First version of the SOurce SDK 2013

1 files changed, 1273 insertions, 0 deletions

diff --git a/mp/src/mathlib/vmatrix.cpp b/mp/src/mathlib/vmatrix.cpp
new file mode 100644
index 00000000..77c0656f
--- /dev/null
+++ b/mp/src/mathlib/vmatrix.cpp
@@ -0,0 +1,1273 @@
+//========= Copyright Valve Corporation, All rights reserved. ============//

+//

+// Purpose: 

+//

+// $NoKeywords: $

+//

+//=============================================================================//

+

+#if !defined(_STATIC_LINKED) || defined(_SHARED_LIB)

+

+#include "basetypes.h"

+#include "mathlib/vmatrix.h"

+#include "mathlib/mathlib.h"

+#include <string.h>

+#include "mathlib/vector4d.h"

+#include "tier0/dbg.h"

+

+// memdbgon must be the last include file in a .cpp file!!!

+#include "tier0/memdbgon.h"

+

+#pragma warning (disable : 4700) // local variable 'x' used without having been initialized

+

+// ------------------------------------------------------------------------------------------- //

+// Helper functions.

+// ------------------------------------------------------------------------------------------- //

+

+#ifndef VECTOR_NO_SLOW_OPERATIONS

+

+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);

+}

+

+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

+		);

+}

+

+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

+		);

+}

+

+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;

+}

+

+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;

+}

+

+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);

+}

+

+VMatrix SetupMatrixAngles(const QAngle &vAngles)

+{

+	VMatrix mRet;

+	MatrixFromAngles( vAngles, mRet );

+	return mRet;

+}

+

+VMatrix SetupMatrixOrgAngles(const Vector &origin, const QAngle &vAngles)

+{

+	VMatrix mRet;

+	mRet.SetupMatrixOrgAngles( origin, vAngles );

+	return mRet;

+}

+

+#endif // VECTOR_NO_SLOW_OPERATIONS

+

+

+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;

+	}

+}

+

+

+

+// ------------------------------------------------------------------------------------------- //

+// VMatrix functions.

+// ------------------------------------------------------------------------------------------- //

+

+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;

+}

+

+bool VMatrix::operator==( const VMatrix& src ) const

+{

+	return !memcmp( src.m, m, sizeof(m) );

+}

+

+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]

+		);

+}

+

+#ifndef VECTOR_NO_SLOW_OPERATIONS

+

+VMatrix VMatrix::operator*(const VMatrix &vm) const

+{

+	VMatrix ret;

+	MatrixMul( vm, ret );

+	return ret;

+}

+

+#endif

+

+bool VMatrix::InverseGeneral(VMatrix &vInverse) const

+{

+	return MatrixInverseGeneral( *this, vInverse );

+}

+

+

+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;

+}

+

+

+//-----------------------------------------------------------------------------

+// Does a fast inverse, assuming the matrix only contains translation and rotation.

+//-----------------------------------------------------------------------------

+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;

+}

+

+

+void VMatrix::InverseTR( VMatrix &ret ) const

+{

+	MatrixInverseTR( *this, ret );

+}

+

+void MatrixInverseTranspose( const VMatrix& src, VMatrix& dst )

+{

+	src.InverseGeneral( dst );

+	MatrixTranspose( dst, dst );

+}

+

+//-----------------------------------------------------------------------------

+// Computes the inverse transpose

+//-----------------------------------------------------------------------------

+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

+

+VMatrix VMatrix::InverseTR() const

+{

+	VMatrix ret;

+	MatrixInverseTR( *this, ret );

+	return ret;

+}

+

+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()

+		);

+}

+

+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

+		);

+}

+

+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;

+}

+

+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.

+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

+

+

+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;

+}

+

+void VMatrix::SetupMatrixOrgAngles( const Vector &origin, 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;

+	

+	// 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;

+}

+

+

+//-----------------------------------------------------------------------------

+// Sets matrix to identity

+//-----------------------------------------------------------------------------

+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;

+}

+

+

+//-----------------------------------------------------------------------------

+// Setup a matrix from euler angles. 

