//========= Copyright (c) 1996-2005, 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 #include "mathlib/vector4d.h" #include "ssemath.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; // sin, cos, 1-cos 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); } // Basically takes a cross product and then does the same thing as SetupMatrixAxisRot // above, but takes advantage of the fact that the sin angle is precomputed. VMatrix SetupMatrixAxisToAxisRot(const Vector &vFromAxis, const Vector &vToAxis) { Assert( vFromAxis.LengthSqr() == 1 ); // these axes Assert( vToAxis.LengthSqr() == 1 ); // must be normal. vec_t s, c, t; // sin(theta), cos(theta), 1-cos vec_t tx, ty, tz; vec_t sx, sy, sz; Vector vAxis = vFromAxis.Cross(vToAxis); s = vAxis.Length(); c = vFromAxis.Dot(vToAxis); t = 1.0f - c; if ( s > 0 ) { vAxis *= 1.0/s; 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); } else { return SetupMatrixIdentity(); } } 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 #if 1 bool PlaneIntersection( const VPlane &vp1, const VPlane &vp2, const VPlane &vp3, Vector &vOut ) { Vector v2Cross3 = CrossProduct( vp2.m_Normal, vp3.m_Normal ); float flDenom = DotProduct( vp1.m_Normal, v2Cross3 ); if ( fabs( flDenom ) < FLT_EPSILON ) return false; Vector vRet = vp1.m_Dist * v2Cross3 + vp2.m_Dist * CrossProduct( vp3.m_Normal, vp1.m_Normal ) + vp3.m_Dist * CrossProduct( vp1.m_Normal, vp2.m_Normal ); vOut = vRet * ( 1.0 / flDenom ); return true; } #else // old slow innaccurate code 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; } } #endif // ------------------------------------------------------------------------------------------- // // 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 = 1e-6f; 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(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(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(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(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(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, VPlane &plane ) { 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, plane.m_Normal ); VectorNormalize( plane.m_Normal ); plane.m_Dist = DotProduct( plane.m_Normal, world1 ); } void FrustumPlanesFromMatrix( const VMatrix &clipToWorld, Frustum_t &frustum ) { VPlane planes[6]; FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 0.0f, 0.0f, 0.0f ), Vector( 1.0f, 0.0f, 0.0f ), Vector( 0.0f, 1.0f, 0.0f ), planes[FRUSTUM_NEARZ] ); FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 0.0f, 0.0f, 1.0f ), Vector( 0.0f, 1.0f, 1.0f ), Vector( 1.0f, 0.0f, 1.0f ), planes[FRUSTUM_FARZ] ); FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 1.0f, 0.0f, 0.0f ), Vector( 1.0f, 1.0f, 1.0f ), Vector( 1.0f, 1.0f, 0.0f ), planes[FRUSTUM_RIGHT] ); FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 0.0f, 0.0f, 0.0f ), Vector( 0.0f, 1.0f, 1.0f ), Vector( 0.0f, 0.0f, 1.0f ), planes[FRUSTUM_LEFT] ); FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 1.0f, 1.0f, 0.0f ), Vector( 1.0f, 1.0f, 1.0f ), Vector( 0.0f, 1.0f, 1.0f ), planes[FRUSTUM_TOP] ); FrustumPlanesFromMatrixHelper( clipToWorld, Vector( 1.0f, 0.0f, 0.0f ), Vector( 0.0f, 0.0f, 1.0f ), Vector( 1.0f, 0.0f, 1.0f ), planes[FRUSTUM_BOTTOM] ); frustum.SetPlanes(planes); } // BEWARE: top/bottom are FLIPPED relative to D3DXMatrixOrthoOffCenterRH(). 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 MatrixBuildPerspectiveX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar ) { float flWidth = 2.0f * flZNear * tanf( flFovX * M_PI / 360.0f ); float flHeight = flWidth / flAspect; dst.Init( 2.0f * flZNear / flWidth, 0.0f, 0.0f, 0.0f, 0.0f, 2.0f * flZNear/ flHeight, 0.0f, 0.0f, 0.0f, 0.0f, flZFar / ( flZNear - flZFar ), flZNear * flZFar / ( flZNear - flZFar ), 0.0f, 0.0f, -1.0f, 0.0f ); } void MatrixBuildPerspectiveOffCenterX( VMatrix& dst, double flFovX, double flAspect, double flZNear, double flZFar, double bottom, double top, double left, double right ) { float flWidth = 2.0f * flZNear * tanf( flFovX * M_PI / 360.0f ); float flHeight = flWidth / flAspect; // bottom, top, left, right are 0..1 so convert to -/2../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( (2.0f * flZNear) / (flRight-flLeft), 0.0f, (flLeft+flRight)/(flRight-flLeft), 0.0f, 0.0f, 2.0f*flZNear/(flTop-flBottom), (flTop+flBottom)/(flTop-flBottom), 0.0f, 0.0f, 0.0f, flZFar/(flZNear-flZFar), flZNear*flZFar/(flZNear-flZFar), 0.0f, 0.0f, -1.0f, 0.0f ); } void ExtractClipPlanesFromNonTransposedMatrix( const VMatrix &viewProjMatrix, VPlane *pPlanesOut, bool bD3DClippingRange ) { // Left Vector4D vPlane = MatrixGetRowAsVector4D( viewProjMatrix, 0 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); pPlanesOut[ FRUSTUM_LEFT ].Init( vPlane.AsVector3D(), -vPlane.w ); // Right vPlane = -MatrixGetRowAsVector4D( viewProjMatrix, 0 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); pPlanesOut[ FRUSTUM_RIGHT ].Init( vPlane.AsVector3D(), -vPlane.w ); // Bottom vPlane = MatrixGetRowAsVector4D( viewProjMatrix, 1 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); pPlanesOut[ FRUSTUM_BOTTOM ].Init( vPlane.AsVector3D(), -vPlane.w ); // Top vPlane = -MatrixGetRowAsVector4D( viewProjMatrix, 1 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); pPlanesOut[ FRUSTUM_TOP ].Init( vPlane.AsVector3D(), -vPlane.w ); // Near if ( bD3DClippingRange ) { // [0,1] Z clipping range (D3D-style) vPlane = MatrixGetRowAsVector4D( viewProjMatrix, 2 ); } else { // [-1,1] Z clipping range (OpenGL-style) vPlane = MatrixGetRowAsVector4D( viewProjMatrix, 2 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); } pPlanesOut[ FRUSTUM_NEARZ ].Init( vPlane.AsVector3D(), -vPlane.w ); // Far vPlane = -MatrixGetRowAsVector4D( viewProjMatrix, 2 ) + MatrixGetRowAsVector4D( viewProjMatrix, 3 ); pPlanesOut[ FRUSTUM_FARZ ].Init( vPlane.AsVector3D(), -vPlane.w ); for ( uint i = 0; i < FRUSTUM_NUMPLANES; ++i ) { float flLen2 = pPlanesOut[i].m_Normal.x * pPlanesOut[i].m_Normal.x + pPlanesOut[i].m_Normal.y * pPlanesOut[i].m_Normal.y + pPlanesOut[i].m_Normal.z * pPlanesOut[i].m_Normal.z; if ( flLen2 != 0.0f ) { float flScale = 1.0f / sqrt( flLen2 ); pPlanesOut[i].m_Normal *= flScale; pPlanesOut[i].m_Dist *= flScale; } } } #endif // !_STATIC_LINKED || _SHARED_LIB