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Modified source engine (2017) developed by valve and leaked in 2020. Not for commercial purporses
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source-engine/public/mathlib/vmatrix.h

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//========= Copyright Valve Corporation, All rights reserved. ============//
//
// Purpose:
//
// $NoKeywords: $
//
//=============================================================================//
//
// VMatrix always postmultiply vectors as in Ax = b.
// Given a set of basis vectors ((F)orward, (L)eft, (U)p), and a (T)ranslation,
// a matrix to transform a vector into that space looks like this:
// Fx Lx Ux Tx
// Fy Ly Uy Ty
// Fz Lz Uz Tz
// 0 0 0 1
// Note that concatenating matrices needs to multiply them in reverse order.
// ie: if I want to apply matrix A, B, then C, the equation needs to look like this:
// C * B * A * v
// ie:
// v = A * v;
// v = B * v;
// v = C * v;
//=============================================================================
#ifndef VMATRIX_H
#define VMATRIX_H
#ifdef _WIN32
#pragma once
#endif
#include <math.h>
#include <string.h>
#include "mathlib/vector.h"
#include "mathlib/vplane.h"
#include "mathlib/vector4d.h"
#include "mathlib/mathlib.h"
struct cplane_t;
#ifndef M_PI
#define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h
#endif
class alignas(16) VMatrix
{
public:
VMatrix();
VMatrix(
vec_t m00, vec_t m01, vec_t m02, vec_t m03,
vec_t m10, vec_t m11, vec_t m12, vec_t m13,
vec_t m20, vec_t m21, vec_t m22, vec_t m23,
vec_t m30, vec_t m31, vec_t m32, vec_t m33
);
// Creates a matrix where the X axis = forward
// the Y axis = left, and the Z axis = up
VMatrix( const Vector& forward, const Vector& left, const Vector& up );
VMatrix( const Vector& forward, const Vector& left, const Vector& up, const Vector& translation );
// Construct from a 3x4 matrix
VMatrix( const matrix3x4_t& matrix3x4 );
VMatrix( const VMatrix& ) = default;
// Set the values in the matrix.
void Init(
vec_t m00, vec_t m01, vec_t m02, vec_t m03,
vec_t m10, vec_t m11, vec_t m12, vec_t m13,
vec_t m20, vec_t m21, vec_t m22, vec_t m23,
vec_t m30, vec_t m31, vec_t m32, vec_t m33
);
// Initialize from a 3x4
void Init( const matrix3x4_t& matrix3x4 );
// array access
inline float* operator[](int i)
{
return m[i];
}
inline const float* operator[](int i) const
{
return m[i];
}
// Get a pointer to m[0][0]
inline float *Base()
{
return &m[0][0];
}
inline const float *Base() const
{
return &m[0][0];
}
void SetLeft(const Vector &vLeft);
void SetUp(const Vector &vUp);
void SetForward(const Vector &vForward);
void GetBasisVectors(Vector &vForward, Vector &vLeft, Vector &vUp) const;
void SetBasisVectors(const Vector &vForward, const Vector &vLeft, const Vector &vUp);
// Get/set the translation.
Vector & GetTranslation( Vector &vTrans ) const;
void SetTranslation(const Vector &vTrans);
void PreTranslate(const Vector &vTrans);
void PostTranslate(const Vector &vTrans);
const matrix3x4_t& As3x4() const;
void CopyFrom3x4( const matrix3x4_t &m3x4 );
void Set3x4( const matrix3x4_t& matrix3x4 );
bool operator==( const VMatrix& src ) const {
return src.m[0][0] == m[0][0] && src.m[0][1] == m[0][1] && src.m[0][2] == m[0][2] && src.m[0][3] == m[0][3] &&
src.m[1][0] == m[1][0] && src.m[1][1] == m[1][1] && src.m[1][2] == m[1][2] && src.m[1][3] == m[1][3] &&
src.m[2][0] == m[2][0] && src.m[2][1] == m[2][1] && src.m[2][2] == m[2][2] && src.m[2][3] == m[2][3] &&
src.m[3][0] == m[3][0] && src.m[3][1] == m[3][1] && src.m[3][2] == m[3][2] && src.m[3][3] == m[3][3];
}
bool operator!=( const VMatrix& src ) const { return !( *this == src ); }
#ifndef VECTOR_NO_SLOW_OPERATIONS
// Access the basis vectors.
Vector GetLeft() const;
Vector GetUp() const;
Vector GetForward() const;
Vector GetTranslation() const;
#endif
// Matrix->vector operations.
public:
// Multiply by a 3D vector (same as operator*).
void V3Mul(const Vector &vIn, Vector &vOut) const;
// Multiply by a 4D vector.
void V4Mul(const Vector4D &vIn, Vector4D &vOut) const;
#ifndef VECTOR_NO_SLOW_OPERATIONS
// Applies the rotation (ignores translation in the matrix). (This just calls VMul3x3).
Vector ApplyRotation(const Vector &vVec) const;
// Multiply by a vector (divides by w, assumes input w is 1).
Vector operator*(const Vector &vVec) const;
// Multiply by the upper 3x3 part of the matrix (ie: only apply rotation).
Vector VMul3x3(const Vector &vVec) const;
// Apply the inverse (transposed) rotation (only works on pure rotation matrix)
Vector VMul3x3Transpose(const Vector &vVec) const;
// Multiply by the upper 3 rows.
Vector VMul4x3(const Vector &vVec) const;
// Apply the inverse (transposed) transformation (only works on pure rotation/translation)
Vector VMul4x3Transpose(const Vector &vVec) const;
#endif
// Matrix->plane operations.
public:
// Transform the plane. The matrix can only contain translation and rotation.
void TransformPlane( const VPlane &inPlane, VPlane &outPlane ) const;
#ifndef VECTOR_NO_SLOW_OPERATIONS
// Just calls TransformPlane and returns the result.
VPlane operator*(const VPlane &thePlane) const;
#endif
// Matrix->matrix operations.
public:
VMatrix& operator=(const VMatrix &mOther);
// Multiply two matrices (out = this * vm).
void MatrixMul( const VMatrix &vm, VMatrix &out ) const;
// Add two matrices.
const VMatrix& operator+=(const VMatrix &other);
#ifndef VECTOR_NO_SLOW_OPERATIONS
// Just calls MatrixMul and returns the result.
VMatrix operator*(const VMatrix &mOther) const;
// Add/Subtract two matrices.
VMatrix operator+(const VMatrix &other) const;
VMatrix operator-(const VMatrix &other) const;
// Negation.
VMatrix operator-() const;
// Return inverse matrix. Be careful because the results are undefined
// if the matrix doesn't have an inverse (ie: InverseGeneral returns false).
VMatrix operator~() const;
#endif
// Matrix operations.
public:
// Set to identity.
void Identity();
bool IsIdentity() const;
// Setup a matrix for origin and angles.
void SetupMatrixOrgAngles( const Vector &origin, const QAngle &vAngles );
// Setup a matrix for angles and no translation.
void SetupMatrixAngles( const QAngle &vAngles );
// General inverse. This may fail so check the return!
bool InverseGeneral(VMatrix &vInverse) const;
// Does a fast inverse, assuming the matrix only contains translation and rotation.
void InverseTR( VMatrix &mRet ) const;
// Usually used for debug checks. Returns true if the upper 3x3 contains
// unit vectors and they are all orthogonal.
bool IsRotationMatrix() const;
#ifndef VECTOR_NO_SLOW_OPERATIONS
// This calls the other InverseTR and returns the result.
VMatrix InverseTR() const;
// Get the scale of the matrix's basis vectors.
Vector GetScale() const;
// (Fast) multiply by a scaling matrix setup from vScale.
VMatrix Scale(const Vector &vScale);
// Normalize the basis vectors.
VMatrix NormalizeBasisVectors() const;
// Transpose.
VMatrix Transpose() const;
// Transpose upper-left 3x3.
VMatrix Transpose3x3() const;
#endif
public:
// The matrix.
vec_t m[4][4];
};
inline void MatrixSetColumn( VMatrix &src, int nCol, const Vector &column )
{
Assert( (nCol >= 0) && (nCol <= 3) );
src.m[0][nCol] = column.x;
src.m[1][nCol] = column.y;
src.m[2][nCol] = column.z;
}
//-----------------------------------------------------------------------------
// Vector3DMultiplyPosition treats src2 as if it's a point (adds the translation)
//-----------------------------------------------------------------------------
// NJS: src2 is passed in as a full vector rather than a reference to prevent the need
// for 2 branches and a potential copy in the body. (ie, handling the case when the src2
// reference is the same as the dst reference ).
inline void Vector3DMultiplyPosition( const VMatrix& src1, const VectorByValue src2, Vector& dst )
{
dst[0] = src1[0][0] * src2.x + src1[0][1] * src2.y + src1[0][2] * src2.z + src1[0][3];
dst[1] = src1[1][0] * src2.x + src1[1][1] * src2.y + src1[1][2] * src2.z + src1[1][3];
dst[2] = src1[2][0] * src2.x + src1[2][1] * src2.y + src1[2][2] * src2.z + src1[2][3];
}
//-----------------------------------------------------------------------------
// Sets matrix to identity
//-----------------------------------------------------------------------------
inline void MatrixSetIdentity( VMatrix &dst )
{
dst[0][0] = 1.0f; dst[0][1] = 0.0f; dst[0][2] = 0.0f; dst[0][3] = 0.0f;
dst[1][0] = 0.0f; dst[1][1] = 1.0f; dst[1][2] = 0.0f; dst[1][3] = 0.0f;
dst[2][0] = 0.0f; dst[2][1] = 0.0f; dst[2][2] = 1.0f; dst[2][3] = 0.0f;
dst[3][0] = 0.0f; dst[3][1] = 0.0f; dst[3][2] = 0.0f; dst[3][3] = 1.0f;
}
//-----------------------------------------------------------------------------
// Matrix/vector multiply
//-----------------------------------------------------------------------------
inline void Vector3DMultiply( const VMatrix &src1, const Vector &src2, Vector &dst )
{
// Make sure it works if src2 == dst
Vector tmp;
const Vector &v = (&src2 == &dst) ? static_cast<const Vector&>(tmp) : src2;
if( &src2 == &dst )
VectorCopy( src2, tmp );
dst[0] = src1[0][0] * v[0] + src1[0][1] * v[1] + src1[0][2] * v[2];
dst[1] = src1[1][0] * v[0] + src1[1][1] * v[1] + src1[1][2] * v[2];
dst[2] = src1[2][0] * v[0] + src1[2][1] * v[1] + src1[2][2] * v[2];
}
inline bool MatrixInverseGeneral(const VMatrix& src, VMatrix& dst)
{
int iRow, i, j, iTemp, iTest;
vec_t mul, fTest, fLargest;
vec_t mat[4][8];
int rowMap[4], iLargest;
vec_t *pOut, *pRow, *pScaleRow;
// How it's done.
