Rocstar-legacy/determinant_8h_source.html

 // ======================================================================

 //

 // Copyright (c) 1999 The CGAL Consortium


 // This software and related documentation is part of the Computational

 // Geometry Algorithms Library (CGAL).

 // This software and documentation is provided "as-is" and without warranty

 // of any kind. In no event shall the CGAL Consortium be liable for any

 // damage of any kind.

 //

 // Every use of CGAL requires a license.

 //

 // Academic research and teaching license

 // - For academic research and teaching purposes, permission to use and copy

 //   the software and its documentation is hereby granted free of charge,

 //   provided that it is not a component of a commercial product, and this

 //   notice appears in all copies of the software and related documentation.

 //

 // Commercial licenses

 // - A commercial license is available through Algorithmic Solutions, who also

 //   markets LEDA (http://www.algorithmic-solutions.de).

 // - Commercial users may apply for an evaluation license by writing to

 //   Algorithmic Solutions (contact@algorithmic-solutions.com).

 //

 // The CGAL Consortium consists of Utrecht University (The Netherlands),

 // ETH Zurich (Switzerland), Free University of Berlin (Germany),

 // INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg

 // (Germany), Max-Planck-Institute Saarbrucken (Germany), RISC Linz (Austria),

 // and Tel-Aviv University (Israel).

 //

 // ----------------------------------------------------------------------

 //

 // release       : CGAL-2.2

 // release_date  : 2000, September 30

 //

 // source        : determinant.fw

 // file          : include/CGAL/determinant.h

 // package       : Kernel_basic (3.14)

 // revision      : 3.14

 // revision_date : 15 Sep 2000

 // author(s)     : Sylvain Pion

 //                 Stefan Schirra

 //

 // coordinator   : MPI, Saarbruecken  (<Stefan.Schirra>)

 // email         : contact@cgal.org

 // www           : http://www.cgal.org

 //

 // ======================================================================


 #ifndef CGAL_DETERMINANT_H

 #define CGAL_DETERMINANT_H


 CGAL_BEGIN_NAMESPACE


 template <class FT>

 inline

 FT

 det2x2_by_formula(

  const FT& a00,  const FT& a01,

  const FT& a10,  const FT& a11)

 {

 // First compute the det2x2

   const FT m01 = a00*a11 - a10*a01;

   return m01;

 }


 template <class FT>

 CGAL_KERNEL_MEDIUM_INLINE

 FT

 det3x3_by_formula(

  const FT& a00,  const FT& a01,  const FT& a02,

  const FT& a10,  const FT& a11,  const FT& a12,

  const FT& a20,  const FT& a21,  const FT& a22)

 {

 // First compute the det2x2

   const FT m01 = a00*a11 - a10*a01;

   const FT m02 = a00*a21 - a20*a01;

   const FT m12 = a10*a21 - a20*a11;

 // Now compute the minors of rank 3

   const FT m012 = m01*a22 - m02*a12 + m12*a02;

   return m012;

 }


 template <class FT>

 CGAL_KERNEL_LARGE_INLINE

 FT

 det4x4_by_formula(

  const FT& a00,  const FT& a01,  const FT& a02,  const FT& a03,

  const FT& a10,  const FT& a11,  const FT& a12,  const FT& a13,

  const FT& a20,  const FT& a21,  const FT& a22,  const FT& a23,

  const FT& a30,  const FT& a31,  const FT& a32,  const FT& a33)

 {

 // First compute the det2x2

   const FT m01 = a10*a01 - a00*a11;

   const FT m02 = a20*a01 - a00*a21;

   const FT m03 = a30*a01 - a00*a31;

   const FT m12 = a20*a11 - a10*a21;

   const FT m13 = a30*a11 - a10*a31;

   const FT m23 = a30*a21 - a20*a31;

 // Now compute the minors of rank 3

   const FT m012 = m12*a02 - m02*a12 + m01*a22;

   const FT m013 = m13*a02 - m03*a12 + m01*a32;

   const FT m023 = m23*a02 - m03*a22 + m02*a32;

   const FT m123 = m23*a12 - m13*a22 + m12*a32;

 // Now compute the minors of rank 4

   const FT m0123 = m123*a03 - m023*a13 + m013*a23 - m012*a33;

   return m0123;

