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#ifndef __CGLA_ARITHSQMAT4X4FLOAT_H
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#ifndef __CGLA_ARITHSQMAT4X4FLOAT_H
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#define __CGLA_ARITHSQMAT4X4FLOAT_H
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#define __CGLA_ARITHSQMAT4X4FLOAT_H
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#include "ExceptionStandard.h"
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#include "ExceptionStandard.h"
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#include "CGLA.h"
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#include "CGLA.h"
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#include "Vec3f.h"
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#include "Vec3f.h"
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#include "Vec3Hf.h"
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#include "Vec3Hf.h"
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#include "Vec4f.h"
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#include "Vec4f.h"
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#include "ArithSqMatFloat.h"
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#include "ArithSqMatFloat.h"
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namespace CGLA
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namespace CGLA
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{
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{
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CGLA_DERIVEEXCEPTION(Mat4x4fException)
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CGLA_DERIVEEXCEPTION(Mat4x4fException)
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CGLA_DERIVEEXCEPTION(Mat4x4fNotAffine)
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CGLA_DERIVEEXCEPTION(Mat4x4fNotAffine)
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CGLA_DERIVEEXCEPTION(Mat4x4fSingular)
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CGLA_DERIVEEXCEPTION(Mat4x4fSingular)
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/** \brief 4 by 4 float matrix template.
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/** \brief 4 by 4 float matrix template.
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this class template is useful for transformations such as perspective
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this class template is useful for transformations such as perspective
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projections or translation where 3x3 matrices do not suffice. */
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projections or translation where 3x3 matrices do not suffice. */
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template<class VT, class M>
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template<class VT, class M>
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class ArithSqMat4x4Float: public ArithSqMatFloat<VT, M, 4>
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class ArithSqMat4x4Float: public ArithSqMatFloat<VT, M, 4>
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{
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{
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public:
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public:
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/// Vector type
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/// Vector type
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typedef VT VectorType;
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typedef VT VectorType;
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/// The type of a matrix element
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/// The type of a matrix element
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typedef typename VT::ScalarType ScalarType;
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typedef typename VT::ScalarType ScalarType;
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public:
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public:
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/// Construct a Mat4x4f from four V vectors
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/// Construct a Mat4x4f from four V vectors
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ArithSqMat4x4Float(VT a, VT b, VT c, VT d):
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ArithSqMat4x4Float(VT a, VT b, VT c, VT d):
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ArithSqMatFloat<VT, M, 4> (a,b,c,d) {}
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ArithSqMatFloat<VT, M, 4> (a,b,c,d) {}
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/// Construct the NAN matrix
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/// Construct the NAN matrix
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ArithSqMat4x4Float() {}
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ArithSqMat4x4Float() {}
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/// Construct matrix where all values are equal to constructor argument.
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/// Construct matrix where all values are equal to constructor argument.
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explicit ArithSqMat4x4Float(ScalarType _a):
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explicit ArithSqMat4x4Float(ScalarType _a):
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ArithSqMatFloat<VT,M,4>(_a) {}
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ArithSqMatFloat<VT,M,4>(_a) {}
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/** Multiply vector onto matrix. Here the fourth coordinate
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/** Multiply vector onto matrix. Here the fourth coordinate
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is se to 0. This removes any translation from the matrix.
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is se to 0. This removes any translation from the matrix.
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Useful if one wants to transform a vector which does not
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Useful if one wants to transform a vector which does not
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represent a point but a direction. Note that this is not
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represent a point but a direction. Note that this is not
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correct for transforming normal vectors if the matric
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correct for transforming normal vectors if the matric
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contains anisotropic scaling. */
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contains anisotropic scaling. */
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template<class T, class VecT>
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template<class T, class VecT>
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const VecT mul_3D_vector(const ArithVec3Float<T,VecT>& v_in) const
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const VecT mul_3D_vector(const ArithVec3Float<T,VecT>& v_in) const
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{
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{
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],0);
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],0);
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return VecT(v_out[0],v_out[1],v_out[2]);
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return VecT(v_out[0],v_out[1],v_out[2]);
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}
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}
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/** Multiply 3D point onto matrix. Here the fourth coordinate
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/** Multiply 3D point onto matrix. Here the fourth coordinate
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becomes 1 to ensure that the point is translated. Note that
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becomes 1 to ensure that the point is translated. Note that
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the vector is converted back into a Vec3f without any
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the vector is converted back into a Vec3f without any
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division by w. This is deliberate: Typically, w=1 except
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division by w. This is deliberate: Typically, w=1 except
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for projections. If we are doing projection, we can use
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for projections. If we are doing projection, we can use
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project_3D_point instead */
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project_3D_point instead */
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template<class T, class VecT>
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template<class T, class VecT>
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const VecT mul_3D_point(const ArithVec3Float<T,VecT> & v_in) const
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const VecT mul_3D_point(const ArithVec3Float<T,VecT> & v_in) const
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{
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{
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],1);
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],1);
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return VecT(v_out[0],v_out[1],v_out[2]);
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return VecT(v_out[0],v_out[1],v_out[2]);
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}
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}
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/** Multiply 3D point onto matrix. We set w=1 before
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/** Multiply 3D point onto matrix. We set w=1 before
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multiplication and divide by w after multiplication. */
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multiplication and divide by w after multiplication. */
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template<class T, class VecT>
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template<class T, class VecT>
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const VecT project_3D_point(const ArithVec3Float<T,VecT>& v_in) const
