UE4投影矩阵[通俗易懂]

class FOrthoMatrix
: public FMatrix
{ 

public:
/** * Constructor * * @param Width view space width * @param Height view space height * @param ZScale scale in the Z axis * @param ZOffset offset in the Z axis */
FOrthoMatrix(float Width,float Height,float ZScale,float ZOffset);
};
class FReversedZOrthoMatrix : public FMatrix
{ 

public:
FReversedZOrthoMatrix(float Width,float Height,float ZScale,float ZOffset);
};
FORCEINLINE FOrthoMatrix::FOrthoMatrix(float Width,float Height,float ZScale,float ZOffset)
: FMatrix(
FPlane((Width)? (1.0f / Width) : 1.0f,	0.0f,								0.0f,				0.0f),
FPlane(0.0f,							(Height)? (1.0f / Height) : 1.f,	0.0f,				0.0f),
FPlane(0.0f,							0.0f,								ZScale,				0.0f),
FPlane(0.0f,							0.0f,								ZOffset * ZScale,	1.0f)
)
{ 
 }
FORCEINLINE FReversedZOrthoMatrix::FReversedZOrthoMatrix(float Width,float Height,float ZScale,float ZOffset)
: FMatrix(
FPlane((Width)? (1.0f / Width) : 1.0f,	0.0f,								0.0f,					0.0f),
FPlane(0.0f,							(Height)? (1.0f / Height) : 1.f,	0.0f,					0.0f),
FPlane(0.0f,							0.0f,								-ZScale,				0.0f),
FPlane(0.0f,							0.0f,								1.0 - ZOffset * ZScale,	1.0f)
)
{ 
 }

class FPerspectiveMatrix
: public FMatrix
{ 

public:
// Note: the value of this must match the mirror in Common.usf!
#define Z_PRECISION 0.0f
/** * Constructor * * @param HalfFOVX Half FOV in the X axis * @param HalfFOVY Half FOV in the Y axis * @param MultFOVX multiplier on the X axis * @param MultFOVY multiplier on the y axis * @param MinZ distance to the near Z plane * @param MaxZ distance to the far Z plane */
FPerspectiveMatrix(float HalfFOVX, float HalfFOVY, float MultFOVX, float MultFOVY, float MinZ, float MaxZ);
/** * Constructor * * @param HalfFOV half Field of View in the Y direction * @param Width view space width * @param Height view space height * @param MinZ distance to the near Z plane * @param MaxZ distance to the far Z plane * @note that the FOV you pass in is actually half the FOV, unlike most perspective matrix functions (D3DXMatrixPerspectiveFovLH). */
FPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ, float MaxZ);
/** * Constructor * * @param HalfFOV half Field of View in the Y direction * @param Width view space width * @param Height view space height * @param MinZ distance to the near Z plane * @note that the FOV you pass in is actually half the FOV, unlike most perspective matrix functions (D3DXMatrixPerspectiveFovLH). */
FPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ);
};
class FReversedZPerspectiveMatrix : public FMatrix
{ 

