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xnamathmisc.inl
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/*++
Copyright (c) Microsoft Corporation. All rights reserved.
Module Name:
xnamathmisc.inl
Abstract:
XNA math library for Windows and Xbox 360: Quaternion, plane, and color functions.
--*/
#if defined(_MSC_VER) && (_MSC_VER > 1000)
#pragma once
#endif
#ifndef __XNAMATHMISC_INL__
#define __XNAMATHMISC_INL__
/****************************************************************************
*
* Quaternion
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
XMFINLINE BOOL XMQuaternionEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
)
{
return XMVector4Equal(Q1, Q2);
}
//------------------------------------------------------------------------------
XMFINLINE BOOL XMQuaternionNotEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
)
{
return XMVector4NotEqual(Q1, Q2);
}
//------------------------------------------------------------------------------
XMFINLINE BOOL XMQuaternionIsNaN
(
FXMVECTOR Q
)
{
return XMVector4IsNaN(Q);
}
//------------------------------------------------------------------------------
XMFINLINE BOOL XMQuaternionIsInfinite
(
FXMVECTOR Q
)
{
return XMVector4IsInfinite(Q);
}
//------------------------------------------------------------------------------
XMFINLINE BOOL XMQuaternionIsIdentity
(
FXMVECTOR Q
)
{
#if defined(_XM_NO_INTRINSICS_)
return XMVector4Equal(Q, g_XMIdentityR3.v);
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR vTemp = _mm_cmpeq_ps(Q,g_XMIdentityR3);
return (_mm_movemask_ps(vTemp)==0x0f) ? true : false;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionDot
(
FXMVECTOR Q1,
FXMVECTOR Q2
)
{
return XMVector4Dot(Q1, Q2);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionMultiply
(
FXMVECTOR Q1,
FXMVECTOR Q2
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR NegativeQ1;
XMVECTOR Q2X;
XMVECTOR Q2Y;
XMVECTOR Q2Z;
XMVECTOR Q2W;
XMVECTOR Q1WZYX;
XMVECTOR Q1ZWXY;
XMVECTOR Q1YXWZ;
XMVECTOR Result;
CONST XMVECTORU32 ControlWZYX = {XM_PERMUTE_0W, XM_PERMUTE_1Z, XM_PERMUTE_0Y, XM_PERMUTE_1X};
CONST XMVECTORU32 ControlZWXY = {XM_PERMUTE_0Z, XM_PERMUTE_0W, XM_PERMUTE_1X, XM_PERMUTE_1Y};
CONST XMVECTORU32 ControlYXWZ = {XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_1Z};
NegativeQ1 = XMVectorNegate(Q1);
Q2W = XMVectorSplatW(Q2);
Q2X = XMVectorSplatX(Q2);
Q2Y = XMVectorSplatY(Q2);
Q2Z = XMVectorSplatZ(Q2);
Q1WZYX = XMVectorPermute(Q1, NegativeQ1, ControlWZYX.v);
Q1ZWXY = XMVectorPermute(Q1, NegativeQ1, ControlZWXY.v);
Q1YXWZ = XMVectorPermute(Q1, NegativeQ1, ControlYXWZ.v);
Result = XMVectorMultiply(Q1, Q2W);
Result = XMVectorMultiplyAdd(Q1WZYX, Q2X, Result);
Result = XMVectorMultiplyAdd(Q1ZWXY, Q2Y, Result);
Result = XMVectorMultiplyAdd(Q1YXWZ, Q2Z, Result);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
static CONST XMVECTORF32 ControlWZYX = { 1.0f,-1.0f, 1.0f,-1.0f};
static CONST XMVECTORF32 ControlZWXY = { 1.0f, 1.0f,-1.0f,-1.0f};
