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Add XMMatrixPerspectiveFovInfiniteReverseZLH/RH #334

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2 changes: 2 additions & 0 deletions Inc/DirectXMath.h
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Original file line number Diff line number Diff line change
Expand Up @@ -1650,6 +1650,8 @@ namespace DirectX
XMMATRIX XM_CALLCONV XMMatrixPerspectiveRH(float ViewWidth, float ViewHeight, float NearZ, float FarZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovLH(float FovAngleY, float AspectRatio, float NearZ, float FarZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovRH(float FovAngleY, float AspectRatio, float NearZ, float FarZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovInfiniteReverseZLH(float FovAngleY, float AspectRatio, float NearZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovInfiniteReverseZRH(float FovAngleY, float AspectRatio, float NearZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveOffCenterLH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixPerspectiveOffCenterRH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ) noexcept;
XMMATRIX XM_CALLCONV XMMatrixOrthographicLH(float ViewWidth, float ViewHeight, float NearZ, float FarZ) noexcept;
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215 changes: 215 additions & 0 deletions Inc/DirectXMathMatrix.inl
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Expand Up @@ -2639,6 +2639,221 @@ inline XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovRH
#endif
}

//------------------------------------------------------------------------------
// Infinite reversed-z perspective projection (FarZ = +infinity, depth maps NearZ->1, Infinity->0)
// This avoids NaN that would result from passing infinity to XMMatrixPerspectiveFovLH.
// Left-handed coordinate system.

inline XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovInfiniteReverseZLH
(
float FovAngleY,
float AspectRatio,
float NearZ
) noexcept
{
assert(NearZ > 0.f);
assert(!XMScalarNearEqual(FovAngleY, 0.0f, 0.00001f * 2.0f));
assert(!XMScalarNearEqual(AspectRatio, 0.0f, 0.00001f));

#if defined(_XM_NO_INTRINSICS_)

float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
float Width = Height / AspectRatio;

// As FarZ -> +inf in XMMatrixPerspectiveFovLH:
// fRange = FarZ / (FarZ - NearZ) -> 1
// -fRange * NearZ -> -NearZ
// But for reversed-z we want depth in [1, 0] instead of [0, 1],
// so M[2][2] = 0 and M[3][2] = NearZ (limit of fRange*(FarZ-NearZ)/FarZ * ... see derivation).
// Derivation: reversed-z maps NearZ->1, inf->0. The standard row-major DX projection:
// z' = M22*z + M32, w' = z
// NDC_z = z'/w' = M22 + M32/z
// For NearZ->1: M22 + M32/NearZ = 1
// For inf->0: M22 = 0
// Therefore: M32 = NearZ, M22 = 0.
XMMATRIX M;
M.m[0][0] = Width;
M.m[0][1] = 0.0f;
M.m[0][2] = 0.0f;
M.m[0][3] = 0.0f;

M.m[1][0] = 0.0f;
M.m[1][1] = Height;
M.m[1][2] = 0.0f;
M.m[1][3] = 0.0f;

M.m[2][0] = 0.0f;
M.m[2][1] = 0.0f;
M.m[2][2] = 0.0f;
M.m[2][3] = 1.0f;

M.m[3][0] = 0.0f;
M.m[3][1] = 0.0f;
M.m[3][2] = NearZ;
M.m[3][3] = 0.0f;
return M;

#elif defined(_XM_ARM_NEON_INTRINSICS_)
float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
float Width = Height / AspectRatio;
const float32x4_t Zero = vdupq_n_f32(0);

XMMATRIX M;
M.r[0] = vsetq_lane_f32(Width, Zero, 0);
M.r[1] = vsetq_lane_f32(Height, Zero, 1);
// M.r[2] = (0, 0, 0, 1) -- g_XMIdentityR3 is {0,0,0,1}
M.r[2] = g_XMIdentityR3.v;
// M.r[3] = (0, 0, NearZ, 0)
M.r[3] = vsetq_lane_f32(NearZ, Zero, 2);
return M;
#elif defined(_XM_SSE_INTRINSICS_)
float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
// Note: This is recorded on the stack
XMVECTOR rMem = {
Height / AspectRatio,
Height,
0.0f,
NearZ
};
// Copy from memory to SSE register
XMVECTOR vValues = rMem;
XMVECTOR vTemp = _mm_setzero_ps();
// Copy x only
vTemp = _mm_move_ss(vTemp, vValues);
// Width,0,0,0
XMMATRIX M;
M.r[0] = vTemp;
// 0,Height,0,0
vTemp = vValues;
vTemp = _mm_and_ps(vTemp, g_XMMaskY);
M.r[1] = vTemp;
// 0,0,0,1
M.r[2] = g_XMIdentityR3;
// 0,0,NearZ,0 -- place NearZ into lane z of a zero vector.
// _mm_set_ss(NearZ) = {NearZ, 0, 0, 0}. _MM_SHUFFLE(3,0,0,0) picks:
// result = {g_XMZero[0], g_XMZero[0], b[0], b[3]} = {0, 0, NearZ, 0}.
vTemp = _mm_shuffle_ps(g_XMZero, _mm_set_ss(NearZ), _MM_SHUFFLE(3, 0, 0, 0)); // (0, 0, NearZ, 0)
M.r[3] = vTemp;
return M;
#endif
}