 }


 template <class FT>

 CGAL_KERNEL_LARGE_INLINE

 FT

 det5x5_by_formula(

  const FT& a00,  const FT& a01,  const FT& a02,  const FT& a03,  const FT& a04,

  const FT& a10,  const FT& a11,  const FT& a12,  const FT& a13,  const FT& a14,

  const FT& a20,  const FT& a21,  const FT& a22,  const FT& a23,  const FT& a24,

  const FT& a30,  const FT& a31,  const FT& a32,  const FT& a33,  const FT& a34,

  const FT& a40,  const FT& a41,  const FT& a42,  const FT& a43,  const FT& a44)

 {

 // First compute the det2x2

   const FT m01 = a10*a01 - a00*a11;

   const FT m02 = a20*a01 - a00*a21;

   const FT m03 = a30*a01 - a00*a31;

   const FT m04 = a40*a01 - a00*a41;

   const FT m12 = a20*a11 - a10*a21;

   const FT m13 = a30*a11 - a10*a31;

   const FT m14 = a40*a11 - a10*a41;

   const FT m23 = a30*a21 - a20*a31;

   const FT m24 = a40*a21 - a20*a41;

   const FT m34 = a40*a31 - a30*a41;

 // Now compute the minors of rank 3

   const FT m012 = m12*a02 - m02*a12 + m01*a22;

   const FT m013 = m13*a02 - m03*a12 + m01*a32;

   const FT m014 = m14*a02 - m04*a12 + m01*a42;

   const FT m023 = m23*a02 - m03*a22 + m02*a32;

   const FT m024 = m24*a02 - m04*a22 + m02*a42;

   const FT m034 = m34*a02 - m04*a32 + m03*a42;

   const FT m123 = m23*a12 - m13*a22 + m12*a32;

   const FT m124 = m24*a12 - m14*a22 + m12*a42;

   const FT m134 = m34*a12 - m14*a32 + m13*a42;

   const FT m234 = m34*a22 - m24*a32 + m23*a42;

 // Now compute the minors of rank 4

   const FT m0123 = m123*a03 - m023*a13 + m013*a23 - m012*a33;

   const FT m0124 = m124*a03 - m024*a13 + m014*a23 - m012*a43;

   const FT m0134 = m134*a03 - m034*a13 + m014*a33 - m013*a43;

   const FT m0234 = m234*a03 - m034*a23 + m024*a33 - m023*a43;

   const FT m1234 = m234*a13 - m134*a23 + m124*a33 - m123*a43;

 // Now compute the minors of rank 5

   const FT m01234 = m1234*a04 - m0234*a14 + m0134*a24 - m0124*a34 + m0123*a44;

   return m01234;

 }


 template <class FT>

 FT

 det6x6_by_formula(

  const FT& a00, const FT& a01, const FT& a02, const FT& a03, const FT& a04, const FT& a05,

  const FT& a10, const FT& a11, const FT& a12, const FT& a13, const FT& a14, const FT& a15,

  const FT& a20, const FT& a21, const FT& a22, const FT& a23, const FT& a24, const FT& a25,

  const FT& a30, const FT& a31, const FT& a32, const FT& a33, const FT& a34, const FT& a35,

  const FT& a40, const FT& a41, const FT& a42, const FT& a43, const FT& a44, const FT& a45,

  const FT& a50, const FT& a51, const FT& a52, const FT& a53, const FT& a54, const FT& a55)

 {

 // First compute the det2x2

   const FT m01 = a00*a11 - a10*a01;

   const FT m02 = a00*a21 - a20*a01;

   const FT m03 = a00*a31 - a30*a01;

   const FT m04 = a00*a41 - a40*a01;

   const FT m05 = a00*a51 - a50*a01;

   const FT m12 = a10*a21 - a20*a11;

   const FT m13 = a10*a31 - a30*a11;

   const FT m14 = a10*a41 - a40*a11;

   const FT m15 = a10*a51 - a50*a11;

   const FT m23 = a20*a31 - a30*a21;

   const FT m24 = a20*a41 - a40*a21;

   const FT m25 = a20*a51 - a50*a21;

   const FT m34 = a30*a41 - a40*a31;

   const FT m35 = a30*a51 - a50*a31;

   const FT m45 = a40*a51 - a50*a41;