static CONST XMVECTORF32 ControlYXWZ = {-1.0f, 1.0f, 1.0f,-1.0f};
// Copy to SSE registers and use as few as possible for x86
XMVECTOR Q2X = Q2;
XMVECTOR Q2Y = Q2;
XMVECTOR Q2Z = Q2;
XMVECTOR vResult = Q2;
// Splat with one instruction
vResult = _mm_shuffle_ps(vResult,vResult,_MM_SHUFFLE(3,3,3,3));
Q2X = _mm_shuffle_ps(Q2X,Q2X,_MM_SHUFFLE(0,0,0,0));
Q2Y = _mm_shuffle_ps(Q2Y,Q2Y,_MM_SHUFFLE(1,1,1,1));
Q2Z = _mm_shuffle_ps(Q2Z,Q2Z,_MM_SHUFFLE(2,2,2,2));
// Retire Q1 and perform Q1*Q2W
vResult = _mm_mul_ps(vResult,Q1);
XMVECTOR Q1Shuffle = Q1;
// Shuffle the copies of Q1
Q1Shuffle = _mm_shuffle_ps(Q1Shuffle,Q1Shuffle,_MM_SHUFFLE(0,1,2,3));
// Mul by Q1WZYX
Q2X = _mm_mul_ps(Q2X,Q1Shuffle);
Q1Shuffle = _mm_shuffle_ps(Q1Shuffle,Q1Shuffle,_MM_SHUFFLE(2,3,0,1));
// Flip the signs on y and z
Q2X = _mm_mul_ps(Q2X,ControlWZYX);
// Mul by Q1ZWXY
Q2Y = _mm_mul_ps(Q2Y,Q1Shuffle);
Q1Shuffle = _mm_shuffle_ps(Q1Shuffle,Q1Shuffle,_MM_SHUFFLE(0,1,2,3));
// Flip the signs on z and w
Q2Y = _mm_mul_ps(Q2Y,ControlZWXY);
// Mul by Q1YXWZ
Q2Z = _mm_mul_ps(Q2Z,Q1Shuffle);
vResult = _mm_add_ps(vResult,Q2X);
// Flip the signs on x and w
Q2Z = _mm_mul_ps(Q2Z,ControlYXWZ);
Q2Y = _mm_add_ps(Q2Y,Q2Z);
vResult = _mm_add_ps(vResult,Q2Y);
return vResult;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionLengthSq
(
FXMVECTOR Q
)
{
return XMVector4LengthSq(Q);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionReciprocalLength
(
FXMVECTOR Q
)
{
return XMVector4ReciprocalLength(Q);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionLength
(
FXMVECTOR Q
)
{
return XMVector4Length(Q);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionNormalizeEst
(
FXMVECTOR Q
)
{
return XMVector4NormalizeEst(Q);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionNormalize
(
FXMVECTOR Q
)
{
return XMVector4Normalize(Q);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionConjugate
(
FXMVECTOR Q
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Result = {
-Q.vector4_f32[0],
-Q.vector4_f32[1],
-Q.vector4_f32[2],
Q.vector4_f32[3]
};
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 NegativeOne3 = {-1.0f,-1.0f,-1.0f,1.0f};
XMVECTOR Result = _mm_mul_ps(Q,NegativeOne3);
return Result;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionInverse
(
FXMVECTOR Q
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Conjugate;
XMVECTOR L;
XMVECTOR Control;
XMVECTOR Result;
CONST XMVECTOR Zero = XMVectorZero();
L = XMVector4LengthSq(Q);
Conjugate = XMQuaternionConjugate(Q);
Control = XMVectorLessOrEqual(L, g_XMEpsilon.v);
L = XMVectorReciprocal(L);
Result = XMVectorMultiply(Conjugate, L);
Result = XMVectorSelect(Result, Zero, Control);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR Conjugate;
XMVECTOR L;
XMVECTOR Control;
XMVECTOR Result;
XMVECTOR Zero = XMVectorZero();
L = XMVector4LengthSq(Q);
Conjugate = XMQuaternionConjugate(Q);
Control = XMVectorLessOrEqual(L, g_XMEpsilon);