public:
FReversedZPerspectiveMatrix(float HalfFOVX, float HalfFOVY, float MultFOVX, float MultFOVY, float MinZ, float MaxZ);
FReversedZPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ, float MaxZ);
FReversedZPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ);
};
#if _MSC_VER
#pragma warning (push)
// Disable possible division by 0 warning
#pragma warning (disable : 4723)
#endif
FORCEINLINE FPerspectiveMatrix::FPerspectiveMatrix(float HalfFOVX, float HalfFOVY, float MultFOVX, float MultFOVY, float MinZ, float MaxZ)
: FMatrix(
FPlane(MultFOVX / FMath::Tan(HalfFOVX),	0.0f,								0.0f,																	0.0f),
FPlane(0.0f,							MultFOVY / FMath::Tan(HalfFOVY),	0.0f,																	0.0f),
FPlane(0.0f,							0.0f,								((MinZ == MaxZ) ? (1.0f - Z_PRECISION) : MaxZ / (MaxZ - MinZ)),			1.0f),
FPlane(0.0f,							0.0f,								-MinZ * ((MinZ == MaxZ) ? (1.0f - Z_PRECISION) : MaxZ / (MaxZ - MinZ)),	0.0f)
)
{ 
 }
FORCEINLINE FPerspectiveMatrix::FPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ, float MaxZ)
: FMatrix(
FPlane(1.0f / FMath::Tan(HalfFOV),	0.0f,									0.0f,							0.0f),
FPlane(0.0f,						Width / FMath::Tan(HalfFOV) / Height,	0.0f,							0.0f),
FPlane(0.0f,						0.0f,									((MinZ == MaxZ) ? (1.0f - Z_PRECISION) : MaxZ / (MaxZ - MinZ)),			1.0f),
FPlane(0.0f,						0.0f,									-MinZ * ((MinZ == MaxZ) ? (1.0f - Z_PRECISION) : MaxZ / (MaxZ - MinZ)),	0.0f)
)
{ 
 }
FORCEINLINE FPerspectiveMatrix::FPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ)
: FMatrix(
FPlane(1.0f / FMath::Tan(HalfFOV),	0.0f,									0.0f,							0.0f),
FPlane(0.0f,						Width / FMath::Tan(HalfFOV) / Height,	0.0f,							0.0f),
FPlane(0.0f,						0.0f,									(1.0f - Z_PRECISION),			1.0f),
FPlane(0.0f,						0.0f,									-MinZ * (1.0f - Z_PRECISION),	0.0f)
)
{ 
 }
FORCEINLINE FReversedZPerspectiveMatrix::FReversedZPerspectiveMatrix(float HalfFOVX, float HalfFOVY, float MultFOVX, float MultFOVY, float MinZ, float MaxZ)
: FMatrix(
FPlane(MultFOVX / FMath::Tan(HalfFOVX),	0.0f,								0.0f,													0.0f),
FPlane(0.0f,							MultFOVY / FMath::Tan(HalfFOVY),	0.0f,													0.0f),
FPlane(0.0f,							0.0f,								((MinZ == MaxZ) ? 0.0f : MinZ / (MinZ - MaxZ)),			1.0f),
FPlane(0.0f,							0.0f,								((MinZ == MaxZ) ? MinZ : -MaxZ * MinZ / (MinZ - MaxZ)),	0.0f)
)
{ 
 }
FORCEINLINE FReversedZPerspectiveMatrix::FReversedZPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ, float MaxZ)
: FMatrix(
FPlane(1.0f / FMath::Tan(HalfFOV),	0.0f,									0.0f,													0.0f),
FPlane(0.0f,						Width / FMath::Tan(HalfFOV) / Height,	0.0f,													0.0f),
FPlane(0.0f,						0.0f,									((MinZ == MaxZ) ? 0.0f : MinZ / (MinZ - MaxZ)),			1.0f),
FPlane(0.0f,						0.0f,									((MinZ == MaxZ) ? MinZ : -MaxZ * MinZ / (MinZ - MaxZ)),	0.0f)
)
{ 
 }
FORCEINLINE FReversedZPerspectiveMatrix::FReversedZPerspectiveMatrix(float HalfFOV, float Width, float Height, float MinZ)
: FMatrix(
FPlane(1.0f / FMath::Tan(HalfFOV),	0.0f,									0.0f, 0.0f),
FPlane(0.0f,						Width / FMath::Tan(HalfFOV) / Height,	0.0f, 0.0f),
FPlane(0.0f,						0.0f,									0.0f, 1.0f),
FPlane(0.0f,						0.0f,									MinZ, 0.0f)
)
{ 
 }

FMinimalViewInfo::CalculateProjectionMatrixGivenView(ControllingActorViewInfo, AspectRatioAxisConstraint, Viewport, /*inout*/ ViewInitOptions);
{ 

if (ViewInfo.ProjectionMode == ECameraProjectionMode::Orthographic)
{ 

const float YScale = 1.0f / ViewInfo.AspectRatio;
const float OrthoWidth = ViewInfo.OrthoWidth / 2.0f;
const float OrthoHeight = ViewInfo.OrthoWidth / 2.0f * YScale;
const float NearPlane = ViewInfo.OrthoNearClipPlane;
const float FarPlane = ViewInfo.OrthoFarClipPlane;
const float ZScale = 1.0f / (FarPlane - NearPlane);
const float ZOffset = -NearPlane;
InOutProjectionData.ProjectionMatrix = FReversedZOrthoMatrix(
OrthoWidth,
OrthoHeight,
ZScale,
ZOffset
);
}
else
{ 

// Avoid divide by zero in the projection matrix calculation by clamping FOV
InOutProjectionData.ProjectionMatrix = FReversedZPerspectiveMatrix(
FMath::Max(0.001f, ViewInfo.FOV) * (float)PI / 360.0f,
ViewInfo.AspectRatio,
1.0f,
GNearClippingPlane );
}
}