// AX = I
// A = this
// X = the matrix we're looking for
// I = identity
// Setup AI
for(i=0; i < 4; i++)
{
const vec_t *pIn = src[i];
pOut = mat[i];
for(j=0; j < 4; j++)
{
pOut[j] = pIn[j];
}
pOut[4] = 0.0f;
pOut[5] = 0.0f;
pOut[6] = 0.0f;
pOut[7] = 0.0f;
pOut[i+4] = 1.0f;
rowMap[i] = i;
}
// Use row operations to get to reduced row-echelon form using these rules:
// 1. Multiply or divide a row by a nonzero number.
// 2. Add a multiple of one row to another.
// 3. Interchange two rows.
for(iRow=0; iRow < 4; iRow++)
{
// Find the row with the largest element in this column.
fLargest = 0.00001f;
iLargest = -1;
for(iTest=iRow; iTest < 4; iTest++)
{
fTest = (vec_t)FloatMakePositive(mat[rowMap[iTest]][iRow]);
if(fTest > fLargest)
{
iLargest = iTest;
fLargest = fTest;
}
}
// They're all too small.. sorry.
if(iLargest == -1)
{
return false;
}
// Swap the rows.
iTemp = rowMap[iLargest];
rowMap[iLargest] = rowMap[iRow];
rowMap[iRow] = iTemp;
pRow = mat[rowMap[iRow]];
// Divide this row by the element.
mul = 1.0f / pRow[iRow];
for(j=0; j < 8; j++)
pRow[j] *= mul;
pRow[iRow] = 1.0f; // Preserve accuracy...
// Eliminate this element from the other rows using operation 2.
for(i=0; i < 4; i++)
{
if(i == iRow)
continue;
pScaleRow = mat[rowMap[i]];
// Multiply this row by -(iRow*the element).
mul = -pScaleRow[iRow];
for(j=0; j < 8; j++)
{
pScaleRow[j] += pRow[j] * mul;
}
pScaleRow[iRow] = 0.0f; // Preserve accuracy...
}
}
// The inverse is on the right side of AX now (the identity is on the left).
for(i=0; i < 4; i++)
{
const vec_t *pIn = mat[rowMap[i]] + 4;
pOut = dst.m[i];
for(j=0; j < 4; j++)
{
pOut[j] = pIn[j];
}
}
return true;
}
static inline void SetupMatrixAnglesInternal( vec_t m[4][4], const QAngle & vAngles )
{
float sr, sp, sy, cr, cp, cy;
SinCos( DEG2RAD( vAngles[YAW] ), &sy, &cy );
SinCos( DEG2RAD( vAngles[PITCH] ), &sp, &cp );
SinCos( DEG2RAD( vAngles[ROLL] ), &sr, &cr );
// matrix = (YAW * PITCH) * ROLL
m[0][0] = cp*cy;
m[1][0] = cp*sy;
m[2][0] = -sp;
m[0][1] = sr*sp*cy+cr*-sy;
m[1][1] = sr*sp*sy+cr*cy;
m[2][1] = sr*cp;
m[0][2] = (cr*sp*cy+-sr*-sy);
m[1][2] = (cr*sp*sy+-sr*cy);
m[2][2] = cr*cp;
m[0][3] = 0.f;
m[1][3] = 0.f;
m[2][3] = 0.f;
}
//-----------------------------------------------------------------------------
// Transpose
//-----------------------------------------------------------------------------
inline void Swap( float& a, float& b )
{
float tmp = a;
a = b;
b = tmp;
}
inline void MatrixTranspose( const VMatrix& src, VMatrix& dst )
{
if (&src == &dst)
{
Swap( dst[0][1], dst[1][0] );
Swap( dst[0][2], dst[2][0] );
Swap( dst[0][3], dst[3][0] );
Swap( dst[1][2], dst[2][1] );
Swap( dst[1][3], dst[3][1] );
Swap( dst[2][3], dst[3][2] );
}
else
{
dst[0][0] = src[0][0]; dst[0][1] = src[1][0]; dst[0][2] = src[2][0]; dst[0][3] = src[3][0];
dst[1][0] = src[0][1]; dst[1][1] = src[1][1]; dst[1][2] = src[2][1]; dst[1][3] = src[3][1];
dst[2][0] = src[0][2]; dst[2][1] = src[1][2]; dst[2][2] = src[2][2]; dst[2][3] = src[3][2];
dst[3][0] = src[0][3]; dst[3][1] = src[1][3]; dst[3][2] = src[2][3]; dst[3][3] = src[3][3];
}
}
//-----------------------------------------------------------------------------
// Does a fast inverse, assuming the matrix only contains translation and rotation.
//-----------------------------------------------------------------------------
inline void MatrixInverseTR( const VMatrix& src, VMatrix &dst )
{
Vector vTrans, vNewTrans;
// Transpose the upper 3x3.
dst.m[0][0] = src.m[0][0]; dst.m[0][1] = src.m[1][0]; dst.m[0][2] = src.m[2][0];
dst.m[1][0] = src.m[0][1]; dst.m[1][1] = src.m[1][1]; dst.m[1][2] = src.m[2][1];
dst.m[2][0] = src.m[0][2]; dst.m[2][1] = src.m[1][2]; dst.m[2][2] = src.m[2][2];
// Transform the translation.
vTrans.Init( -src.m[0][3], -src.m[1][3], -src.m[2][3] );
Vector3DMultiply( dst, vTrans, vNewTrans );
MatrixSetColumn( dst, 3, vNewTrans );
// Fill in the bottom row.
dst.m[3][0] = dst.m[3][1] = dst.m[3][2] = 0.0f;
dst.m[3][3] = 1.0f;
}
inline void VMatrix::Init(
vec_t m00, vec_t m01, vec_t m02, vec_t m03,
vec_t m10, vec_t m11, vec_t m12, vec_t m13,
vec_t m20, vec_t m21, vec_t m22, vec_t m23,
vec_t m30, vec_t m31, vec_t m32, vec_t m33
)
{
m[0][0] = m00;
m[0][1] = m01;
m[0][2] = m02;
m[0][3] = m03;
m[1][0] = m10;
m[1][1] = m11;
m[1][2] = m12;
m[1][3] = m13;
m[2][0] = m20;
m[2][1] = m21;
m[2][2] = m22;
m[2][3] = m23;
m[3][0] = m30;
m[3][1] = m31;
m[3][2] = m32;
m[3][3] = m33;
}
//-----------------------------------------------------------------------------
// Initialize from a 3x4
//-----------------------------------------------------------------------------
inline void VMatrix::Init( const matrix3x4_t& _m )
{
m[0][0] = _m[0][0]; m[0][1] = _m[0][1]; m[0][2] = _m[0][2]; m[0][3] = _m[0][3];
m[1][0] = _m[1][0]; m[1][1] = _m[1][1]; m[1][2] = _m[1][2]; m[1][3] = _m[1][3];
m[2][0] = _m[2][0]; m[2][1] = _m[2][1]; m[2][2] = _m[2][2]; m[2][3] = _m[2][3];
m[3][0] = 0.0f; m[3][1] = 0.0f; m[3][2] = 0.0f; m[3][3] = 1.0f;
}
//-----------------------------------------------------------------------------
// VMatrix inlines.
