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/*
===========================================================================
Doom 3 BFG Edition GPL Source Code
Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").
Doom 3 BFG Edition Source Code is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Doom 3 BFG Edition Source Code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Doom 3 BFG Edition Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 BFG Edition Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 BFG Edition Source Code. If not, please request a copy in writing from id Software at the address below.
If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.
===========================================================================
*/
#ifndef __RENDERMATRIX_H__
#define __RENDERMATRIX_H__
static const int NUM_FRUSTUM_CORNERS = 8;
struct frustumCorners_t
{
float x[NUM_FRUSTUM_CORNERS];
float y[NUM_FRUSTUM_CORNERS];
float z[NUM_FRUSTUM_CORNERS];
};
enum frustumCull_t
{
FRUSTUM_CULL_FRONT = 1,
FRUSTUM_CULL_BACK = 2,
FRUSTUM_CULL_CROSS = 3
};
/*
================================================================================================
idRenderMatrix
This is a row-major matrix and transforms are applied with left-multiplication.
================================================================================================
*/
class idRenderMatrix
{
public:
idRenderMatrix() {}
ID_INLINE idRenderMatrix( float a0, float a1, float a2, float a3,
float b0, float b1, float b2, float b3,
float c0, float c1, float c2, float c3,
float d0, float d1, float d2, float d3 );
const float* operator[]( int index ) const
{
assert( index >= 0 && index < 4 );
return &m[index * 4];
}
float* operator[]( int index )
{
assert( index >= 0 && index < 4 );
return &m[index * 4];
}
void Zero()
{
memset( m, 0, sizeof( m ) );
}
ID_INLINE void Identity();
// Matrix classification (only meant to be used for asserts).
ID_INLINE bool IsZero( float epsilon ) const;
ID_INLINE bool IsIdentity( float epsilon ) const;
ID_INLINE bool IsAffineTransform( float epsilon ) const;
ID_INLINE bool IsUniformScale( float epsilon ) const;
// Transform a point.
// NOTE: the idVec3 out variant does not divide by W.
ID_INLINE void TransformPoint( const idVec3& in, idVec3& out ) const;
ID_INLINE void TransformPoint( const idVec3& in, idVec4& out ) const;
ID_INLINE void TransformPoint( const idVec4& in, idVec4& out ) const;
// These assume the matrix has no non-uniform scaling or shearing.
// NOTE: a direction will only stay normalized if the matrix has no skewing or scaling.
ID_INLINE void TransformDir( const idVec3& in, idVec3& out, bool normalize ) const;
ID_INLINE void TransformPlane( const idPlane& in, idPlane& out, bool normalize ) const;
// These transforms work with non-uniform scaling and shearing by multiplying
// with 'transpose(inverse(M))' where this matrix is assumed to be 'inverse(M)'.
ID_INLINE void InverseTransformDir( const idVec3& in, idVec3& out, bool normalize ) const;
ID_INLINE void InverseTransformPlane( const idPlane& in, idPlane& out, bool normalize ) const;
// Project a point.
static ID_INLINE void TransformModelToClip( const idVec3& src, const idRenderMatrix& modelMatrix, const idRenderMatrix& projectionMatrix, idVec4& eye, idVec4& clip );
static ID_INLINE void TransformClipToDevice( const idVec4& clip, idVec3& ndc );
// Create a matrix that goes from local space to the space defined by the 'origin' and 'axis'.
static void CreateFromOriginAxis( const idVec3& origin, const idMat3& axis, idRenderMatrix& out );
static void CreateFromOriginAxisScale( const idVec3& origin, const idMat3& axis, const idVec3& scale, idRenderMatrix& out );
// Create a matrix that goes from a global coordinate to a view coordinate (OpenGL looking down -Z) based on the given view origin/axis.
static void CreateViewMatrix( const idVec3& origin, const idMat3& axis, idRenderMatrix& out );
// Create a projection matrix.