//------------------------------------------------------------------------------
// Infinite reversed-z perspective projection (FarZ = +infinity, depth maps NearZ->1, Infinity->0)
// This avoids NaN that would result from passing infinity to XMMatrixPerspectiveFovRH.
// Right-handed coordinate system.

inline XMMATRIX XM_CALLCONV XMMatrixPerspectiveFovInfiniteReverseZRH
(
float FovAngleY,
float AspectRatio,
float NearZ
) noexcept
{
assert(NearZ > 0.f);
assert(!XMScalarNearEqual(FovAngleY, 0.0f, 0.00001f * 2.0f));
assert(!XMScalarNearEqual(AspectRatio, 0.0f, 0.00001f));

#if defined(_XM_NO_INTRINSICS_)

float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
float Width = Height / AspectRatio;

// As FarZ -> +inf in XMMatrixPerspectiveFovRH (RH flips the sign of z in clip):
// M22 = 0, M32 = -NearZ
// Derivation (same as LH but w' = -z for RH):
// NDC_z = M22 + M32/z. For inf->0: M22=0. For NearZ->1: M32 = -NearZ.
XMMATRIX M;
M.m[0][0] = Width;
M.m[0][1] = 0.0f;
M.m[0][2] = 0.0f;
M.m[0][3] = 0.0f;

M.m[1][0] = 0.0f;
M.m[1][1] = Height;
M.m[1][2] = 0.0f;
M.m[1][3] = 0.0f;

M.m[2][0] = 0.0f;
M.m[2][1] = 0.0f;
M.m[2][2] = 0.0f;
M.m[2][3] = -1.0f;

M.m[3][0] = 0.0f;
M.m[3][1] = 0.0f;
M.m[3][2] = -NearZ;
M.m[3][3] = 0.0f;
return M;

#elif defined(_XM_ARM_NEON_INTRINSICS_)
float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
float Width = Height / AspectRatio;
const float32x4_t Zero = vdupq_n_f32(0);

XMMATRIX M;
M.r[0] = vsetq_lane_f32(Width, Zero, 0);
M.r[1] = vsetq_lane_f32(Height, Zero, 1);
// M.r[2] = (0, 0, 0, -1) -- g_XMNegIdentityR3 is {0,0,0,-1}
M.r[2] = g_XMNegIdentityR3.v;
// M.r[3] = (0, 0, -NearZ, 0)
M.r[3] = vsetq_lane_f32(-NearZ, Zero, 2);
return M;
#elif defined(_XM_SSE_INTRINSICS_)
float SinFov;
float CosFov;
XMScalarSinCos(&SinFov, &CosFov, 0.5f * FovAngleY);

float Height = CosFov / SinFov;
// Note: This is recorded on the stack
XMVECTOR rMem = {
Height / AspectRatio,
Height,
0.0f,
-NearZ
};
// Copy from memory to SSE register
XMVECTOR vValues = rMem;
XMVECTOR vTemp = _mm_setzero_ps();
// Copy x only
vTemp = _mm_move_ss(vTemp, vValues);
// Width,0,0,0
XMMATRIX M;
M.r[0] = vTemp;
// 0,Height,0,0
vTemp = vValues;
vTemp = _mm_and_ps(vTemp, g_XMMaskY);
M.r[1] = vTemp;
// 0,0,0,-1
M.r[2] = g_XMNegIdentityR3;
// 0,0,-NearZ,0 -- place -NearZ into lane z of a zero vector.
// _mm_set_ss(-NearZ) = {-NearZ, 0, 0, 0}. Same shuffle: {0, 0, -NearZ, 0}.
vTemp = _mm_shuffle_ps(g_XMZero, _mm_set_ss(-NearZ), _MM_SHUFFLE(3, 0, 0, 0)); // (0, 0, -NearZ, 0)
M.r[3] = vTemp;
return M;
#endif
}


//------------------------------------------------------------------------------

inline XMMATRIX XM_CALLCONV XMMatrixPerspectiveOffCenterLH
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