Result = _mm_div_ps(Conjugate,L);
Result = XMVectorSelect(Result, Zero, Control);
return Result;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionLn
(
FXMVECTOR Q
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Q0;
XMVECTOR QW;
XMVECTOR Theta;
XMVECTOR SinTheta;
XMVECTOR S;
XMVECTOR ControlW;
XMVECTOR Result;
static CONST XMVECTOR OneMinusEpsilon = {1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f};
QW = XMVectorSplatW(Q);
Q0 = XMVectorSelect(g_XMSelect1110.v, Q, g_XMSelect1110.v);
ControlW = XMVectorInBounds(QW, OneMinusEpsilon);
Theta = XMVectorACos(QW);
SinTheta = XMVectorSin(Theta);
S = XMVectorReciprocal(SinTheta);
S = XMVectorMultiply(Theta, S);
Result = XMVectorMultiply(Q0, S);
Result = XMVectorSelect(Q0, Result, ControlW);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
static CONST XMVECTORF32 OneMinusEpsilon = {1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f};
static CONST XMVECTORF32 NegOneMinusEpsilon = {-(1.0f - 0.00001f), -(1.0f - 0.00001f),-(1.0f - 0.00001f),-(1.0f - 0.00001f)};
// Get W only
XMVECTOR QW = _mm_shuffle_ps(Q,Q,_MM_SHUFFLE(3,3,3,3));
// W = 0
XMVECTOR Q0 = _mm_and_ps(Q,g_XMMask3);
// Use W if within bounds
XMVECTOR ControlW = _mm_cmple_ps(QW,OneMinusEpsilon);
XMVECTOR vTemp2 = _mm_cmpge_ps(QW,NegOneMinusEpsilon);
ControlW = _mm_and_ps(ControlW,vTemp2);
// Get theta
XMVECTOR vTheta = XMVectorACos(QW);
// Get Sine of theta
vTemp2 = XMVectorSin(vTheta);
// theta/sine of theta
vTheta = _mm_div_ps(vTheta,vTemp2);
// Here's the answer
vTheta = _mm_mul_ps(vTheta,Q0);
// Was W in bounds? If not, return input as is
vTheta = XMVectorSelect(Q0,vTheta,ControlW);
return vTheta;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionExp
(
FXMVECTOR Q
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Theta;
XMVECTOR SinTheta;
XMVECTOR CosTheta;
XMVECTOR S;
XMVECTOR Control;
XMVECTOR Zero;
XMVECTOR Result;
Theta = XMVector3Length(Q);
XMVectorSinCos(&SinTheta, &CosTheta, Theta);
S = XMVectorReciprocal(Theta);
S = XMVectorMultiply(SinTheta, S);
Result = XMVectorMultiply(Q, S);
Zero = XMVectorZero();
Control = XMVectorNearEqual(Theta, Zero, g_XMEpsilon.v);
Result = XMVectorSelect(Result, Q, Control);
Result = XMVectorSelect(CosTheta, Result, g_XMSelect1110.v);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR Theta;
XMVECTOR SinTheta;
XMVECTOR CosTheta;
XMVECTOR S;
XMVECTOR Control;
XMVECTOR Zero;
XMVECTOR Result;
Theta = XMVector3Length(Q);
XMVectorSinCos(&SinTheta, &CosTheta, Theta);
S = _mm_div_ps(SinTheta,Theta);
Result = _mm_mul_ps(Q, S);
Zero = XMVectorZero();
Control = XMVectorNearEqual(Theta, Zero, g_XMEpsilon);
Result = XMVectorSelect(Result,Q,Control);
Result = _mm_and_ps(Result,g_XMMask3);
CosTheta = _mm_and_ps(CosTheta,g_XMMaskW);
Result = _mm_or_ps(Result,CosTheta);
return Result;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMINLINE XMVECTOR XMQuaternionSlerp
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FLOAT t
)