static void CreateProjectionMatrix( float xMin, float xMax, float yMin, float yMax, float zNear, float zFar, idRenderMatrix& out );
static void CreateProjectionMatrixFov( float xFovDegrees, float yFovDegrees, float zNear, float zFar, float xOffset, float yOffset, idRenderMatrix& out );
// Apply depth hacks to a projection matrix.
static ID_INLINE void ApplyDepthHack( idRenderMatrix& src );
static ID_INLINE void ApplyModelDepthHack( idRenderMatrix& src, float value );
// Offset and scale the given matrix such that the result matrix transforms the unit-cube to exactly cover the given bounds (and the inverse).
static void OffsetScaleForBounds( const idRenderMatrix& src, const idBounds& bounds, idRenderMatrix& out );
static void InverseOffsetScaleForBounds( const idRenderMatrix& src, const idBounds& bounds, idRenderMatrix& out );
// Basic matrix operations.
static void Transpose( const idRenderMatrix& src, idRenderMatrix& out );
static void Multiply( const idRenderMatrix& a, const idRenderMatrix& b, idRenderMatrix& out );
static bool Inverse( const idRenderMatrix& src, idRenderMatrix& out );
static void InverseByTranspose( const idRenderMatrix& src, idRenderMatrix& out );
static bool InverseByDoubles( const idRenderMatrix& src, idRenderMatrix& out );
// Copy or create a matrix that is stored directly into four float4 vectors which is useful for directly setting vertex program uniforms.
static void CopyMatrix( const idRenderMatrix& matrix, idVec4& row0, idVec4& row1, idVec4& row2, idVec4& row3 );
static void SetMVP( const idRenderMatrix& mvp, idVec4& row0, idVec4& row1, idVec4& row2, idVec4& row3, bool& negativeDeterminant );
static void SetMVPForBounds( const idRenderMatrix& mvp, const idBounds& bounds, idVec4& row0, idVec4& row1, idVec4& row2, idVec4& row3, bool& negativeDeterminant );
static void SetMVPForInverseProject( const idRenderMatrix& mvp, const idRenderMatrix& inverseProject, idVec4& row0, idVec4& row1, idVec4& row2, idVec4& row3, bool& negativeDeterminant );
// Cull to a Model-View-Projection (MVP) matrix.
static bool CullPointToMVP( const idRenderMatrix& mvp, const idVec3& point, bool zeroToOne = false );
static bool CullPointToMVPbits( const idRenderMatrix& mvp, const idVec3& point, byte* outBits, bool zeroToOne = false );
static bool CullBoundsToMVP( const idRenderMatrix& mvp, const idBounds& bounds, bool zeroToOne = false );
static bool CullBoundsToMVPbits( const idRenderMatrix& mvp, const idBounds& bounds, byte* outBits, bool zeroToOne = false );
static bool CullExtrudedBoundsToMVP( const idRenderMatrix& mvp, const idBounds& bounds, const idVec3& extrudeDirection, const idPlane& clipPlane, bool zeroToOne = false );
static bool CullExtrudedBoundsToMVPbits( const idRenderMatrix& mvp, const idBounds& bounds, const idVec3& extrudeDirection, const idPlane& clipPlane, byte* outBits, bool zeroToOne = false );
// Calculate the projected bounds.
static void ProjectedBounds( idBounds& projected, const idRenderMatrix& mvp, const idBounds& bounds, bool windowSpace = true );
static void ProjectedNearClippedBounds( idBounds& projected, const idRenderMatrix& mvp, const idBounds& bounds, bool windowSpace = true );
static void ProjectedFullyClippedBounds( idBounds& projected, const idRenderMatrix& mvp, const idBounds& bounds, bool windowSpace = true );
// Calculate the projected depth bounds.