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const VecT project_3D_point(const ArithVec3Float<T,VecT>& v_in) const
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{
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{
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],1);
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VT v_out = (*this) * VT(v_in[0],v_in[1],v_in[2],1);
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v_out.de_homogenize();
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v_out.de_homogenize();
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return VecT(v_out[0],v_out[1],v_out[2]);
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return VecT(v_out[0],v_out[1],v_out[2]);
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}
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}
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};
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};
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/** Compute the adjoint of a matrix. This is the matrix where each
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/** Compute the adjoint of a matrix. This is the matrix where each
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entry is the subdeterminant of 'in' where the row and column of
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entry is the subdeterminant of 'in' where the row and column of
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the element is removed. Use mostly to compute the inverse */
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the element is removed. Use mostly to compute the inverse */
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template<class VT, class M>
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template<class VT, class M>
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M adjoint(const ArithSqMat4x4Float<VT,M>&);
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M adjoint(const ArithSqMat4x4Float<VT,M>&);
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/** Compute the determinant of a 4x4 matrix. The code below is what
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/** Compute the determinant of a 4x4 matrix. The code below is what
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I found to be most robust. The original implementation used direct
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I found to be most robust. The original implementation used direct
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computation of the 3x3 sub-determinants and I also tried a direct
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computation of the 3x3 sub-determinants and I also tried a direct
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computation based on enumerating all permutations. The code below
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computation based on enumerating all permutations. The code below
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is better. */
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is better. */
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template<class V, class M>
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template<class V, class M>
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inline double determinant(const ArithSqMat4x4Float<V,M>& m)
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inline double determinant(const ArithSqMat4x4Float<V,M>& m)
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{
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{
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/* return m[0][0] * (m[1][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */
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/* return m[0][0] * (m[1][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */
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/* m[2][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])+ */
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/* m[2][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])+ */
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/* m[3][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])) */
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/* m[3][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])) */
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/* - m[1][0] * (m[0][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */
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/* - m[1][0] * (m[0][1]*(m[2][2]*m[3][3]-m[3][2]*m[2][3])- */
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/* m[2][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */
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/* m[2][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */
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/* m[3][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])) */
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/* m[3][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])) */
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/* + m[2][0] * (m[0][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])- */
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/* + m[2][0] * (m[0][1]*(m[1][2]*m[3][3]-m[3][2]*m[1][3])- */
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/* m[1][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */
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/* m[1][1]*(m[0][2]*m[3][3]-m[3][2]*m[0][3])+ */
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/* m[3][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])) */
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/* m[3][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])) */
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/* - m[3][0] * (m[0][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])- */
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/* - m[3][0] * (m[0][1]*(m[1][2]*m[2][3]-m[2][2]*m[1][3])- */
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/* m[1][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])+ */
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/* m[1][1]*(m[0][2]*m[2][3]-m[2][2]*m[0][3])+ */
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/* m[2][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])); */
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/* m[2][1]*(m[0][2]*m[1][3]-m[1][2]*m[0][3])); */
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typedef typename M::ScalarType ScalarType;
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typedef typename M::ScalarType ScalarType;
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ScalarType a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;
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ScalarType a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;
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/* assign to individual variable names to aid selecting */
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/* assign to individual variable names to aid selecting */
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/* correct elements */
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/* correct elements */
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a1 = m[0][0]; b1 = m[1][0]; c1 = m[2][0]; d1 = m[3][0];
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a1 = m[0][0]; b1 = m[1][0]; c1 = m[2][0]; d1 = m[3][0];
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a2 = m[0][1]; b2 = m[1][1]; c2 = m[2][1]; d2 = m[3][1];
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a2 = m[0][1]; b2 = m[1][1]; c2 = m[2][1]; d2 = m[3][1];
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a3 = m[0][2]; b3 = m[1][2]; c3 = m[2][2]; d3 = m[3][2];
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a3 = m[0][2]; b3 = m[1][2]; c3 = m[2][2]; d3 = m[3][2];
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a4 = m[0][3]; b4 = m[1][3]; c4 = m[2][3]; d4 = m[3][3];
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a4 = m[0][3]; b4 = m[1][3]; c4 = m[2][3]; d4 = m[3][3];
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return
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return
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a1 * (b2*(c3*d4-d3*c4)-c2*(b3*d4-d3*b4)+d2*(b3*c4-c3*b4))
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a1 * (b2*(c3*d4-d3*c4)-c2*(b3*d4-d3*b4)+d2*(b3*c4-c3*b4))
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- b1 * (a2*(c3*d4-d3*c4)-c2*(a3*d4-d3*a4)+d2*(a3*c4-c3*a4))
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- b1 * (a2*(c3*d4-d3*c4)-c2*(a3*d4-d3*a4)+d2*(a3*c4-c3*a4))
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+ c1 * (a2*(b3*d4-d3*b4)-b2*(a3*d4-d3*a4)+d2*(a3*b4-b3*a4))
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+ c1 * (a2*(b3*d4-d3*b4)-b2*(a3*d4-d3*a4)+d2*(a3*b4-b3*a4))
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- d1 * (a2*(b3*c4-c3*b4)-b2*(a3*c4-c3*a4)+c2*(a3*b4-b3*a4));
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- d1 * (a2*(b3*c4-c3*b4)-b2*(a3*c4-c3*a4)+c2*(a3*b4-b3*a4));
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}
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}
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/// Compute the inverse matrix of a Mat4x4f.
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/// Compute the inverse matrix of a Mat4x4f.
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template<class VT, class M>
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template<class VT, class M>
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M invert(const ArithSqMat4x4Float<VT,M>&);
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M invert(const ArithSqMat4x4Float<VT,M>&);
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/// Compute the inverse matrix of a Mat4x4f that is affine
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/// Compute the inverse matrix of a Mat4x4f that is affine
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template<class VT, class M>
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template<class VT, class M>
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M invert_affine(const ArithSqMat4x4Float<VT,M>&);
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M invert_affine(const ArithSqMat4x4Float<VT,M>&);
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}
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}
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#endif
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#endif
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