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSlerpV(Q0, Q1, T);
}
//------------------------------------------------------------------------------
XMINLINE XMVECTOR XMQuaternionSlerpV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR T
)
{
#if defined(_XM_NO_INTRINSICS_)
// Result = Q0 * sin((1.0 - t) * Omega) / sin(Omega) + Q1 * sin(t * Omega) / sin(Omega)
XMVECTOR Omega;
XMVECTOR CosOmega;
XMVECTOR SinOmega;
XMVECTOR InvSinOmega;
XMVECTOR V01;
XMVECTOR C1000;
XMVECTOR SignMask;
XMVECTOR S0;
XMVECTOR S1;
XMVECTOR Sign;
XMVECTOR Control;
XMVECTOR Result;
XMVECTOR Zero;
CONST XMVECTOR OneMinusEpsilon = {1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f};
XMASSERT((T.vector4_f32[1] == T.vector4_f32[0]) && (T.vector4_f32[2] == T.vector4_f32[0]) && (T.vector4_f32[3] == T.vector4_f32[0]));
CosOmega = XMQuaternionDot(Q0, Q1);
Zero = XMVectorZero();
Control = XMVectorLess(CosOmega, Zero);
Sign = XMVectorSelect(g_XMOne.v, g_XMNegativeOne.v, Control);
CosOmega = XMVectorMultiply(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
SinOmega = XMVectorNegativeMultiplySubtract(CosOmega, CosOmega, g_XMOne.v);
SinOmega = XMVectorSqrt(SinOmega);
Omega = XMVectorATan2(SinOmega, CosOmega);
SignMask = XMVectorSplatSignMask();
C1000 = XMVectorSetBinaryConstant(1, 0, 0, 0);
V01 = XMVectorShiftLeft(T, Zero, 2);
SignMask = XMVectorShiftLeft(SignMask, Zero, 3);
V01 = XMVectorXorInt(V01, SignMask);
V01 = XMVectorAdd(C1000, V01);
InvSinOmega = XMVectorReciprocal(SinOmega);
S0 = XMVectorMultiply(V01, Omega);
S0 = XMVectorSin(S0);
S0 = XMVectorMultiply(S0, InvSinOmega);
S0 = XMVectorSelect(V01, S0, Control);
S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = XMVectorMultiply(S1, Sign);
Result = XMVectorMultiply(Q0, S0);
Result = XMVectorMultiplyAdd(Q1, S1, Result);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
// Result = Q0 * sin((1.0 - t) * Omega) / sin(Omega) + Q1 * sin(t * Omega) / sin(Omega)
XMVECTOR Omega;
XMVECTOR CosOmega;
XMVECTOR SinOmega;
XMVECTOR V01;
XMVECTOR S0;
XMVECTOR S1;
XMVECTOR Sign;
XMVECTOR Control;
XMVECTOR Result;
XMVECTOR Zero;
static const XMVECTORF32 OneMinusEpsilon = {1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f};
static const XMVECTORI32 SignMask2 = {0x80000000,0x00000000,0x00000000,0x00000000};
static const XMVECTORI32 MaskXY = {0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000000};
XMASSERT((XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)));
CosOmega = XMQuaternionDot(Q0, Q1);
Zero = XMVectorZero();
Control = XMVectorLess(CosOmega, Zero);
Sign = XMVectorSelect(g_XMOne, g_XMNegativeOne, Control);
CosOmega = _mm_mul_ps(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
SinOmega = _mm_mul_ps(CosOmega,CosOmega);
SinOmega = _mm_sub_ps(g_XMOne,SinOmega);
SinOmega = _mm_sqrt_ps(SinOmega);
Omega = XMVectorATan2(SinOmega, CosOmega);
V01 = _mm_shuffle_ps(T,T,_MM_SHUFFLE(2,3,0,1));
V01 = _mm_and_ps(V01,MaskXY);
V01 = _mm_xor_ps(V01,SignMask2);
