Project-Reboot-3.0/Project Reboot 3.0/UnrealMath.cpp

#include "Rotator.h"
#include "Quat.h"
#include "UnrealMathUtility.h"

#define INV_PI			(0.31830988618f)
#define HALF_PI			(1.57079632679f)
#define PI 					(3.1415926535897932f)

static FORCEINLINE void SinCos(float* ScalarSin, float* ScalarCos, float  Value)
{
	// Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
	float quotient = (INV_PI * 0.5f) * Value;
	if (Value >= 0.0f)
	{
		quotient = (float)((int)(quotient + 0.5f));
	}
	else
	{
		quotient = (float)((int)(quotient - 0.5f));
	}
	float y = Value - (2.0f * PI) * quotient;

	// Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
	float sign;
	if (y > HALF_PI)
	{
		y = PI - y;
		sign = -1.0f;
	}
	else if (y < -HALF_PI)
	{
		y = -PI - y;
		sign = -1.0f;
	}
	else
	{
		sign = +1.0f;
	}

	float y2 = y * y;

	// 11-degree minimax approximation
	*ScalarSin = (((((-2.3889859e-08f * y2 + 2.7525562e-06f) * y2 - 0.00019840874f) * y2 + 0.0083333310f) * y2 - 0.16666667f) * y2 + 1.0f) * y;

	// 10-degree minimax approximation
	float p = ((((-2.6051615e-07f * y2 + 2.4760495e-05f) * y2 - 0.0013888378f) * y2 + 0.041666638f) * y2 - 0.5f) * y2 + 1.0f;
	*ScalarCos = sign * p;
}

struct FQuat FRotator::Quaternion()
{
#if PLATFORM_ENABLE_VECTORINTRINSICS
	const VectorRegister Angles = MakeVectorRegister(Rotator.Pitch, Rotator.Yaw, Rotator.Roll, 0.0f);
	const VectorRegister HalfAngles = VectorMultiply(Angles, DEG_TO_RAD_HALF);

	VectorRegister SinAngles, CosAngles;
	VectorSinCos(&SinAngles, &CosAngles, &HalfAngles);

	// Vectorized conversion, measured 20% faster than using scalar version after VectorSinCos.
	// Indices within VectorRegister (for shuffles): P=0, Y=1, R=2
	const VectorRegister SR = VectorReplicate(SinAngles, 2);
	const VectorRegister CR = VectorReplicate(CosAngles, 2);

	const VectorRegister SY_SY_CY_CY_Temp = VectorShuffle(SinAngles, CosAngles, 1, 1, 1, 1);

	const VectorRegister SP_SP_CP_CP = VectorShuffle(SinAngles, CosAngles, 0, 0, 0, 0);
	const VectorRegister SY_CY_SY_CY = VectorShuffle(SY_SY_CY_CY_Temp, SY_SY_CY_CY_Temp, 0, 2, 0, 2);

	const VectorRegister CP_CP_SP_SP = VectorShuffle(CosAngles, SinAngles, 0, 0, 0, 0);
	const VectorRegister CY_SY_CY_SY = VectorShuffle(SY_SY_CY_CY_Temp, SY_SY_CY_CY_Temp, 2, 0, 2, 0);

	const uint32 Neg = uint32(1 << 31);
	const uint32 Pos = uint32(0);
	const VectorRegister SignBitsLeft = MakeVectorRegister(Pos, Neg, Pos, Pos);
	const VectorRegister SignBitsRight = MakeVectorRegister(Neg, Neg, Neg, Pos);
	const VectorRegister LeftTerm = VectorBitwiseXor(SignBitsLeft, VectorMultiply(CR, VectorMultiply(SP_SP_CP_CP, SY_CY_SY_CY)));
	const VectorRegister RightTerm = VectorBitwiseXor(SignBitsRight, VectorMultiply(SR, VectorMultiply(CP_CP_SP_SP, CY_SY_CY_SY)));

	FQuat RotationQuat;
	const VectorRegister Result = VectorAdd(LeftTerm, RightTerm);
	VectorStoreAligned(Result, &RotationQuat);
#else
	const float DEG_TO_RAD = PI / (180.f);
	const float DIVIDE_BY_2 = DEG_TO_RAD / 2.f;
	float SP, SY, SR;
	float CP, CY, CR;

	SinCos(&SP, &CP, Pitch * DIVIDE_BY_2);
	SinCos(&SY, &CY, Yaw * DIVIDE_BY_2);
	SinCos(&SR, &CR, Roll * DIVIDE_BY_2);

	FQuat RotationQuat{};
	RotationQuat.X = CR * SP * SY - SR * CP * CY;
	RotationQuat.Y = -CR * SP * CY - SR * CP * SY;
	RotationQuat.Z = CR * CP * SY - SR * SP * CY;
	RotationQuat.W = CR * CP * CY + SR * SP * SY;
#endif // PLATFORM_ENABLE_VECTORINTRINSICS

#if ENABLE_NAN_DIAGNOSTIC || DO_CHECK
	// Very large inputs can cause NaN's. Want to catch this here
	ensureMsgf(!RotationQuat.ContainsNaN(), TEXT("Invalid input to FRotator::Quaternion - generated NaN output: %s"), *RotationQuat.ToString());
#endif

	return RotationQuat;
}

FVector FRotator::Vector() const
{
	float CP, SP, CY, SY;
	SinCos(&SP, &CP, Pitch * (PI / 180.0f));
	SinCos(&SY, &CY, Yaw * (PI / 180.0f));
	FVector V = FVector(CP * CY, CP * SY, SP);

	return V;
}

FRotator FQuat::Rotator() const
{
	const float SingularityTest = Z * X - W * Y;
	const float YawY = 2.f * (W * Z + X * Y);
	const float YawX = (1.f - 2.f * (FMath::Square(Y) + FMath::Square(Z)));

	// reference 
	// http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
	// http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/

	// this value was found from experience, the above websites recommend different values
	// but that isn't the case for us, so I went through different testing, and finally found the case 
	// where both of world lives happily. 
	const float SINGULARITY_THRESHOLD = 0.4999995f;
	const float RAD_TO_DEG = (180.f) / PI;
	FRotator RotatorFromQuat;

	if (SingularityTest < -SINGULARITY_THRESHOLD)
	{
		RotatorFromQuat.Pitch = -90.f;
		RotatorFromQuat.Yaw = FMath::Atan2(YawY, YawX) * RAD_TO_DEG;
		RotatorFromQuat.Roll = FRotator::NormalizeAxis(-RotatorFromQuat.Yaw - (2.f * FMath::Atan2(X, W) * RAD_TO_DEG));
	}
	else if (SingularityTest > SINGULARITY_THRESHOLD)
	{
		RotatorFromQuat.Pitch = 90.f;
		RotatorFromQuat.Yaw = FMath::Atan2(YawY, YawX) * RAD_TO_DEG;
		RotatorFromQuat.Roll = FRotator::NormalizeAxis(RotatorFromQuat.Yaw - (2.f * FMath::Atan2(X, W) * RAD_TO_DEG));
	}
	else
	{
		RotatorFromQuat.Pitch = FMath::FastAsin(2.f * (SingularityTest)) * RAD_TO_DEG;
		RotatorFromQuat.Yaw = FMath::Atan2(YawY, YawX) * RAD_TO_DEG;
		RotatorFromQuat.Roll = FMath::Atan2(-2.f * (W * X + Y * Z), (1.f - 2.f * (FMath::Square(X) + FMath::Square(Y)))) * RAD_TO_DEG;
	}

	return RotatorFromQuat;
}