//-----------------------------------------------------------------------------
inline VMatrix::VMatrix()
{
Init(
0.f, 0.f, 0.f, 0.f,
0.f, 0.f, 0.f, 0.f,
0.f, 0.f, 0.f, 0.f,
0.f, 0.f, 0.f, 0.f
);
}
inline VMatrix::VMatrix(
vec_t m00, vec_t m01, vec_t m02, vec_t m03,
vec_t m10, vec_t m11, vec_t m12, vec_t m13,
vec_t m20, vec_t m21, vec_t m22, vec_t m23,
vec_t m30, vec_t m31, vec_t m32, vec_t m33)
{
Init(
m00, m01, m02, m03,
m10, m11, m12, m13,
m20, m21, m22, m23,
m30, m31, m32, m33
);
}
inline VMatrix::VMatrix( const matrix3x4_t& matrix3x4 )
{
Init( matrix3x4 );
}
//-----------------------------------------------------------------------------
// Creates a matrix where the X axis = forward
// the Y axis = left, and the Z axis = up
//-----------------------------------------------------------------------------
inline VMatrix::VMatrix( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis )
{
Init(
xAxis.x, yAxis.x, zAxis.x, 0.0f,
xAxis.y, yAxis.y, zAxis.y, 0.0f,
xAxis.z, yAxis.z, zAxis.z, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
);
}
inline VMatrix::VMatrix( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector& translation )
{
Init(
xAxis.x, yAxis.x, zAxis.x, translation.x,
xAxis.y, yAxis.y, zAxis.y, translation.y,
xAxis.z, yAxis.z, zAxis.z, translation.z,
0.0f, 0.0f, 0.0f, 1.0f
);
}
//-----------------------------------------------------------------------------
// Methods related to the basis vectors of the matrix
//-----------------------------------------------------------------------------
inline VMatrix& VMatrix::operator=(const VMatrix &mOther)
{
m[0][0] = mOther.m[0][0];
m[0][1] = mOther.m[0][1];
m[0][2] = mOther.m[0][2];
m[0][3] = mOther.m[0][3];
m[1][0] = mOther.m[1][0];
m[1][1] = mOther.m[1][1];
m[1][2] = mOther.m[1][2];
m[1][3] = mOther.m[1][3];
m[2][0] = mOther.m[2][0];
m[2][1] = mOther.m[2][1];
m[2][2] = mOther.m[2][2];
m[2][3] = mOther.m[2][3];
m[3][0] = mOther.m[3][0];
m[3][1] = mOther.m[3][1];
m[3][2] = mOther.m[3][2];
m[3][3] = mOther.m[3][3];
return *this;
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline VMatrix VMatrix::operator+(const VMatrix &other) const
{
VMatrix ret;
for(int i=0; i < 16; i++)
{
((float*)ret.m)[i] = ((float*)m)[i] + ((float*)other.m)[i];
}
return ret;
}
inline VMatrix VMatrix::operator-(const VMatrix &other) const
{
VMatrix ret;
for(int i=0; i < 16; i++)
{
((float*)ret.m)[i] = ((float*)m)[i] - ((float*)other.m)[i];
}
return ret;
}
inline VMatrix VMatrix::operator-() const
{
VMatrix ret;
for( int i=0; i < 16; i++ )
{
((float*)ret.m)[i] = ((float*)m)[i];
}
return ret;
}
//-----------------------------------------------------------------------------
// Matrix math operations
//-----------------------------------------------------------------------------
inline const VMatrix& VMatrix::operator+=(const VMatrix &other)
{
for(int i=0; i < 16; i++)
{
((float*)m)[i] += ((float*)other.m)[i];
}
return *this;
}
inline Vector VMatrix::operator*(const Vector &vVec) const
{
Vector vRet;
vRet.x = m[0][0]*vVec.x + m[0][1]*vVec.y + m[0][2]*vVec.z + m[0][3];
vRet.y = m[1][0]*vVec.x + m[1][1]*vVec.y + m[1][2]*vVec.z + m[1][3];
vRet.z = m[2][0]*vVec.x + m[2][1]*vVec.y + m[2][2]*vVec.z + m[2][3];
return vRet;
}
//-----------------------------------------------------------------------------
// Plane transformation
//-----------------------------------------------------------------------------
inline void VMatrix::TransformPlane( const VPlane &inPlane, VPlane &outPlane ) const
{
Vector vTrans;
Vector3DMultiply( *this, inPlane.m_Normal, outPlane.m_Normal );
outPlane.m_Dist = inPlane.m_Dist * DotProduct( outPlane.m_Normal, outPlane.m_Normal );
outPlane.m_Dist += DotProduct( outPlane.m_Normal, GetTranslation( vTrans ) );
}
inline VPlane VMatrix::operator*(const VPlane &thePlane) const
{
VPlane ret;
TransformPlane( thePlane, ret );
return ret;
}
inline bool VMatrix::InverseGeneral(VMatrix &vInverse) const
{
return MatrixInverseGeneral( *this, vInverse );
}
inline VMatrix VMatrix::operator~() const
{
VMatrix mRet;
InverseGeneral(mRet);
return mRet;
}
inline void VMatrix::MatrixMul( const VMatrix &vm, VMatrix &out ) const
{
out.Init(
m[0][0]*vm.m[0][0] + m[0][1]*vm.m[1][0] + m[0][2]*vm.m[2][0] + m[0][3]*vm.m[3][0],
m[0][0]*vm.m[0][1] + m[0][1]*vm.m[1][1] + m[0][2]*vm.m[2][1] + m[0][3]*vm.m[3][1],
m[0][0]*vm.m[0][2] + m[0][1]*vm.m[1][2] + m[0][2]*vm.m[2][2] + m[0][3]*vm.m[3][2],
m[0][0]*vm.m[0][3] + m[0][1]*vm.m[1][3] + m[0][2]*vm.m[2][3] + m[0][3]*vm.m[3][3],
m[1][0]*vm.m[0][0] + m[1][1]*vm.m[1][0] + m[1][2]*vm.m[2][0] + m[1][3]*vm.m[3][0],
m[1][0]*vm.m[0][1] + m[1][1]*vm.m[1][1] + m[1][2]*vm.m[2][1] + m[1][3]*vm.m[3][1],
m[1][0]*vm.m[0][2] + m[1][1]*vm.m[1][2] + m[1][2]*vm.m[2][2] + m[1][3]*vm.m[3][2],
m[1][0]*vm.m[0][3] + m[1][1]*vm.m[1][3] + m[1][2]*vm.m[2][3] + m[1][3]*vm.m[3][3],
m[2][0]*vm.m[0][0] + m[2][1]*vm.m[1][0] + m[2][2]*vm.m[2][0] + m[2][3]*vm.m[3][0],
m[2][0]*vm.m[0][1] + m[2][1]*vm.m[1][1] + m[2][2]*vm.m[2][1] + m[2][3]*vm.m[3][1],
m[2][0]*vm.m[0][2] + m[2][1]*vm.m[1][2] + m[2][2]*vm.m[2][2] + m[2][3]*vm.m[3][2],
m[2][0]*vm.m[0][3] + m[2][1]*vm.m[1][3] + m[2][2]*vm.m[2][3] + m[2][3]*vm.m[3][3],
m[3][0]*vm.m[0][0] + m[3][1]*vm.m[1][0] + m[3][2]*vm.m[2][0] + m[3][3]*vm.m[3][0],
m[3][0]*vm.m[0][1] + m[3][1]*vm.m[1][1] + m[3][2]*vm.m[2][1] + m[3][3]*vm.m[3][1],
m[3][0]*vm.m[0][2] + m[3][1]*vm.m[1][2] + m[3][2]*vm.m[2][2] + m[3][3]*vm.m[3][2],
m[3][0]*vm.m[0][3] + m[3][1]*vm.m[1][3] + m[3][2]*vm.m[2][3] + m[3][3]*vm.m[3][3]
);
}
inline VMatrix VMatrix::operator*(const VMatrix &vm) const
{
VMatrix ret;
MatrixMul( vm, ret );
return ret;
}
inline Vector VMatrix::GetForward() const
{
return Vector(m[0][0], m[1][0], m[2][0]);
}
inline Vector VMatrix::GetLeft() const
{
return Vector(m[0][1], m[1][1], m[2][1]);
}
inline Vector VMatrix::GetUp() const
{
return Vector(m[0][2], m[1][2], m[2][2]);
}
#endif
inline void VMatrix::SetForward(const Vector &vForward)
{
m[0][0] = vForward.x;
m[1][0] = vForward.y;
m[2][0] = vForward.z;
}
inline void VMatrix::SetLeft(const Vector &vLeft)
{
m[0][1] = vLeft.x;
m[1][1] = vLeft.y;
m[2][1] = vLeft.z;
}
inline void VMatrix::SetUp(const Vector &vUp)
{
m[0][2] = vUp.x;
m[1][2] = vUp.y;
m[2][2] = vUp.z;
}
inline void VMatrix::GetBasisVectors(Vector &vForward, Vector &vLeft, Vector &vUp) const
{
vForward.Init( m[0][0], m[1][0], m[2][0] );
vLeft.Init( m[0][1], m[1][1], m[2][1] );
vUp.Init( m[0][2], m[1][2], m[2][2] );
}
inline void VMatrix::SetBasisVectors(const Vector &vForward, const Vector &vLeft, const Vector &vUp)
{
SetForward(vForward);
SetLeft(vLeft);
SetUp(vUp);
}
//-----------------------------------------------------------------------------
// Methods related to the translation component of the matrix
//-----------------------------------------------------------------------------
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline Vector VMatrix::GetTranslation() const
{
return Vector(m[0][3], m[1][3], m[2][3]);
}
#endif
inline Vector& VMatrix::GetTranslation( Vector &vTrans ) const
{
vTrans.x = m[0][3];
vTrans.y = m[1][3];
vTrans.z = m[2][3];
return vTrans;
}
inline void VMatrix::SetTranslation(const Vector &vTrans)
{
m[0][3] = vTrans.x;
m[1][3] = vTrans.y;
m[2][3] = vTrans.z;
}
//-----------------------------------------------------------------------------
// appply translation to this matrix in the input space
//-----------------------------------------------------------------------------
inline void VMatrix::PreTranslate(const Vector &vTrans)
{
Vector tmp;
Vector3DMultiplyPosition( *this, vTrans, tmp );
m[0][3] = tmp.x;
m[1][3] = tmp.y;
m[2][3] = tmp.z;
}
//-----------------------------------------------------------------------------
// appply translation to this matrix in the output space
//-----------------------------------------------------------------------------
inline void VMatrix::PostTranslate(const Vector &vTrans)
{
m[0][3] += vTrans.x;
m[1][3] += vTrans.y;
m[2][3] += vTrans.z;
}
inline const matrix3x4_t& VMatrix::As3x4() const
{
return *((const matrix3x4_t*)this);
}