static void DepthBoundsForBounds( float& min, float& max, const idRenderMatrix& mvp, const idBounds& bounds, bool windowSpace = true );
static void DepthBoundsForExtrudedBounds( float& min, float& max, const idRenderMatrix& mvp, const idBounds& bounds, const idVec3& extrudeDirection, const idPlane& clipPlane, bool windowSpace = true );
static void DepthBoundsForShadowBounds( float& min, float& max, const idRenderMatrix& mvp, const idBounds& bounds, const idVec3& localLightOrigin, bool windowSpace = true );
// Create frustum planes and corners from a matrix.
static void GetFrustumPlanes( idPlane planes[6], const idRenderMatrix& frustum, bool zeroToOne, bool normalize );
static void GetFrustumCorners( frustumCorners_t& corners, const idRenderMatrix& frustumTransform, const idBounds& frustumBounds );
static frustumCull_t CullFrustumCornersToPlane( const frustumCorners_t& corners, const idPlane& plane );
private:
float m[16];
};
extern const idRenderMatrix renderMatrix_identity;
extern const idRenderMatrix renderMatrix_flipToOpenGL;
extern const idRenderMatrix renderMatrix_windowSpaceToClipSpace;
/*
========================
idRenderMatrix::idRenderMatrix
========================
*/
ID_INLINE idRenderMatrix::idRenderMatrix( float a0, float a1, float a2, float a3,
float b0, float b1, float b2, float b3,
float c0, float c1, float c2, float c3,
float d0, float d1, float d2, float d3 )
{
m[0 * 4 + 0] = a0;
m[0 * 4 + 1] = a1;
m[0 * 4 + 2] = a2;
m[0 * 4 + 3] = a3;
m[1 * 4 + 0] = b0;
m[1 * 4 + 1] = b1;
m[1 * 4 + 2] = b2;
m[1 * 4 + 3] = b3;
m[2 * 4 + 0] = c0;
m[2 * 4 + 1] = c1;
m[2 * 4 + 2] = c2;
m[2 * 4 + 3] = c3;
m[3 * 4 + 0] = d0;
m[3 * 4 + 1] = d1;
m[3 * 4 + 2] = d2;
m[3 * 4 + 3] = d3;
}
/*
========================
idRenderMatrix::Identity
========================
*/
ID_INLINE void idRenderMatrix::Identity()
{
m[0 * 4 + 0] = 1.0f;
m[0 * 4 + 1] = 0.0f;
m[0 * 4 + 2] = 0.0f;
m[0 * 4 + 3] = 0.0f;
m[1 * 4 + 0] = 0.0f;
m[1 * 4 + 1] = 1.0f;
m[1 * 4 + 2] = 0.0f;
m[1 * 4 + 3] = 0.0f;
m[2 * 4 + 0] = 0.0f;
m[2 * 4 + 1] = 0.0f;
m[2 * 4 + 2] = 1.0f;
m[2 * 4 + 3] = 0.0f;
m[3 * 4 + 0] = 0.0f;
m[3 * 4 + 1] = 0.0f;
m[3 * 4 + 2] = 0.0f;
m[3 * 4 + 3] = 1.0f;
}
/*
========================
idRenderMatrix::IsZero
========================
*/
ID_INLINE bool idRenderMatrix::IsZero( float epsilon ) const
{
for( int i = 0; i < 16; i++ )
{
if( idMath::Fabs( m[i] ) > epsilon )
{
return false;
}
}
return true;
}
/*
========================
idRenderMatrix::IsIdentity
========================
*/
ID_INLINE bool idRenderMatrix::IsIdentity( float epsilon ) const
{
for( int i = 0; i < 4; i++ )
{
for( int j = 0; j < 4; j++ )
{
if( i == j )
{
if( idMath::Fabs( m[i * 4 + j] - 1.0f ) > epsilon )
{
return false;
}
}
else
{
if( idMath::Fabs( m[i * 4 + j] ) > epsilon )
{
return false;
}
}
}
}
return true;
}
/*
========================