+//-----------------------------------------------------------------------------

+void MatrixFromAngles( const QAngle& vAngles, VMatrix& dst )

+{

+	dst.SetupMatrixOrgAngles( vec3_origin, vAngles );

+}

+

+

+//-----------------------------------------------------------------------------

+// Creates euler angles from a matrix 

+//-----------------------------------------------------------------------------

+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;

+	}

+}

+

+

+//-----------------------------------------------------------------------------

+// Transpose

+//-----------------------------------------------------------------------------

+inline void Swap( float& a, float& b )

+{

+	float tmp = a;

+	a = b;

+	b = tmp;

+}

+

+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];

+	}

+}

+

+

+//-----------------------------------------------------------------------------

+// Matrix copy

+//-----------------------------------------------------------------------------

+

+void MatrixCopy( const VMatrix& src, VMatrix& dst )

+{

+	if (&src != &dst)

+	{

+		memcpy( dst.m, src.m, 16 * sizeof(float) );

+	}

+}

+

+//-----------------------------------------------------------------------------

+// Matrix multiply

+//-----------------------------------------------------------------------------

+typedef float VMatrixRaw_t[4];

+

+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];

+}

+

+//-----------------------------------------------------------------------------

+// Matrix/vector multiply

+//-----------------------------------------------------------------------------

+

+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

+//-----------------------------------------------------------------------------

+

+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];

+}

+

+

+

+//-----------------------------------------------------------------------------

+// Matrix/vector multiply

+//-----------------------------------------------------------------------------

+

+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];

+}

+

+

+//-----------------------------------------------------------------------------

+// Vector3DMultiplyPositionProjective treats src2 as if it's a point 

+// and does the perspective divide at the end

+//-----------------------------------------------------------------------------

+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

+//-----------------------------------------------------------------------------

+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

+//-----------------------------------------------------------------------------

+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

+//-----------------------------------------------------------------------------

+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];

+}

+

+

+//-----------------------------------------------------------------------------

+// Transform a plane

+//-----------------------------------------------------------------------------

+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) );

+}

+

+

+#ifndef VECTOR_NO_SLOW_OPERATIONS

+

+VPlane VMatrix::operator*(const VPlane &thePlane) const

+{

+	VPlane ret;

+	TransformPlane( thePlane, ret );

+	return ret;

+}

+

+#endif

+

+

+//-----------------------------------------------------------------------------

+// Builds a rotation matrix that rotates one direction vector into another

+//-----------------------------------------------------------------------------

+void MatrixBuildTranslation( VMatrix& dst, float x, float y, float z )

+{

+	MatrixSetIdentity( dst );

+	dst[0][3] = x;

+	dst[1][3] = y;

+	dst[2][3] = z;

+}

+

+void MatrixBuildTranslation( VMatrix& dst, const Vector &translation )

+{

+	MatrixSetIdentity( dst );

+	dst[0][3] = translation[0];

+	dst[1][3] = translation[1];

+	dst[2][3] = translation[2];

+}

+

+

+//-----------------------------------------------------------------------------

+// 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 - 

+//-----------------------------------------------------------------------------

+void MatrixBuildRotationAboutAxis( VMatrix &dst, const Vector &vAxisOfRot, float angleDegrees )

+{

+	MatrixBuildRotationAboutAxis( vAxisOfRot, angleDegrees, 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

+//-----------------------------------------------------------------------------

+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

+}

+

+//-----------------------------------------------------------------------------

+//-----------------------------------------------------------------------------

+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

+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;

+}

+

+void MatrixBuildScale( VMatrix &dst, const Vector& scale )

+{

+	MatrixBuildScale( dst, scale.x, scale.y, scale.z );

+}

+

+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 );

+

+	memset( dst.Base(), 0, sizeof( dst ) );

+	dst[0][0]  = 2.0F * zNear / width;

+	dst[1][1]  = 2.0F * zNear / height;

+	dst[2][2] = -zFar / ( zNear - zFar );

+	dst[3][2] = 1.0f;

+	dst[2][3] = zNear * zFar / ( zNear - zFar );

+

+	// 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.

+//-----------------------------------------------------------------------------

+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 );

+}

+

+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.

+//-----------------------------------------------------------------------------

+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.

+//-----------------------------------------------------------------------------

+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 );	

+}

+

+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 );

+}

+

+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 );

+}

+

+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 );

+}

+

+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 );

+}

+

+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 // !_STATIC_LINKED || _SHARED_LIB

+