inline void VMatrix::CopyFrom3x4( const matrix3x4_t &m3x4 )
{
Init(m3x4);
}
inline void VMatrix::Set3x4( const matrix3x4_t& _m )
{
m[0][0] = _m[0][0]; m[0][1] = _m[0][1]; m[0][2] = _m[0][2]; m[0][3] = _m[0][3];
m[1][0] = _m[1][0]; m[1][1] = _m[1][1]; m[1][2] = _m[1][2]; m[1][3] = _m[1][3];
m[2][0] = _m[2][0]; m[2][1] = _m[2][1]; m[2][2] = _m[2][2]; m[2][3] = _m[2][3];
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline Vector VMatrix::VMul4x3(const Vector &vVec) const
{
Vector vResult;
Vector3DMultiplyPosition( *this, vVec, vResult );
return vResult;
}
inline Vector VMatrix::VMul4x3Transpose(const Vector &vVec) const
{
Vector tmp = vVec;
tmp.x -= m[0][3];
tmp.y -= m[1][3];
tmp.z -= m[2][3];
return Vector(
m[0][0]*tmp.x + m[1][0]*tmp.y + m[2][0]*tmp.z,
m[0][1]*tmp.x + m[1][1]*tmp.y + m[2][1]*tmp.z,
m[0][2]*tmp.x + m[1][2]*tmp.y + m[2][2]*tmp.z
);
}
inline Vector VMatrix::VMul3x3(const Vector &vVec) const
{
return Vector(
m[0][0]*vVec.x + m[0][1]*vVec.y + m[0][2]*vVec.z,
m[1][0]*vVec.x + m[1][1]*vVec.y + m[1][2]*vVec.z,
m[2][0]*vVec.x + m[2][1]*vVec.y + m[2][2]*vVec.z
);
}
inline Vector VMatrix::VMul3x3Transpose(const Vector &vVec) const
{
return Vector(
m[0][0]*vVec.x + m[1][0]*vVec.y + m[2][0]*vVec.z,
m[0][1]*vVec.x + m[1][1]*vVec.y + m[2][1]*vVec.z,
m[0][2]*vVec.x + m[1][2]*vVec.y + m[2][2]*vVec.z
);
}
#endif // VECTOR_NO_SLOW_OPERATIONS
inline void VMatrix::V3Mul(const Vector &vIn, Vector &vOut) const
{
vec_t rw;
rw = 1.0f / (m[3][0]*vIn.x + m[3][1]*vIn.y + m[3][2]*vIn.z + m[3][3]);
vOut.x = (m[0][0]*vIn.x + m[0][1]*vIn.y + m[0][2]*vIn.z + m[0][3]) * rw;
vOut.y = (m[1][0]*vIn.x + m[1][1]*vIn.y + m[1][2]*vIn.z + m[1][3]) * rw;
vOut.z = (m[2][0]*vIn.x + m[2][1]*vIn.y + m[2][2]*vIn.z + m[2][3]) * rw;
}
inline void VMatrix::V4Mul(const Vector4D &vIn, Vector4D &vOut) const
{
vOut[0] = m[0][0]*vIn[0] + m[0][1]*vIn[1] + m[0][2]*vIn[2] + m[0][3]*vIn[3];
vOut[1] = m[1][0]*vIn[0] + m[1][1]*vIn[1] + m[1][2]*vIn[2] + m[1][3]*vIn[3];
vOut[2] = m[2][0]*vIn[0] + m[2][1]*vIn[1] + m[2][2]*vIn[2] + m[2][3]*vIn[3];
vOut[3] = m[3][0]*vIn[0] + m[3][1]*vIn[1] + m[3][2]*vIn[2] + m[3][3]*vIn[3];
}
//-----------------------------------------------------------------------------
// Other random stuff
//-----------------------------------------------------------------------------
inline void VMatrix::Identity()
{
MatrixSetIdentity( *this );
}
inline bool VMatrix::IsIdentity() const
{
return
m[0][0] == 1.0f && m[0][1] == 0.0f && m[0][2] == 0.0f && m[0][3] == 0.0f &&
m[1][0] == 0.0f && m[1][1] == 1.0f && m[1][2] == 0.0f && m[1][3] == 0.0f &&
m[2][0] == 0.0f && m[2][1] == 0.0f && m[2][2] == 1.0f && m[2][3] == 0.0f &&
m[3][0] == 0.0f && m[3][1] == 0.0f && m[3][2] == 0.0f && m[3][3] == 1.0f;
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline Vector VMatrix::ApplyRotation(const Vector &vVec) const
{
return VMul3x3(vVec);
}
#endif
inline void VMatrix::InverseTR( VMatrix &ret ) const
{
MatrixInverseTR( *this, ret );
}
inline void MatrixInverseTranspose( const VMatrix& src, VMatrix& dst )
{
src.InverseGeneral( dst );
MatrixTranspose( dst, dst );
}
//-----------------------------------------------------------------------------
// Computes the inverse transpose
//-----------------------------------------------------------------------------
inline void MatrixInverseTranspose( const matrix3x4_t& src, matrix3x4_t& dst )
{
VMatrix tmp, out;
tmp.CopyFrom3x4( src );
::MatrixInverseTranspose( tmp, out );
out.Set3x4( dst );
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline VMatrix VMatrix::InverseTR() const
{
VMatrix ret;
MatrixInverseTR( *this, ret );
return ret;
}
inline Vector VMatrix::GetScale() const
{
Vector vecs[3];
GetBasisVectors(vecs[0], vecs[1], vecs[2]);
return Vector(
vecs[0].Length(),
vecs[1].Length(),
vecs[2].Length()
);
}
inline VMatrix VMatrix::Scale(const Vector &vScale)
{
return VMatrix(
m[0][0]*vScale.x, m[0][1]*vScale.y, m[0][2]*vScale.z, m[0][3],
m[1][0]*vScale.x, m[1][1]*vScale.y, m[1][2]*vScale.z, m[1][3],
m[2][0]*vScale.x, m[2][1]*vScale.y, m[2][2]*vScale.z, m[2][3],
m[3][0]*vScale.x, m[3][1]*vScale.y, m[3][2]*vScale.z, 1.0f
);
}
inline VMatrix VMatrix::NormalizeBasisVectors() const
{
Vector vecs[3];
VMatrix mRet;
GetBasisVectors(vecs[0], vecs[1], vecs[2]);
VectorNormalize( vecs[0] );
VectorNormalize( vecs[1] );
VectorNormalize( vecs[2] );
mRet.SetBasisVectors(vecs[0], vecs[1], vecs[2]);
// Set everything but basis vectors to identity.
mRet.m[3][0] = mRet.m[3][1] = mRet.m[3][2] = 0.0f;
mRet.m[3][3] = 1.0f;
return mRet;
}
inline VMatrix VMatrix::Transpose() const
{
return VMatrix(
m[0][0], m[1][0], m[2][0], m[3][0],
m[0][1], m[1][1], m[2][1], m[3][1],
m[0][2], m[1][2], m[2][2], m[3][2],
m[0][3], m[1][3], m[2][3], m[3][3]);
}
// Transpose upper-left 3x3.
inline VMatrix VMatrix::Transpose3x3() const
{
return VMatrix(
m[0][0], m[1][0], m[2][0], m[0][3],
m[0][1], m[1][1], m[2][1], m[1][3],
m[0][2], m[1][2], m[2][2], m[2][3],
m[3][0], m[3][1], m[3][2], m[3][3]);
}
#endif // VECTOR_NO_SLOW_OPERATIONS
inline bool VMatrix::IsRotationMatrix() const
{
Vector &v1 = (Vector&)m[0][0];
Vector &v2 = (Vector&)m[1][0];
Vector &v3 = (Vector&)m[2][0];
return
FloatMakePositive( 1 - v1.Length() ) < 0.01f &&
FloatMakePositive( 1 - v2.Length() ) < 0.01f &&
FloatMakePositive( 1 - v3.Length() ) < 0.01f &&
FloatMakePositive( v1.Dot(v2) ) < 0.01f &&
FloatMakePositive( v1.Dot(v3) ) < 0.01f &&
FloatMakePositive( v2.Dot(v3) ) < 0.01f;
}
inline void VMatrix::SetupMatrixOrgAngles( const Vector &origin, const QAngle &vAngles )
{
SetupMatrixAnglesInternal( m, vAngles );
// Add translation
m[0][3] = origin.x;
m[1][3] = origin.y;
m[2][3] = origin.z;
m[3][0] = 0.0f;
m[3][1] = 0.0f;
m[3][2] = 0.0f;
m[3][3] = 1.0f;
}
inline void VMatrix::SetupMatrixAngles( const QAngle &vAngles )
{
SetupMatrixAnglesInternal( m, vAngles );
// Zero everything else
m[0][3] = 0.0f;
m[1][3] = 0.0f;
m[2][3] = 0.0f;
m[3][0] = 0.0f;
m[3][1] = 0.0f;
m[3][2] = 0.0f;
m[3][3] = 1.0f;
}
//-----------------------------------------------------------------------------
// Creates euler angles from a matrix
//-----------------------------------------------------------------------------
inline void MatrixToAngles( const VMatrix& src, QAngle& vAngles )
{
float forward[3];
float left[3];
float up[3];
// Extract the basis vectors from the matrix. Since we only need the Z
// component of the up vector, we don't get X and Y.
forward[0] = src[0][0];
forward[1] = src[1][0];
forward[2] = src[2][0];
left[0] = src[0][1];
left[1] = src[1][1];
left[2] = src[2][1];
up[2] = src[2][2];
float xyDist = sqrtf( forward[0] * forward[0] + forward[1] * forward[1] );
// enough here to get angles?
if ( xyDist > 0.001f )
{
// (yaw) y = ATAN( forward.y, forward.x ); -- in our space, forward is the X axis
vAngles[1] = RAD2DEG( atan2f( forward[1], forward[0] ) );
// The engine does pitch inverted from this, but we always end up negating it in the DLL
// UNDONE: Fix the engine to make it consistent
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
vAngles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
// (roll) z = ATAN( left.z, up.z );
vAngles[2] = RAD2DEG( atan2f( left[2], up[2] ) );
}
else // forward is mostly Z, gimbal lock-
{
// (yaw) y = ATAN( -left.x, left.y ); -- forward is mostly z, so use right for yaw
vAngles[1] = RAD2DEG( atan2f( -left[0], left[1] ) );
// The engine does pitch inverted from this, but we always end up negating it in the DLL
// UNDONE: Fix the engine to make it consistent
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
vAngles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );
// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
vAngles[2] = 0;
}
}
//-----------------------------------------------------------------------------
// Transform a plane
//-----------------------------------------------------------------------------
inline void MatrixTransformPlane( const VMatrix &src, const cplane_t &inPlane, cplane_t &outPlane )
{
// What we want to do is the following:
// 1) transform the normal into the new space.