idRenderMatrix::IsAffineTransform
========================
*/
ID_INLINE bool idRenderMatrix::IsAffineTransform( float epsilon ) const
{
if( idMath::Fabs( m[3 * 4 + 0] ) > epsilon ||
idMath::Fabs( m[3 * 4 + 1] ) > epsilon ||
idMath::Fabs( m[3 * 4 + 2] ) > epsilon ||
idMath::Fabs( m[3 * 4 + 3] - 1.0f ) > epsilon )
{
return false;
}
return true;
}
/*
========================
idRenderMatrix::IsUniformScale
========================
*/
ID_INLINE bool idRenderMatrix::IsUniformScale( float epsilon ) const
{
float d0 = idMath::InvSqrt( m[0 * 4 + 0] * m[0 * 4 + 0] + m[1 * 4 + 0] * m[1 * 4 + 0] + m[2 * 4 + 0] * m[2 * 4 + 0] );
float d1 = idMath::InvSqrt( m[0 * 4 + 1] * m[0 * 4 + 1] + m[1 * 4 + 1] * m[1 * 4 + 1] + m[2 * 4 + 1] * m[2 * 4 + 1] );
float d2 = idMath::InvSqrt( m[0 * 4 + 2] * m[0 * 4 + 2] + m[1 * 4 + 2] * m[1 * 4 + 2] + m[2 * 4 + 2] * m[2 * 4 + 2] );
if( idMath::Fabs( d0 - d1 ) > epsilon )
{
return false;
}
if( idMath::Fabs( d1 - d2 ) > epsilon )
{
return false;
}
if( idMath::Fabs( d0 - d2 ) > epsilon )
{
return false;
}
return true;
}
/*
========================
idRenderMatrix::TransformPoint
========================
*/
ID_INLINE void idRenderMatrix::TransformPoint( const idVec3& in, idVec3& out ) const
{
assert( in.ToFloatPtr() != out.ToFloatPtr() );
const idRenderMatrix& matrix = *this;
out[0] = in[0] * matrix[0][0] + in[1] * matrix[0][1] + in[2] * matrix[0][2] + matrix[0][3];
out[1] = in[0] * matrix[1][0] + in[1] * matrix[1][1] + in[2] * matrix[1][2] + matrix[1][3];
out[2] = in[0] * matrix[2][0] + in[1] * matrix[2][1] + in[2] * matrix[2][2] + matrix[2][3];
assert( idMath::Fabs( in[0] * matrix[3][0] + in[1] * matrix[3][1] + in[2] * matrix[3][2] + matrix[3][3] - 1.0f ) < 0.01f );
}
/*
========================
idRenderMatrix::TransformPoint
========================
*/
ID_INLINE void idRenderMatrix::TransformPoint( const idVec3& in, idVec4& out ) const
{
assert( in.ToFloatPtr() != out.ToFloatPtr() );
const idRenderMatrix& matrix = *this;
out[0] = in[0] * matrix[0][0] + in[1] * matrix[0][1] + in[2] * matrix[0][2] + matrix[0][3];
out[1] = in[0] * matrix[1][0] + in[1] * matrix[1][1] + in[2] * matrix[1][2] + matrix[1][3];
out[2] = in[0] * matrix[2][0] + in[1] * matrix[2][1] + in[2] * matrix[2][2] + matrix[2][3];
out[3] = in[0] * matrix[3][0] + in[1] * matrix[3][1] + in[2] * matrix[3][2] + matrix[3][3];
}
/*
========================
idRenderMatrix::TransformPoint
========================
*/
ID_INLINE void idRenderMatrix::TransformPoint( const idVec4& in, idVec4& out ) const
{
assert( in.ToFloatPtr() != out.ToFloatPtr() );
const idRenderMatrix& matrix = *this;
out[0] = in[0] * matrix[0][0] + in[1] * matrix[0][1] + in[2] * matrix[0][2] + in[3] * matrix[0][3];
out[1] = in[0] * matrix[1][0] + in[1] * matrix[1][1] + in[2] * matrix[1][2] + in[3] * matrix[1][3];
