ClipProjectionMatrix.h

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// Copyright Epic Games, Inc. All Rights Reserved.
 
#pragma once
 
#include "CoreTypes.h"
#include "Math/Plane.h"
#include "Math/Matrix.h"
 
namespace UE {
namespace Math {
 
/**
 * Realigns the near plane for an existing projection matrix 
 * with an arbitrary clip plane
 * from: http://sourceforge.net/mailarchive/message.php?msg_id=000901c26324%242181ea90%24a1e93942%40firefly
 * Updated for the fact that our FPlane uses Ax+By+Cz=D.
 */
template<typename T>
struct TClipProjectionMatrix : public TMatrix<T>
{
public:
    using TMatrix<T>::M;
    /**
     * Constructor
     *
     * @param   SrcProjMat - source projection matrix to premultiply with the clip matrix
     * @param   Plane - clipping plane used to build the clip matrix (assumed to be in camera space)
     */
    TClipProjectionMatrix( const TMatrix<T>& SrcProjMat, const TPlane<T>& Plane );
 
    // Conversion to other type.
    template<typename FArg, TEMPLATE_REQUIRES(!std::is_same_v<T, FArg>)>
    explicit TClipProjectionMatrix(const TClipProjectionMatrix<FArg>& From) : TMatrix<T>(From) {}
 
private:
    /** return sign of a number */
    FORCEINLINE T sgn(T a );
};
 
 
template<typename T>
FORCEINLINE TClipProjectionMatrix<T>::TClipProjectionMatrix( const TMatrix<T>& SrcProjMat, const TPlane<T>& Plane ) :
TMatrix<T>(SrcProjMat)
{
    // Calculate the clip-space corner point opposite the clipping plane
    // as (sgn(clipPlane.x), sgn(clipPlane.y), 1, 1) and
    // transform it into camera space by multiplying it
    // by the inverse of the projection matrix
    TPlane<T> CornerPlane(
        sgn(Plane.X) / SrcProjMat.M[0][0],
        sgn(Plane.Y) / SrcProjMat.M[1][1],
        1.0f,
        -(1.0f - SrcProjMat.M[2][2]) / SrcProjMat.M[3][2]
    );
 
    // Calculate the scaled plane vector
    TPlane<T> ProjPlane( Plane * (1.0f / (Plane | CornerPlane)) );
 
    // use the projected space clip plane in z column 
    // Note: (account for our negated W coefficient)
    M[0][2] = ProjPlane.X;
    M[1][2] = ProjPlane.Y;
    M[2][2] = ProjPlane.Z;
    M[3][2] = -ProjPlane.W;
}
 
template<typename T>
FORCEINLINE T TClipProjectionMatrix<T>::sgn(T a)
{
    if (a > 0.0f) return (1.0f);
    if (a < 0.0f) return (-1.0f);
    return (0.0f);
}
 
} // namespace Math
} // namespace UE
 
UE_DECLARE_LWC_TYPE(ClipProjectionMatrix, 44);
 
template<> struct TIsUECoreVariant<FClipProjectionMatrix44f> { enum { Value = true }; };
template<> struct TIsUECoreVariant<FClipProjectionMatrix44d> { enum { Value = true }; };