// 2) Determine a point on the old plane given by plane dist * plane normal
// 3) Transform that point into the new space
// 4) Plane dist = DotProduct( new normal, new point )
// An optimized version, which works if the plane is orthogonal.
// 1) Transform the normal into the new space
// 2) Realize that transforming the old plane point into the new space
// is given by [ d * n'x + Tx, d * n'y + Ty, d * n'z + Tz ]
// where d = old plane dist, n' = transformed normal, Tn = translational component of transform
// 3) Compute the new plane dist using the dot product of the normal result of #2
// For a correct result, this should be an inverse-transpose matrix
// but that only matters if there are nonuniform scale or skew factors in this matrix.
Vector vTrans;
Vector3DMultiply( src, inPlane.normal, outPlane.normal );
outPlane.dist = inPlane.dist * DotProduct( outPlane.normal, outPlane.normal );
outPlane.dist += DotProduct( outPlane.normal, src.GetTranslation(vTrans) );
}
//-----------------------------------------------------------------------------
// Helper functions.
//-----------------------------------------------------------------------------
#define VMatToString(mat) (static_cast<const char *>(CFmtStr("[ (%f, %f, %f), (%f, %f, %f), (%f, %f, %f), (%f, %f, %f) ]", mat.m[0][0], mat.m[0][1], mat.m[0][2], mat.m[0][3], mat.m[1][0], mat.m[1][1], mat.m[1][2], mat.m[1][3], mat.m[2][0], mat.m[2][1], mat.m[2][2], mat.m[2][3], mat.m[3][0], mat.m[3][1], mat.m[3][2], mat.m[3][3] ))) // ** Note: this generates a temporary, don't hold reference!
//-----------------------------------------------------------------------------
// Matrix multiply
//-----------------------------------------------------------------------------
typedef ALIGN16 float VMatrixRaw_t[4];
//-----------------------------------------------------------------------------
// Matrix/vector multiply
//-----------------------------------------------------------------------------
inline void Vector4DMultiply( const VMatrix& src1, Vector4D const& src2, Vector4D& dst )
{
// Make sure it works if src2 == dst
Vector4D tmp;
Vector4D const&v = (&src2 == &dst) ? tmp : src2;
if (&src2 == &dst)
{
Vector4DCopy( src2, tmp );
}
dst[0] = src1[0][0] * v[0] + src1[0][1] * v[1] + src1[0][2] * v[2] + src1[0][3] * v[3];
dst[1] = src1[1][0] * v[0] + src1[1][1] * v[1] + src1[1][2] * v[2] + src1[1][3] * v[3];
dst[2] = src1[2][0] * v[0] + src1[2][1] * v[1] + src1[2][2] * v[2] + src1[2][3] * v[3];
dst[3] = src1[3][0] * v[0] + src1[3][1] * v[1] + src1[3][2] * v[2] + src1[3][3] * v[3];
}
//-----------------------------------------------------------------------------
// Matrix/vector multiply
//-----------------------------------------------------------------------------
inline void Vector4DMultiplyPosition( const VMatrix& src1, Vector const& src2, Vector4D& dst )
{
// Make sure it works if src2 == dst
Vector tmp;
Vector const&v = ( &src2 == &dst.AsVector3D() ) ? static_cast<const Vector&>(tmp) : src2;
if (&src2 == &dst.AsVector3D())
{
VectorCopy( src2, tmp );
}
dst[0] = src1[0][0] * v[0] + src1[0][1] * v[1] + src1[0][2] * v[2] + src1[0][3];
dst[1] = src1[1][0] * v[0] + src1[1][1] * v[1] + src1[1][2] * v[2] + src1[1][3];
dst[2] = src1[2][0] * v[0] + src1[2][1] * v[1] + src1[2][2] * v[2] + src1[2][3];
dst[3] = src1[3][0] * v[0] + src1[3][1] * v[1] + src1[3][2] * v[2] + src1[3][3];
}
//-----------------------------------------------------------------------------
// Vector3DMultiplyPositionProjective treats src2 as if it's a point
// and does the perspective divide at the end
//-----------------------------------------------------------------------------
inline void Vector3DMultiplyPositionProjective( const VMatrix& src1, const Vector &src2, Vector& dst )
{
// Make sure it works if src2 == dst
Vector tmp;
const Vector &v = (&src2 == &dst) ? static_cast<const Vector&>(tmp): src2;
if( &src2 == &dst )
{
VectorCopy( src2, tmp );
}
float w = src1[3][0] * v[0] + src1[3][1] * v[1] + src1[3][2] * v[2] + src1[3][3];
if ( w != 0.0f )
{
w = 1.0f / w;
}
dst[0] = src1[0][0] * v[0] + src1[0][1] * v[1] + src1[0][2] * v[2] + src1[0][3];
dst[1] = src1[1][0] * v[0] + src1[1][1] * v[1] + src1[1][2] * v[2] + src1[1][3];
dst[2] = src1[2][0] * v[0] + src1[2][1] * v[1] + src1[2][2] * v[2] + src1[2][3];
dst *= w;
}
//-----------------------------------------------------------------------------
// Vector3DMultiplyProjective treats src2 as if it's a direction
// and does the perspective divide at the end
//-----------------------------------------------------------------------------
inline void Vector3DMultiplyProjective( const VMatrix& src1, const Vector &src2, Vector& dst )
{
// Make sure it works if src2 == dst
Vector tmp;
const Vector &v = (&src2 == &dst) ? static_cast<const Vector&>(tmp) : src2;
if( &src2 == &dst )
{
VectorCopy( src2, tmp );
}
float w;
dst[0] = src1[0][0] * v[0] + src1[0][1] * v[1] + src1[0][2] * v[2];
dst[1] = src1[1][0] * v[0] + src1[1][1] * v[1] + src1[1][2] * v[2];
dst[2] = src1[2][0] * v[0] + src1[2][1] * v[1] + src1[2][2] * v[2];
w = src1[3][0] * v[0] + src1[3][1] * v[1] + src1[3][2] * v[2];
if (w != 0.0f)
{
dst /= w;
}
else
{
dst = vec3_origin;
}
}
//-----------------------------------------------------------------------------
// Multiplies the vector by the transpose of the matrix
//-----------------------------------------------------------------------------
inline void Vector4DMultiplyTranspose( const VMatrix& src1, Vector4D const& src2, Vector4D& dst )
{
// Make sure it works if src2 == dst
bool srcEqualsDst = (&src2 == &dst);
Vector4D tmp;
Vector4D const&v = srcEqualsDst ? tmp : src2;
if (srcEqualsDst)
{
Vector4DCopy( src2, tmp );
}
dst[0] = src1[0][0] * v[0] + src1[1][0] * v[1] + src1[2][0] * v[2] + src1[3][0] * v[3];
dst[1] = src1[0][1] * v[0] + src1[1][1] * v[1] + src1[2][1] * v[2] + src1[3][1] * v[3];
dst[2] = src1[0][2] * v[0] + src1[1][2] * v[1] + src1[2][2] * v[2] + src1[3][2] * v[3];
dst[3] = src1[0][3] * v[0] + src1[1][3] * v[1] + src1[2][3] * v[2] + src1[3][3] * v[3];
}
//-----------------------------------------------------------------------------
// Multiplies the vector by the transpose of the matrix
//-----------------------------------------------------------------------------
inline void Vector3DMultiplyTranspose( const VMatrix& src1, const Vector& src2, Vector& dst )
{
// Make sure it works if src2 == dst
bool srcEqualsDst = (&src2 == &dst);
Vector tmp;
const Vector&v = srcEqualsDst ? static_cast<const Vector&>(tmp) : src2;
if (srcEqualsDst)
{
VectorCopy( src2, tmp );
}
dst[0] = src1[0][0] * v[0] + src1[1][0] * v[1] + src1[2][0] * v[2];
dst[1] = src1[0][1] * v[0] + src1[1][1] * v[1] + src1[2][1] * v[2];
dst[2] = src1[0][2] * v[0] + src1[1][2] * v[1] + src1[2][2] * v[2];
}
//-----------------------------------------------------------------------------
// Matrix copy
//-----------------------------------------------------------------------------
inline void MatrixCopy( const VMatrix& src, VMatrix& dst )
{
if (&src != &dst)
dst = src;
}
inline void MatrixMultiply( const VMatrix& src1, const VMatrix& src2, VMatrix& dst )
{
// Make sure it works if src1 == dst or src2 == dst
VMatrix tmp1, tmp2;
const VMatrixRaw_t* s1 = (&src1 == &dst) ? tmp1.m : src1.m;
const VMatrixRaw_t* s2 = (&src2 == &dst) ? tmp2.m : src2.m;
if (&src1 == &dst)
MatrixCopy( src1, tmp1 );
if (&src2 == &dst)
MatrixCopy( src2, tmp2 );
dst[0][0] = s1[0][0] * s2[0][0] + s1[0][1] * s2[1][0] + s1[0][2] * s2[2][0] + s1[0][3] * s2[3][0];
dst[0][1] = s1[0][0] * s2[0][1] + s1[0][1] * s2[1][1] + s1[0][2] * s2[2][1] + s1[0][3] * s2[3][1];
dst[0][2] = s1[0][0] * s2[0][2] + s1[0][1] * s2[1][2] + s1[0][2] * s2[2][2] + s1[0][3] * s2[3][2];
dst[0][3] = s1[0][0] * s2[0][3] + s1[0][1] * s2[1][3] + s1[0][2] * s2[2][3] + s1[0][3] * s2[3][3];
dst[1][0] = s1[1][0] * s2[0][0] + s1[1][1] * s2[1][0] + s1[1][2] * s2[2][0] + s1[1][3] * s2[3][0];
dst[1][1] = s1[1][0] * s2[0][1] + s1[1][1] * s2[1][1] + s1[1][2] * s2[2][1] + s1[1][3] * s2[3][1];
dst[1][2] = s1[1][0] * s2[0][2] + s1[1][1] * s2[1][2] + s1[1][2] * s2[2][2] + s1[1][3] * s2[3][2];
dst[1][3] = s1[1][0] * s2[0][3] + s1[1][1] * s2[1][3] + s1[1][2] * s2[2][3] + s1[1][3] * s2[3][3];
dst[2][0] = s1[2][0] * s2[0][0] + s1[2][1] * s2[1][0] + s1[2][2] * s2[2][0] + s1[2][3] * s2[3][0];
dst[2][1] = s1[2][0] * s2[0][1] + s1[2][1] * s2[1][1] + s1[2][2] * s2[2][1] + s1[2][3] * s2[3][1];
dst[2][2] = s1[2][0] * s2[0][2] + s1[2][1] * s2[1][2] + s1[2][2] * s2[2][2] + s1[2][3] * s2[3][2];
dst[2][3] = s1[2][0] * s2[0][3] + s1[2][1] * s2[1][3] + s1[2][2] * s2[2][3] + s1[2][3] * s2[3][3];