out[2] = in[0] * matrix[2][0] + in[1] * matrix[2][1] + in[2] * matrix[2][2] + in[3] * matrix[2][3];
out[3] = in[0] * matrix[3][0] + in[1] * matrix[3][1] + in[2] * matrix[3][2] + in[3] * matrix[3][3];
}
/*
========================
idRenderMatrix::TransformDir
========================
*/
ID_INLINE void idRenderMatrix::TransformDir( const idVec3& in, idVec3& out, bool normalize ) const
{
const idRenderMatrix& matrix = *this;
float p0 = in[0] * matrix[0][0] + in[1] * matrix[0][1] + in[2] * matrix[0][2];
float p1 = in[0] * matrix[1][0] + in[1] * matrix[1][1] + in[2] * matrix[1][2];
float p2 = in[0] * matrix[2][0] + in[1] * matrix[2][1] + in[2] * matrix[2][2];
if( normalize )
{
float r = idMath::InvSqrt( p0 * p0 + p1 * p1 + p2 * p2 );
p0 *= r;
p1 *= r;
p2 *= r;
}
out[0] = p0;
out[1] = p1;
out[2] = p2;
}
/*
========================
idRenderMatrix::TransformPlane
========================
*/
ID_INLINE void idRenderMatrix::TransformPlane( const idPlane& in, idPlane& out, bool normalize ) const
{
assert( IsUniformScale( 0.01f ) );
const idRenderMatrix& matrix = *this;
float p0 = in[0] * matrix[0][0] + in[1] * matrix[0][1] + in[2] * matrix[0][2];
float p1 = in[0] * matrix[1][0] + in[1] * matrix[1][1] + in[2] * matrix[1][2];
float p2 = in[0] * matrix[2][0] + in[1] * matrix[2][1] + in[2] * matrix[2][2];
float d0 = matrix[0][3] - p0 * in[3];
float d1 = matrix[1][3] - p1 * in[3];
float d2 = matrix[2][3] - p2 * in[3];
if( normalize )
{
float r = idMath::InvSqrt( p0 * p0 + p1 * p1 + p2 * p2 );
p0 *= r;
p1 *= r;
p2 *= r;
}
out[0] = p0;
out[1] = p1;
out[2] = p2;
out[3] = - p0 * d0 - p1 * d1 - p2 * d2;
}
/*
========================
idRenderMatrix::InverseTransformDir
========================
*/
ID_INLINE void idRenderMatrix::InverseTransformDir( const idVec3& in, idVec3& out, bool normalize ) const
{
assert( in.ToFloatPtr() != out.ToFloatPtr() );
const idRenderMatrix& matrix = *this;
float p0 = in[0] * matrix[0][0] + in[1] * matrix[1][0] + in[2] * matrix[2][0];
float p1 = in[0] * matrix[0][1] + in[1] * matrix[1][1] + in[2] * matrix[2][1];
float p2 = in[0] * matrix[0][2] + in[1] * matrix[1][2] + in[2] * matrix[2][2];
if( normalize )
{
float r = idMath::InvSqrt( p0 * p0 + p1 * p1 + p2 * p2 );
p0 *= r;
p1 *= r;
p2 *= r;
}
out[0] = p0;
out[1] = p1;
out[2] = p2;
}
/*
========================
idRenderMatrix::InverseTransformPlane
========================
*/
ID_INLINE void idRenderMatrix::InverseTransformPlane( const idPlane& in, idPlane& out, bool normalize ) const
{
assert( in.ToFloatPtr() != out.ToFloatPtr() );
const idRenderMatrix& matrix = *this;
float p0 = in[0] * matrix[0][0] + in[1] * matrix[1][0] + in[2] * matrix[2][0] + in[3] * matrix[3][0];
float p1 = in[0] * matrix[0][1] + in[1] * matrix[1][1] + in[2] * matrix[2][1] + in[3] * matrix[3][1];
float p2 = in[0] * matrix[0][2] + in[1] * matrix[1][2] + in[2] * matrix[2][2] + in[3] * matrix[3][2];