V01 = _mm_add_ps(g_XMIdentityR0, V01);
S0 = _mm_mul_ps(V01, Omega);
S0 = XMVectorSin(S0);
S0 = _mm_div_ps(S0, SinOmega);
S0 = XMVectorSelect(V01, S0, Control);
S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = _mm_mul_ps(S1, Sign);
Result = _mm_mul_ps(Q0, S0);
S1 = _mm_mul_ps(S1, Q1);
Result = _mm_add_ps(Result,S1);
return Result;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionSquad
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
CXMVECTOR Q3,
FLOAT t
)
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSquadV(Q0, Q1, Q2, Q3, T);
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionSquadV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
CXMVECTOR Q3,
CXMVECTOR T
)
{
XMVECTOR Q03;
XMVECTOR Q12;
XMVECTOR TP;
XMVECTOR Two;
XMVECTOR Result;
XMASSERT( (XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)) );
TP = T;
Two = XMVectorSplatConstant(2, 0);
Q03 = XMQuaternionSlerpV(Q0, Q3, T);
Q12 = XMQuaternionSlerpV(Q1, Q2, T);
TP = XMVectorNegativeMultiplySubtract(TP, TP, TP);
TP = XMVectorMultiply(TP, Two);
Result = XMQuaternionSlerpV(Q03, Q12, TP);
return Result;
}
//------------------------------------------------------------------------------
XMINLINE VOID XMQuaternionSquadSetup
(
XMVECTOR* pA,
XMVECTOR* pB,
XMVECTOR* pC,
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
CXMVECTOR Q3
)
{
XMVECTOR SQ0, SQ2, SQ3;
XMVECTOR InvQ1, InvQ2;
XMVECTOR LnQ0, LnQ1, LnQ2, LnQ3;
XMVECTOR ExpQ02, ExpQ13;
XMVECTOR LS01, LS12, LS23;
XMVECTOR LD01, LD12, LD23;
XMVECTOR Control0, Control1, Control2;
XMVECTOR NegativeOneQuarter;
XMASSERT(pA);
XMASSERT(pB);
XMASSERT(pC);
LS12 = XMQuaternionLengthSq(XMVectorAdd(Q1, Q2));
LD12 = XMQuaternionLengthSq(XMVectorSubtract(Q1, Q2));
SQ2 = XMVectorNegate(Q2);
Control1 = XMVectorLess(LS12, LD12);
SQ2 = XMVectorSelect(Q2, SQ2, Control1);
LS01 = XMQuaternionLengthSq(XMVectorAdd(Q0, Q1));
LD01 = XMQuaternionLengthSq(XMVectorSubtract(Q0, Q1));
SQ0 = XMVectorNegate(Q0);
LS23 = XMQuaternionLengthSq(XMVectorAdd(SQ2, Q3));
LD23 = XMQuaternionLengthSq(XMVectorSubtract(SQ2, Q3));
SQ3 = XMVectorNegate(Q3);
Control0 = XMVectorLess(LS01, LD01);
Control2 = XMVectorLess(LS23, LD23);
SQ0 = XMVectorSelect(Q0, SQ0, Control0);
SQ3 = XMVectorSelect(Q3, SQ3, Control2);
InvQ1 = XMQuaternionInverse(Q1);
InvQ2 = XMQuaternionInverse(SQ2);
LnQ0 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ0));
LnQ2 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ2));
LnQ1 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, Q1));
LnQ3 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, SQ3));
NegativeOneQuarter = XMVectorSplatConstant(-1, 2);
ExpQ02 = XMVectorMultiply(XMVectorAdd(LnQ0, LnQ2), NegativeOneQuarter);
ExpQ13 = XMVectorMultiply(XMVectorAdd(LnQ1, LnQ3), NegativeOneQuarter);
ExpQ02 = XMQuaternionExp(ExpQ02);
ExpQ13 = XMQuaternionExp(ExpQ13);
*pA = XMQuaternionMultiply(Q1, ExpQ02);
*pB = XMQuaternionMultiply(SQ2, ExpQ13);
*pC = SQ2;