dst[3][0] = s1[3][0] * s2[0][0] + s1[3][1] * s2[1][0] + s1[3][2] * s2[2][0] + s1[3][3] * s2[3][0];
dst[3][1] = s1[3][0] * s2[0][1] + s1[3][1] * s2[1][1] + s1[3][2] * s2[2][1] + s1[3][3] * s2[3][1];
dst[3][2] = s1[3][0] * s2[0][2] + s1[3][1] * s2[1][2] + s1[3][2] * s2[2][2] + s1[3][3] * s2[3][2];
dst[3][3] = s1[3][0] * s2[0][3] + s1[3][1] * s2[1][3] + s1[3][2] * s2[2][3] + s1[3][3] * s2[3][3];
}
//-----------------------------------------------------------------------------
// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
//
// | ax2 + (1 - ax2)cosQ axay(1 - cosQ) - azsinQ azax(1 - cosQ) + aysinQ |
// Ra(Q) = | axay(1 - cosQ) + azsinQ ay2 + (1 - ay2)cosQ ayaz(1 - cosQ) - axsinQ |
// | azax(1 - cosQ) - aysinQ ayaz(1 - cosQ) + axsinQ az2 + (1 - az2)cosQ |
//
// Input : mat -
// vAxisOrRot -
// angle -
//-----------------------------------------------------------------------------
inline void MatrixBuildRotationAboutAxis( const Vector &vAxisOfRot, float angleDegrees, matrix3x4_t &dst )
{
float radians;
float axisXSquared;
float axisYSquared;
float axisZSquared;
float fSin;
float fCos;
radians = angleDegrees * ( M_PI / 180.0 );
fSin = sinf( radians );
fCos = cosf( radians );
axisXSquared = vAxisOfRot[0] * vAxisOfRot[0];
axisYSquared = vAxisOfRot[1] * vAxisOfRot[1];
axisZSquared = vAxisOfRot[2] * vAxisOfRot[2];
// Column 0:
dst[0][0] = axisXSquared + (1 - axisXSquared) * fCos;
dst[1][0] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) + vAxisOfRot[2] * fSin;
dst[2][0] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) - vAxisOfRot[1] * fSin;
// Column 1:
dst[0][1] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) - vAxisOfRot[2] * fSin;
dst[1][1] = axisYSquared + (1 - axisYSquared) * fCos;
dst[2][1] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) + vAxisOfRot[0] * fSin;
// Column 2:
dst[0][2] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) + vAxisOfRot[1] * fSin;
dst[1][2] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) - vAxisOfRot[0] * fSin;
dst[2][2] = axisZSquared + (1 - axisZSquared) * fCos;
// Column 3:
dst[0][3] = 0;
dst[1][3] = 0;
dst[2][3] = 0;
}
//-----------------------------------------------------------------------------
// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
//
// | ax2 + (1 - ax2)cosQ axay(1 - cosQ) - azsinQ azax(1 - cosQ) + aysinQ |
// Ra(Q) = | axay(1 - cosQ) + azsinQ ay2 + (1 - ay2)cosQ ayaz(1 - cosQ) - axsinQ |
// | azax(1 - cosQ) - aysinQ ayaz(1 - cosQ) + axsinQ az2 + (1 - az2)cosQ |
//
// Input : mat -
// vAxisOrRot -
// angle -
//-----------------------------------------------------------------------------
inline void MatrixBuildRotationAboutAxis( VMatrix &dst, const Vector &vAxisOfRot, float angleDegrees )
{
MatrixBuildRotationAboutAxis( vAxisOfRot, angleDegrees, const_cast< matrix3x4_t &> ( dst.As3x4() ) );
dst[3][0] = 0;
dst[3][1] = 0;
dst[3][2] = 0;
dst[3][3] = 1;
}
//-----------------------------------------------------------------------------
// Builds a rotation matrix that rotates one direction vector into another
//-----------------------------------------------------------------------------
inline void MatrixBuildTranslation( VMatrix& dst, float x, float y, float z )
{
MatrixSetIdentity( dst );
dst[0][3] = x;
dst[1][3] = y;
dst[2][3] = z;
}
inline void MatrixBuildTranslation( VMatrix& dst, const Vector &translation )
{
MatrixSetIdentity( dst );
dst[0][3] = translation[0];
dst[1][3] = translation[1];
dst[2][3] = translation[2];
}
inline void MatrixTranslate( VMatrix& dst, const Vector &translation )
{
VMatrix matTranslation, temp;
MatrixBuildTranslation( matTranslation, translation );
MatrixMultiply( dst, matTranslation, temp );
dst = temp;
}
inline void MatrixRotate( VMatrix& dst, const Vector& vAxisOfRot, float angleDegrees )
{
VMatrix rotation, temp;
MatrixBuildRotationAboutAxis( rotation, vAxisOfRot, angleDegrees );
MatrixMultiply( dst, rotation, temp );
dst = temp;
}
//-----------------------------------------------------------------------------
// Accessors
//-----------------------------------------------------------------------------
inline void MatrixGetColumn( const VMatrix &src, int nCol, Vector *pColumn )
{
Assert( (nCol >= 0) && (nCol <= 3) );
pColumn->x = src[0][nCol];
pColumn->y = src[1][nCol];
pColumn->z = src[2][nCol];
}
inline void MatrixGetRow( const VMatrix &src, int nRow, Vector *pRow )
{
Assert( (nRow >= 0) && (nRow <= 3) );
*pRow = *(Vector*)src[nRow];
}
inline void MatrixSetRow( VMatrix &dst, int nRow, const Vector &row )
{
Assert( (nRow >= 0) && (nRow <= 3) );
*(Vector*)dst[nRow] = row;
}
//-----------------------------------------------------------------------------
// Transform a plane that has an axis-aligned normal
//-----------------------------------------------------------------------------
inline void MatrixTransformAxisAlignedPlane( const VMatrix &src, int nDim, float flSign, float flDist, cplane_t &outPlane )
{
// See MatrixTransformPlane in the .cpp file for an explanation of the algorithm.
MatrixGetColumn( src, nDim, &outPlane.normal );
outPlane.normal *= flSign;
outPlane.dist = flDist * DotProduct( outPlane.normal, outPlane.normal );
// NOTE: Writing this out by hand because it doesn't inline (inline depth isn't large enough)
// This should read outPlane.dist += DotProduct( outPlane.normal, src.GetTranslation );
outPlane.dist += outPlane.normal.x * src.m[0][3] + outPlane.normal.y * src.m[1][3] + outPlane.normal.z * src.m[2][3];
}
//-----------------------------------------------------------------------------
// Matrix equality test
//-----------------------------------------------------------------------------
inline bool MatricesAreEqual( const VMatrix &src1, const VMatrix &src2, float flTolerance )
{
for ( int i = 0; i < 3; ++i )
{
for ( int j = 0; j < 3; ++j )
{
if ( fabs( src1[i][j] - src2[i][j] ) > flTolerance )
return false;
}
}
return true;
}
//-----------------------------------------------------------------------------
//
//-----------------------------------------------------------------------------
void MatrixBuildOrtho( VMatrix& dst, double left, double top, double right, double bottom, double zNear, double zFar );
void MatrixBuildPerspectiveX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar );
void MatrixBuildPerspectiveOffCenterX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar, double bottom, double top, double left, double right );
void MatrixBuildPerspectiveZRange( VMatrix& dst, double flZNear, double flZFar );
inline void MatrixOrtho( VMatrix& dst, double left, double top, double right, double bottom, double zNear, double zFar )
{
VMatrix mat;
MatrixBuildOrtho( mat, left, top, right, bottom, zNear, zFar );
VMatrix temp;
MatrixMultiply( dst, mat, temp );
dst = temp;
}
inline void MatrixPerspectiveX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar )
{
VMatrix mat;
MatrixBuildPerspectiveX( mat, flFovX, flAspect, flZNear, flZFar );
VMatrix temp;
MatrixMultiply( dst, mat, temp );
dst = temp;
}
inline void MatrixPerspectiveOffCenterX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar, double bottom, double top, double left, double right )
{
VMatrix mat;
MatrixBuildPerspectiveOffCenterX( mat, flFovX, flAspect, flZNear, flZFar, bottom, top, left, right );
VMatrix temp;
MatrixMultiply( dst, mat, temp );
dst = temp;
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
inline VMatrix SetupMatrixIdentity()
{
return VMatrix(
1.0f, 0.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
}
inline VMatrix SetupMatrixTranslation(const Vector &vTranslation)
{
return VMatrix(
1.0f, 0.0f, 0.0f, vTranslation.x,
0.0f, 1.0f, 0.0f, vTranslation.y,
0.0f, 0.0f, 1.0f, vTranslation.z,
0.0f, 0.0f, 0.0f, 1.0f
);
}
inline VMatrix SetupMatrixScale(const Vector &vScale)
{
return VMatrix(
vScale.x, 0.0f, 0.0f, 0.0f,
0.0f, vScale.y, 0.0f, 0.0f,
0.0f, 0.0f, vScale.z, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
);
}
inline VMatrix SetupMatrixReflection(const VPlane &thePlane)
{
VMatrix mReflect, mBack, mForward;
Vector vOrigin, N;
N = thePlane.m_Normal;
mReflect.Init(
-2.0f*N.x*N.x + 1.0f, -2.0f*N.x*N.y, -2.0f*N.x*N.z, 0.0f,
-2.0f*N.y*N.x, -2.0f*N.y*N.y + 1.0f, -2.0f*N.y*N.z, 0.0f,
-2.0f*N.z*N.x, -2.0f*N.z*N.y, -2.0f*N.z*N.z + 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
);
vOrigin = thePlane.GetPointOnPlane();
mBack.Identity();
mBack.SetTranslation(-vOrigin);
mForward.Identity();
mForward.SetTranslation(vOrigin);
// (multiplied in reverse order, so it translates to the origin point,
// reflects, and translates back).
