leftKeyIdx == rightKeyIdx) + { + result = leftKey.Value; + return; + } + + const float length = rightKey.Time - leftKey.Time; + + // Scale from arbitrary range to [0, 1] + float t = Math::NearEqual(length, 0.0f) ? 0.0f : (time - leftKey.Time) / length; + + // Evaluate the derivative at the curve + KeyFrame::InterpolateFirstDerivative(leftKey, rightKey, t, length, result); + } + /// /// Evaluates the animation curve key at the specified time. /// @@ -586,6 +645,18 @@ public: Base::Evaluate(data, result, time, loop); } + /// + /// Evaluates the first derivative of the animation curve at the specified time (aka velocity). + /// + /// The calculated first derivative from the curve at provided time. + /// The time to evaluate the curve at. + /// If true the curve will loop when it goes past the end or beginning. Otherwise the curve value will be clamped. + void EvaluateFirstDerivative(T& result, float time, bool loop = true) const + { + typename Base::KeyFrameData data(_keyframes); + Base::EvaluateFirstDerivative(data, result, time, loop); + } + /// /// Evaluates the animation curve key at the specified time. ///