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionBaryCentric
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
FLOAT f,
FLOAT g
)
{
XMVECTOR Q01;
XMVECTOR Q02;
FLOAT s;
XMVECTOR Result;
s = f + g;
if ((s < 0.00001f) && (s > -0.00001f))
{
Result = Q0;
}
else
{
Q01 = XMQuaternionSlerp(Q0, Q1, s);
Q02 = XMQuaternionSlerp(Q0, Q2, s);
Result = XMQuaternionSlerp(Q01, Q02, g / s);
}
return Result;
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionBaryCentricV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
CXMVECTOR F,
CXMVECTOR G
)
{
XMVECTOR Q01;
XMVECTOR Q02;
XMVECTOR S, GS;
XMVECTOR Epsilon;
XMVECTOR Result;
XMASSERT( (XMVectorGetY(F) == XMVectorGetX(F)) && (XMVectorGetZ(F) == XMVectorGetX(F)) && (XMVectorGetW(F) == XMVectorGetX(F)) );
XMASSERT( (XMVectorGetY(G) == XMVectorGetX(G)) && (XMVectorGetZ(G) == XMVectorGetX(G)) && (XMVectorGetW(G) == XMVectorGetX(G)) );
Epsilon = XMVectorSplatConstant(1, 16);
S = XMVectorAdd(F, G);
if (XMVector4InBounds(S, Epsilon))
{
Result = Q0;
}
else
{
Q01 = XMQuaternionSlerpV(Q0, Q1, S);
Q02 = XMQuaternionSlerpV(Q0, Q2, S);
GS = XMVectorReciprocal(S);
GS = XMVectorMultiply(G, GS);
Result = XMQuaternionSlerpV(Q01, Q02, GS);
}
return Result;
}
//------------------------------------------------------------------------------
// Transformation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionIdentity()
{
#if defined(_XM_NO_INTRINSICS_)
return g_XMIdentityR3.v;
#elif defined(_XM_SSE_INTRINSICS_)
return g_XMIdentityR3;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionRotationRollPitchYaw
(
FLOAT Pitch,
FLOAT Yaw,
FLOAT Roll
)
{
XMVECTOR Angles;
XMVECTOR Q;
Angles = XMVectorSet(Pitch, Yaw, Roll, 0.0f);
Q = XMQuaternionRotationRollPitchYawFromVector(Angles);
return Q;
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionRotationRollPitchYawFromVector
(
FXMVECTOR Angles // <Pitch, Yaw, Roll, 0>
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Q, Q0, Q1;
XMVECTOR P0, P1, Y0, Y1, R0, R1;
XMVECTOR HalfAngles;
XMVECTOR SinAngles, CosAngles;
static CONST XMVECTORU32 ControlPitch = {XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X};
static CONST XMVECTORU32 ControlYaw = {XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y};
static CONST XMVECTORU32 ControlRoll = {XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z};
static CONST XMVECTOR Sign = {1.0f, -1.0f, -1.0f, 1.0f};
HalfAngles = XMVectorMultiply(Angles, g_XMOneHalf.v);
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);
P0 = XMVectorPermute(SinAngles, CosAngles, ControlPitch.v);
Y0 = XMVectorPermute(SinAngles, CosAngles, ControlYaw.v);
R0 = XMVectorPermute(SinAngles, CosAngles, ControlRoll.v);
P1 = XMVectorPermute(CosAngles, SinAngles, ControlPitch.v);
Y1 = XMVectorPermute(CosAngles, SinAngles, ControlYaw.v);
R1 = XMVectorPermute(CosAngles, SinAngles, ControlRoll.v);
Q1 = XMVectorMultiply(P1, Sign);
Q0 = XMVectorMultiply(P0, Y0);
Q1 = XMVectorMultiply(Q1, Y1);