return mForward * mReflect * mBack;
}
inline VMatrix SetupMatrixProjection(const Vector &vOrigin, const VPlane &thePlane)
{
vec_t dot;
VMatrix mRet;
#define PN thePlane.m_Normal
#define PD thePlane.m_Dist;
dot = PN[0]*vOrigin.x + PN[1]*vOrigin.y + PN[2]*vOrigin.z - PD;
mRet.m[0][0] = dot - vOrigin.x * PN[0];
mRet.m[0][1] = -vOrigin.x * PN[1];
mRet.m[0][2] = -vOrigin.x * PN[2];
mRet.m[0][3] = -vOrigin.x * -PD;
mRet.m[1][0] = -vOrigin.y * PN[0];
mRet.m[1][1] = dot - vOrigin.y * PN[1];
mRet.m[1][2] = -vOrigin.y * PN[2];
mRet.m[1][3] = -vOrigin.y * -PD;
mRet.m[2][0] = -vOrigin.z * PN[0];
mRet.m[2][1] = -vOrigin.z * PN[1];
mRet.m[2][2] = dot - vOrigin.z * PN[2];
mRet.m[2][3] = -vOrigin.z * -PD;
mRet.m[3][0] = -PN[0];
mRet.m[3][1] = -PN[1];
mRet.m[3][2] = -PN[2];
mRet.m[3][3] = dot + PD;
#undef PN
#undef PD
return mRet;
}
inline VMatrix SetupMatrixAxisRot(const Vector &vAxis, vec_t fDegrees)
{
vec_t s, c, t;
vec_t tx, ty, tz;
vec_t sx, sy, sz;
vec_t fRadians;
fRadians = fDegrees * (M_PI / 180.0f);
s = (vec_t)sin(fRadians);
c = (vec_t)cos(fRadians);
t = 1.0f - c;
tx = t * vAxis.x; ty = t * vAxis.y; tz = t * vAxis.z;
sx = s * vAxis.x; sy = s * vAxis.y; sz = s * vAxis.z;
return VMatrix(
tx*vAxis.x + c, tx*vAxis.y - sz, tx*vAxis.z + sy, 0.0f,
tx*vAxis.y + sz, ty*vAxis.y + c, ty*vAxis.z - sx, 0.0f,
tx*vAxis.z - sy, ty*vAxis.z + sx, tz*vAxis.z + c, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f);
}
//-----------------------------------------------------------------------------
// Setup a matrix from euler angles.
//-----------------------------------------------------------------------------
inline void MatrixFromAngles( const QAngle& vAngles, VMatrix& dst )
{
dst.SetupMatrixOrgAngles( vec3_origin, vAngles );
}
inline VMatrix SetupMatrixAngles(const QAngle &vAngles)
{
VMatrix mRet;
MatrixFromAngles( vAngles, mRet );
return mRet;
}
inline VMatrix SetupMatrixOrgAngles(const Vector &origin, const QAngle &vAngles)
{
VMatrix mRet;
mRet.SetupMatrixOrgAngles( origin, vAngles );
return mRet;
}
#endif // VECTOR_NO_SLOW_OPERATIONS
inline bool PlaneIntersection( const VPlane &vp1, const VPlane &vp2, const VPlane &vp3, Vector &vOut )
{
VMatrix mMat, mInverse;
mMat.Init(
vp1.m_Normal.x, vp1.m_Normal.y, vp1.m_Normal.z, -vp1.m_Dist,
vp2.m_Normal.x, vp2.m_Normal.y, vp2.m_Normal.z, -vp2.m_Dist,
vp3.m_Normal.x, vp3.m_Normal.y, vp3.m_Normal.z, -vp3.m_Dist,
0.0f, 0.0f, 0.0f, 1.0f
);
if(mMat.InverseGeneral(mInverse))
{
//vOut = mInverse * Vector(0.0f, 0.0f, 0.0f);
mInverse.GetTranslation( vOut );
return true;
}
else
{
return false;
}
}
//-----------------------------------------------------------------------------
// Builds a rotation matrix that rotates one direction vector into another
//-----------------------------------------------------------------------------
inline void MatrixBuildRotation( VMatrix &dst, const Vector& initialDirection, const Vector& finalDirection )
{
float angle = DotProduct( initialDirection, finalDirection );
Assert( IsFinite(angle) );
Vector axis;
// No rotation required
if (angle - 1.0 > -1e-3)
{
// parallel case
MatrixSetIdentity(dst);
return;
}
else if (angle + 1.0 < 1e-3)
{
// antiparallel case, pick any axis in the plane
// perpendicular to the final direction. Choose the direction (x,y,z)
// which has the minimum component of the final direction, use that
// as an initial guess, then subtract out the component which is
// parallel to the final direction
int idx = 0;
if (FloatMakePositive(finalDirection[1]) < FloatMakePositive(finalDirection[idx]))
idx = 1;
if (FloatMakePositive(finalDirection[2]) < FloatMakePositive(finalDirection[idx]))
idx = 2;
axis.Init( 0, 0, 0 );
axis[idx] = 1.0f;
VectorMA( axis, -DotProduct( axis, finalDirection ), finalDirection, axis );
VectorNormalize(axis);
angle = 180.0f;
}
else
{
CrossProduct( initialDirection, finalDirection, axis );
VectorNormalize( axis );
angle = acos(angle) * 180 / M_PI;
}
MatrixBuildRotationAboutAxis( dst, axis, angle );
#ifdef _DEBUG
Vector test;
Vector3DMultiply( dst, initialDirection, test );
test -= finalDirection;
Assert( test.LengthSqr() < 1e-3 );
#endif
}
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
inline void MatrixBuildRotateZ( VMatrix &dst, float angleDegrees )
{
float radians = angleDegrees * ( M_PI / 180.0f );
float fSin = ( float )sin( radians );
float fCos = ( float )cos( radians );
dst[0][0] = fCos; dst[0][1] = -fSin; dst[0][2] = 0.0f; dst[0][3] = 0.0f;
dst[1][0] = fSin; dst[1][1] = fCos; dst[1][2] = 0.0f; dst[1][3] = 0.0f;
dst[2][0] = 0.0f; dst[2][1] = 0.0f; dst[2][2] = 1.0f; dst[2][3] = 0.0f;
dst[3][0] = 0.0f; dst[3][1] = 0.0f; dst[3][2] = 0.0f; dst[3][3] = 1.0f;
}
// Builds a scale matrix
inline void MatrixBuildScale( VMatrix &dst, float x, float y, float z )
{
dst[0][0] = x; dst[0][1] = 0.0f; dst[0][2] = 0.0f; dst[0][3] = 0.0f;
dst[1][0] = 0.0f; dst[1][1] = y; dst[1][2] = 0.0f; dst[1][3] = 0.0f;
dst[2][0] = 0.0f; dst[2][1] = 0.0f; dst[2][2] = z; dst[2][3] = 0.0f;
dst[3][0] = 0.0f; dst[3][1] = 0.0f; dst[3][2] = 0.0f; dst[3][3] = 1.0f;
}
inline void MatrixBuildScale( VMatrix &dst, const Vector& scale )
{
MatrixBuildScale( dst, scale.x, scale.y, scale.z );
}
// nillerusr: optimize this bruh later
inline void MatrixBuildPerspective( VMatrix &dst, float fovX, float fovY, float zNear, float zFar )
{
// FIXME: collapse all of this into one matrix after we figure out what all should be in here.
float width = 2 * zNear * tan( fovX * ( M_PI/180.0f ) * 0.5f );
float height = 2 * zNear * tan( fovY * ( M_PI/180.0f ) * 0.5f );
dst. Init(
2.0f * zNear / width, 0.f, 0.f, 0.f,
0.f, 2.0f * zNear / height, 0.f, 0.f,
0.f, 0.f, -zFar / ( zNear - zFar ), zNear * zFar / ( zNear - zFar ),
0.f, 0.f, 1.f, 0.f
);
// negate X and Y so that X points right, and Y points up.
VMatrix negateXY;
negateXY.Identity();
negateXY[0][0] = -1.0f;
negateXY[1][1] = -1.0f;
MatrixMultiply( negateXY, dst, dst );
VMatrix addW;
addW.Identity();
addW[0][3] = 1.0f;
addW[1][3] = 1.0f;
addW[2][3] = 0.0f;
MatrixMultiply( addW, dst, dst );
VMatrix scaleHalf;
scaleHalf.Identity();
scaleHalf[0][0] = 0.5f;
scaleHalf[1][1] = 0.5f;
MatrixMultiply( scaleHalf, dst, dst );
}
static inline void CalculateAABBForNormalizedFrustum_Helper( float x, float y, float z, const VMatrix &volumeToWorld, Vector &mins, Vector &maxs )
{
Vector volumeSpacePos( x, y, z );
// Make sure it's been clipped
Assert( volumeSpacePos[0] >= -1e-3f );
Assert( volumeSpacePos[0] - 1.0f <= 1e-3f );
Assert( volumeSpacePos[1] >= -1e-3f );
Assert( volumeSpacePos[1] - 1.0f <= 1e-3f );
Assert( volumeSpacePos[2] >= -1e-3f );
Assert( volumeSpacePos[2] - 1.0f <= 1e-3f );
Vector worldPos;
Vector3DMultiplyPositionProjective( volumeToWorld, volumeSpacePos, worldPos );
AddPointToBounds( worldPos, mins, maxs );
}
//-----------------------------------------------------------------------------
// Given an inverse projection matrix, take the extremes of the space in transformed into world space and
// get a bounding box.