float p3 = in[0] * matrix[0][3] + in[1] * matrix[1][3] + in[2] * matrix[2][3] + in[3] * matrix[3][3];
if( normalize )
{
float r = idMath::InvSqrt( p0 * p0 + p1 * p1 + p2 * p2 );
p0 *= r;
p1 *= r;
p2 *= r;
p3 *= r;
}
out[0] = p0;
out[1] = p1;
out[2] = p2;
out[3] = p3;
}
/*
========================
idRenderMatrix::TransformModelToClip
========================
*/
ID_INLINE void idRenderMatrix::TransformModelToClip( const idVec3& src, const idRenderMatrix& modelMatrix, const idRenderMatrix& projectionMatrix, idVec4& eye, idVec4& clip )
{
for( int i = 0; i < 4; i++ )
{
eye[i] = modelMatrix[i][0] * src[0] +
modelMatrix[i][1] * src[1] +
modelMatrix[i][2] * src[2] +
modelMatrix[i][3];
}
for( int i = 0; i < 4; i++ )
{
clip[i] = projectionMatrix[i][0] * eye[0] +
projectionMatrix[i][1] * eye[1] +
projectionMatrix[i][2] * eye[2] +
projectionMatrix[i][3] * eye[3];
}
}
/*
========================
idRenderMatrix::TransformClipToDevice
Clip to normalized device coordinates.
========================
*/
ID_INLINE void idRenderMatrix::TransformClipToDevice( const idVec4& clip, idVec3& ndc )
{
assert( idMath::Fabs( clip[3] ) > idMath::FLT_SMALLEST_NON_DENORMAL );
float r = 1.0f / clip[3];
ndc[0] = clip[0] * r;
ndc[1] = clip[1] * r;
ndc[2] = clip[2] * r;
}
/*
========================
idRenderMatrix::ApplyDepthHack
========================
*/
ID_INLINE void idRenderMatrix::ApplyDepthHack( idRenderMatrix& src )
{
// scale projected z by 25%
src.m[2 * 4 + 0] *= 0.25f;
src.m[2 * 4 + 1] *= 0.25f;
src.m[2 * 4 + 2] *= 0.25f;
src.m[2 * 4 + 3] *= 0.25f;
}
/*
========================
idRenderMatrix::ApplyModelDepthHack
========================
*/
ID_INLINE void idRenderMatrix::ApplyModelDepthHack( idRenderMatrix& src, float value )
{
// offset projected z
src.m[2 * 4 + 3] -= value;
}
/*
========================
idRenderMatrix::CullPointToMVP
========================
*/
ID_INLINE bool idRenderMatrix::CullPointToMVP( const idRenderMatrix& mvp, const idVec3& point, bool zeroToOne )
{
byte bits;
return CullPointToMVPbits( mvp, point, &bits, zeroToOne );
}
/*
========================
idRenderMatrix::CullBoundsToMVP
========================
*/
ID_INLINE bool idRenderMatrix::CullBoundsToMVP( const idRenderMatrix& mvp, const idBounds& bounds, bool zeroToOne )
{
byte bits;
return CullBoundsToMVPbits( mvp, bounds, &bits, zeroToOne );
}
/*
========================
idRenderMatrix::CullExtrudedBoundsToMVP
========================
*/
ID_INLINE bool idRenderMatrix::CullExtrudedBoundsToMVP( const idRenderMatrix& mvp, const idBounds& bounds, const idVec3& extrudeDirection, const idPlane& clipPlane, bool zeroToOne )
{
byte bits;
return CullExtrudedBoundsToMVPbits( mvp, bounds, extrudeDirection, clipPlane, &bits, zeroToOne );
}
#endif // !__RENDERMATRIX_H__
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