Q0 = XMVectorMultiply(Q0, R0);
Q = XMVectorMultiplyAdd(Q1, R1, Q0);
return Q;
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR Q, Q0, Q1;
XMVECTOR P0, P1, Y0, Y1, R0, R1;
XMVECTOR HalfAngles;
XMVECTOR SinAngles, CosAngles;
static CONST XMVECTORI32 ControlPitch = {XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X};
static CONST XMVECTORI32 ControlYaw = {XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y};
static CONST XMVECTORI32 ControlRoll = {XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z};
static CONST XMVECTORF32 Sign = {1.0f, -1.0f, -1.0f, 1.0f};
HalfAngles = _mm_mul_ps(Angles, g_XMOneHalf);
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);
P0 = XMVectorPermute(SinAngles, CosAngles, ControlPitch);
Y0 = XMVectorPermute(SinAngles, CosAngles, ControlYaw);
R0 = XMVectorPermute(SinAngles, CosAngles, ControlRoll);
P1 = XMVectorPermute(CosAngles, SinAngles, ControlPitch);
Y1 = XMVectorPermute(CosAngles, SinAngles, ControlYaw);
R1 = XMVectorPermute(CosAngles, SinAngles, ControlRoll);
Q1 = _mm_mul_ps(P1, Sign);
Q0 = _mm_mul_ps(P0, Y0);
Q1 = _mm_mul_ps(Q1, Y1);
Q0 = _mm_mul_ps(Q0, R0);
Q = _mm_mul_ps(Q1, R1);
Q = _mm_add_ps(Q,Q0);
return Q;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionRotationNormal
(
FXMVECTOR NormalAxis,
FLOAT Angle
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Q;
XMVECTOR N;
XMVECTOR Scale;
N = XMVectorSelect(g_XMOne.v, NormalAxis, g_XMSelect1110.v);
XMScalarSinCos(&Scale.vector4_f32[2], &Scale.vector4_f32[3], 0.5f * Angle);
Scale.vector4_f32[0] = Scale.vector4_f32[1] = Scale.vector4_f32[2];
Q = XMVectorMultiply(N, Scale);
return Q;
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR N = _mm_and_ps(NormalAxis,g_XMMask3);
N = _mm_or_ps(N,g_XMIdentityR3);
XMVECTOR Scale = _mm_set_ps1(0.5f * Angle);
XMVECTOR vSine;
XMVECTOR vCosine;
XMVectorSinCos(&vSine,&vCosine,Scale);
Scale = _mm_and_ps(vSine,g_XMMask3);
vCosine = _mm_and_ps(vCosine,g_XMMaskW);
Scale = _mm_or_ps(Scale,vCosine);
N = _mm_mul_ps(N,Scale);
return N;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMFINLINE XMVECTOR XMQuaternionRotationAxis
(
FXMVECTOR Axis,
FLOAT Angle
)
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTOR Normal;
XMVECTOR Q;
XMASSERT(!XMVector3Equal(Axis, XMVectorZero()));
XMASSERT(!XMVector3IsInfinite(Axis));
Normal = XMVector3Normalize(Axis);
Q = XMQuaternionRotationNormal(Normal, Angle);
return Q;
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR Normal;
XMVECTOR Q;
XMASSERT(!XMVector3Equal(Axis, XMVectorZero()));
XMASSERT(!XMVector3IsInfinite(Axis));
Normal = XMVector3Normalize(Axis);
Q = XMQuaternionRotationNormal(Normal, Angle);
return Q;
#else // _XM_VMX128_INTRINSICS_
#endif // _XM_VMX128_INTRINSICS_
}
//------------------------------------------------------------------------------
XMINLINE XMVECTOR XMQuaternionRotationMatrix
(
CXMMATRIX M
)
{
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_SSE_INTRINSICS_)