//-----------------------------------------------------------------------------
inline void CalculateAABBFromProjectionMatrixInverse( const VMatrix &volumeToWorld, Vector *pMins, Vector *pMaxs )
{
// FIXME: Could maybe do better than the compile with all of these multiplies by 0 and 1.
ClearBounds( *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 0, 0, 0, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 0, 0, 1, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 0, 1, 0, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 0, 1, 1, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 1, 0, 0, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 1, 0, 1, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 1, 1, 0, volumeToWorld, *pMins, *pMaxs );
CalculateAABBForNormalizedFrustum_Helper( 1, 1, 1, volumeToWorld, *pMins, *pMaxs );
}
inline void CalculateAABBFromProjectionMatrix( const VMatrix &worldToVolume, Vector *pMins, Vector *pMaxs )
{
VMatrix volumeToWorld;
MatrixInverseGeneral( worldToVolume, volumeToWorld );
CalculateAABBFromProjectionMatrixInverse( volumeToWorld, pMins, pMaxs );
}
//-----------------------------------------------------------------------------
// Given an inverse projection matrix, take the extremes of the space in transformed into world space and
// get a bounding sphere.
//-----------------------------------------------------------------------------
inline void CalculateSphereFromProjectionMatrixInverse( const VMatrix &volumeToWorld, Vector *pCenter, float *pflRadius )
{
// FIXME: Could maybe do better than the compile with all of these multiplies by 0 and 1.
// Need 3 points: the endpoint of the line through the center of the near + far planes,
// and one point on the far plane. From that, we can derive a point somewhere on the center line
// which would produce the smallest bounding sphere.
Vector vecCenterNear, vecCenterFar, vecNearEdge, vecFarEdge;
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.5f, 0.5f, 0.0f ), vecCenterNear );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.5f, 0.5f, 1.0f ), vecCenterFar );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.0f, 0.0f, 0.0f ), vecNearEdge );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.0f, 0.0f, 1.0f ), vecFarEdge );
// Let the distance between the near + far center points = l
// Let the distance between the near center point + near edge point = h1
// Let the distance between the far center point + far edge point = h2
// Let the distance along the center line from the near point to the sphere center point = x
// Then let the distance between the sphere center point + near edge point ==
// the distance between the sphere center point + far edge point == r == radius of sphere
// Then h1^2 + x^2 == r^2 == (l-x)^2 + h2^2
// h1^x + x^2 = l^2 - 2 * l * x + x^2 + h2^2
// 2 * l * x = l^2 + h2^2 - h1^2
// x = (l^2 + h2^2 - h1^2) / (2 * l)
// r = sqrt( hl^1 + x^2 )
Vector vecDelta;
VectorSubtract( vecCenterFar, vecCenterNear, vecDelta );
float l = vecDelta.Length();
float h1Sqr = vecCenterNear.DistToSqr( vecNearEdge );
float h2Sqr = vecCenterFar.DistToSqr( vecFarEdge );
float x = (l*l + h2Sqr - h1Sqr) / (2.0f * l);
VectorMA( vecCenterNear, (x / l), vecDelta, *pCenter );
*pflRadius = sqrt( h1Sqr + x*x );
}
//-----------------------------------------------------------------------------
// Given a projection matrix, take the extremes of the space in transformed into world space and
// get a bounding sphere.
//-----------------------------------------------------------------------------
inline void CalculateSphereFromProjectionMatrix( const VMatrix &worldToVolume, Vector *pCenter, float *pflRadius )
{
VMatrix volumeToWorld;
MatrixInverseGeneral( worldToVolume, volumeToWorld );
CalculateSphereFromProjectionMatrixInverse( volumeToWorld, pCenter, pflRadius );
}
static inline void FrustumPlanesFromMatrixHelper( const VMatrix &shadowToWorld, const Vector &p1, const Vector &p2, const Vector &p3,
Vector &normal, float &dist )
{
Vector world1, world2, world3;
Vector3DMultiplyPositionProjective( shadowToWorld, p1, world1 );
Vector3DMultiplyPositionProjective( shadowToWorld, p2, world2 );
Vector3DMultiplyPositionProjective( shadowToWorld, p3, world3 );
Vector v1, v2;
VectorSubtract( world2, world1, v1 );
VectorSubtract( world3, world1, v2 );
CrossProduct( v1, v2, normal );
VectorNormalize( normal );
dist = DotProduct( normal, world1 );
}
inline void FrustumPlanesFromMatrix( const VMatrix &clipToWorld, Frustum_t &frustum )
{
Vector normal;
float dist;
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 0.0f, 0.0f, 0.0f ), Vector( 1.0f, 0.0f, 0.0f ), Vector( 0.0f, 1.0f, 0.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_NEARZ, PLANE_ANYZ, normal, dist );
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 0.0f, 0.0f, 1.0f ), Vector( 0.0f, 1.0f, 1.0f ), Vector( 1.0f, 0.0f, 1.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_FARZ, PLANE_ANYZ, normal, dist );
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 1.0f, 0.0f, 0.0f ), Vector( 1.0f, 1.0f, 1.0f ), Vector( 1.0f, 1.0f, 0.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_RIGHT, PLANE_ANYZ, normal, dist );
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 0.0f, 0.0f, 0.0f ), Vector( 0.0f, 1.0f, 1.0f ), Vector( 0.0f, 0.0f, 1.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_LEFT, PLANE_ANYZ, normal, dist );
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 1.0f, 1.0f, 0.0f ), Vector( 1.0f, 1.0f, 1.0f ), Vector( 0.0f, 1.0f, 1.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_TOP, PLANE_ANYZ, normal, dist );
FrustumPlanesFromMatrixHelper( clipToWorld,
Vector( 1.0f, 0.0f, 0.0f ), Vector( 0.0f, 0.0f, 1.0f ), Vector( 1.0f, 0.0f, 1.0f ), normal, dist );
frustum.SetPlane( FRUSTUM_BOTTOM, PLANE_ANYZ, normal, dist );
}
inline void MatrixBuildOrtho( VMatrix& dst, double left, double top, double right, double bottom, double zNear, double zFar )
{
// FIXME: This is being used incorrectly! Should read:
// D3DXMatrixOrthoOffCenterRH( &matrix, left, right, bottom, top, zNear, zFar );
// Which is certainly why we need these extra -1 scales in y. Bleah
// NOTE: The camera can be imagined as the following diagram:
// /z
// /
// /____ x Z is going into the screen
// |
// |
// |y
//
// (0,0,z) represents the upper-left corner of the screen.
// Our projection transform needs to transform from this space to a LH coordinate
// system that looks thusly:
//
// y| /z
// | /
// |/____ x Z is going into the screen
//
// Where x,y lies between -1 and 1, and z lies from 0 to 1
// This is because the viewport transformation from projection space to pixels
// introduces a -1 scale in the y coordinates
// D3DXMatrixOrthoOffCenterRH( &matrix, left, right, top, bottom, zNear, zFar );
dst.Init( 2.0f / ( right - left ), 0.0f, 0.0f, ( left + right ) / ( left - right ),
0.0f, 2.0f / ( bottom - top ), 0.0f, ( bottom + top ) / ( top - bottom ),
0.0f, 0.0f, 1.0f / ( zNear - zFar ), zNear / ( zNear - zFar ),
0.0f, 0.0f, 0.0f, 1.0f );
}
inline void MatrixBuildPerspectiveZRange( VMatrix& dst, double flZNear, double flZFar )
{
dst.m[2][0] = 0.0f;
dst.m[2][1] = 0.0f;
dst.m[2][2] = flZFar / ( flZNear - flZFar );
dst.m[2][3] = flZNear * flZFar / ( flZNear - flZFar );
}
inline void MatrixBuildPerspectiveX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar )
{
float flWidthScale = 1.0f / tanf( flFovX * M_PI / 360.0f );
float flHeightScale = flAspect * flWidthScale;
dst.Init( flWidthScale, 0.0f, 0.0f, 0.0f,
0.0f, flHeightScale, 0.0f, 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, -1.0f, 0.0f );
MatrixBuildPerspectiveZRange ( dst, flZNear, flZFar );
}
inline void MatrixBuildPerspectiveOffCenterX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar, double bottom, double top, double left, double right )
{
float flWidth = tanf( flFovX * M_PI / 360.0f );
float flHeight = flWidth / flAspect;
// bottom, top, left, right are 0..1 so convert to -<val>/2..<val>/2
float flLeft = -(flWidth/2.0f) * (1.0f - left) + left * (flWidth/2.0f);
float flRight = -(flWidth/2.0f) * (1.0f - right) + right * (flWidth/2.0f);
float flBottom = -(flHeight/2.0f) * (1.0f - bottom) + bottom * (flHeight/2.0f);
float flTop = -(flHeight/2.0f) * (1.0f - top) + top * (flHeight/2.0f);
dst.Init( 1.0f / (flRight-flLeft), 0.0f, (flLeft+flRight)/(flRight-flLeft), 0.0f,
0.0f, 1.0f /(flTop-flBottom), (flTop+flBottom)/(flTop-flBottom), 0.0f,
0.0f, 0.0f, 0.0f, 0.0f,
0.0f, 0.0f, -1.0f, 0.0f );
MatrixBuildPerspectiveZRange ( dst, flZNear, flZFar );
}
#endif