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UE4投影矩阵

正交投影

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)
	)
{ 
    }

透视投影

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)
	)
{ 
    }

使用

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 );
		}
}

参考链接

UE4 投影矩阵