XMVECTOR Q0, Q1, Q2;
XMVECTOR M00, M11, M22;
XMVECTOR CQ0, CQ1, C;
XMVECTOR CX, CY, CZ, CW;
XMVECTOR SQ1, Scale;
XMVECTOR Rsq, Sqrt, VEqualsNaN;
XMVECTOR A, B, P;
XMVECTOR PermuteSplat, PermuteSplatT;
XMVECTOR SignB, SignBT;
XMVECTOR PermuteControl, PermuteControlT;
XMVECTOR Result;
static CONST XMVECTORF32 OneQuarter = {0.25f, 0.25f, 0.25f, 0.25f};
static CONST XMVECTORF32 SignPNNP = {1.0f, -1.0f, -1.0f, 1.0f};
static CONST XMVECTORF32 SignNPNP = {-1.0f, 1.0f, -1.0f, 1.0f};
static CONST XMVECTORF32 SignNNPP = {-1.0f, -1.0f, 1.0f, 1.0f};
static CONST XMVECTORF32 SignPNPP = {1.0f, -1.0f, 1.0f, 1.0f};
static CONST XMVECTORF32 SignPPNP = {1.0f, 1.0f, -1.0f, 1.0f};
static CONST XMVECTORF32 SignNPPP = {-1.0f, 1.0f, 1.0f, 1.0f};
static CONST XMVECTORU32 Permute0X0X0Y0W = {XM_PERMUTE_0X, XM_PERMUTE_0X, XM_PERMUTE_0Y, XM_PERMUTE_0W};
static CONST XMVECTORU32 Permute0Y0Z0Z1W = {XM_PERMUTE_0Y, XM_PERMUTE_0Z, XM_PERMUTE_0Z, XM_PERMUTE_1W};
static CONST XMVECTORU32 SplatX = {XM_PERMUTE_0X, XM_PERMUTE_0X, XM_PERMUTE_0X, XM_PERMUTE_0X};
static CONST XMVECTORU32 SplatY = {XM_PERMUTE_0Y, XM_PERMUTE_0Y, XM_PERMUTE_0Y, XM_PERMUTE_0Y};
static CONST XMVECTORU32 SplatZ = {XM_PERMUTE_0Z, XM_PERMUTE_0Z, XM_PERMUTE_0Z, XM_PERMUTE_0Z};
static CONST XMVECTORU32 SplatW = {XM_PERMUTE_0W, XM_PERMUTE_0W, XM_PERMUTE_0W, XM_PERMUTE_0W};
static CONST XMVECTORU32 PermuteC = {XM_PERMUTE_0X, XM_PERMUTE_0Z, XM_PERMUTE_1X, XM_PERMUTE_1Y};
static CONST XMVECTORU32 PermuteA = {XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Z, XM_PERMUTE_0W};
static CONST XMVECTORU32 PermuteB = {XM_PERMUTE_1X, XM_PERMUTE_1W, XM_PERMUTE_0Z, XM_PERMUTE_0W};
static CONST XMVECTORU32 Permute0 = {XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1Z, XM_PERMUTE_1Y};
static CONST XMVECTORU32 Permute1 = {XM_PERMUTE_1X, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Z};
static CONST XMVECTORU32 Permute2 = {XM_PERMUTE_1Z, XM_PERMUTE_1Y, XM_PERMUTE_0Z, XM_PERMUTE_1X};
static CONST XMVECTORU32 Permute3 = {XM_PERMUTE_1Y, XM_PERMUTE_1Z, XM_PERMUTE_1X, XM_PERMUTE_0W};
M00 = XMVectorSplatX(M.r[0]);
M11 = XMVectorSplatY(M.r[1]);
M22 = XMVectorSplatZ(M.r[2]);
Q0 = XMVectorMultiply(SignPNNP.v, M00);
Q0 = XMVectorMultiplyAdd(SignNPNP.v, M11, Q0);
Q0 = XMVectorMultiplyAdd(SignNNPP.v, M22, Q0);
Q1 = XMVectorAdd(Q0, g_XMOne.v);
Rsq = XMVectorReciprocalSqrt(Q1);
VEqualsNaN = XMVectorIsNaN(Rsq);
Sqrt = XMVectorMultiply(Q1, Rsq);
Q1 = XMVectorSelect(Sqrt, Q1, VEqualsNaN);
Q1 = XMVectorMultiply(Q1, g_XMOneHalf.v);
SQ1 = XMVectorMultiply(Rsq, g_XMOneHalf.v);
CQ0 = XMVectorPermute(Q0, Q0, Permute0X0X0Y0W.v);
CQ1 = XMVectorPermute(Q0, g_XMEpsilon.v, Permute0Y0Z0Z1W.v);
C = XMVectorGreaterOrEqual(CQ0, CQ1);
CX = XMVectorSplatX(C);
CY = XMVectorSplatY(C);
CZ = XMVectorSplatZ(C);
CW = XMVectorSplatW(C);
PermuteSplat = XMVectorSelect(SplatZ.v, SplatY.v, CZ);
SignB = XMVectorSelect(SignNPPP.v, SignPPNP.v, CZ);
PermuteControl = XMVectorSelect(Permute2.v, Permute1.v, CZ);