 // Now compute the minors of rank 3

   const FT m012 = m01*a22 - m02*a12 + m12*a02;

   const FT m013 = m01*a32 - m03*a12 + m13*a02;

   const FT m014 = m01*a42 - m04*a12 + m14*a02;

   const FT m015 = m01*a52 - m05*a12 + m15*a02;

   const FT m023 = m02*a32 - m03*a22 + m23*a02;

   const FT m024 = m02*a42 - m04*a22 + m24*a02;

   const FT m025 = m02*a52 - m05*a22 + m25*a02;

   const FT m034 = m03*a42 - m04*a32 + m34*a02;

   const FT m035 = m03*a52 - m05*a32 + m35*a02;

   const FT m045 = m04*a52 - m05*a42 + m45*a02;

   const FT m123 = m12*a32 - m13*a22 + m23*a12;

   const FT m124 = m12*a42 - m14*a22 + m24*a12;

   const FT m125 = m12*a52 - m15*a22 + m25*a12;

   const FT m134 = m13*a42 - m14*a32 + m34*a12;

   const FT m135 = m13*a52 - m15*a32 + m35*a12;

   const FT m145 = m14*a52 - m15*a42 + m45*a12;

   const FT m234 = m23*a42 - m24*a32 + m34*a22;

   const FT m235 = m23*a52 - m25*a32 + m35*a22;

   const FT m245 = m24*a52 - m25*a42 + m45*a22;

   const FT m345 = m34*a52 - m35*a42 + m45*a32;

 // Now compute the minors of rank 4

   const FT m0123 = m012*a33 - m013*a23 + m023*a13 - m123*a03;

   const FT m0124 = m012*a43 - m014*a23 + m024*a13 - m124*a03;

   const FT m0125 = m012*a53 - m015*a23 + m025*a13 - m125*a03;

   const FT m0134 = m013*a43 - m014*a33 + m034*a13 - m134*a03;

   const FT m0135 = m013*a53 - m015*a33 + m035*a13 - m135*a03;

   const FT m0145 = m014*a53 - m015*a43 + m045*a13 - m145*a03;

   const FT m0234 = m023*a43 - m024*a33 + m034*a23 - m234*a03;

   const FT m0235 = m023*a53 - m025*a33 + m035*a23 - m235*a03;

   const FT m0245 = m024*a53 - m025*a43 + m045*a23 - m245*a03;

   const FT m0345 = m034*a53 - m035*a43 + m045*a33 - m345*a03;

   const FT m1234 = m123*a43 - m124*a33 + m134*a23 - m234*a13;

   const FT m1235 = m123*a53 - m125*a33 + m135*a23 - m235*a13;

   const FT m1245 = m124*a53 - m125*a43 + m145*a23 - m245*a13;

   const FT m1345 = m134*a53 - m135*a43 + m145*a33 - m345*a13;

   const FT m2345 = m234*a53 - m235*a43 + m245*a33 - m345*a23;

 // Now compute the minors of rank 5

   const FT m01234 = m0123*a44 - m0124*a34 + m0134*a24 - m0234*a14 + m1234*a04;

   const FT m01235 = m0123*a54 - m0125*a34 + m0135*a24 - m0235*a14 + m1235*a04;

   const FT m01245 = m0124*a54 - m0125*a44 + m0145*a24 - m0245*a14 + m1245*a04;

   const FT m01345 = m0134*a54 - m0135*a44 + m0145*a34 - m0345*a14 + m1345*a04;

   const FT m02345 = m0234*a54 - m0235*a44 + m0245*a34 - m0345*a24 + m2345*a04;

   const FT m12345 = m1234*a54 - m1235*a44 + m1245*a34 - m1345*a24 + m2345*a14;

 // Now compute the minors of rank 6

   const FT m012345 = m01234*a55 - m01235*a45 + m01245*a35 - m01345*a25 + m02345*a15 - m12345*a05;

   return m012345;

 }


 CGAL_END_NAMESPACE


 #ifndef CGAL_PREDICATES_SIGN_OF_DETERMINANT_H

 #include <CGAL/predicates/sign_of_determinant.h>

 #endif // CGAL_PREDICATES_SIGN_OF_DETERMINANT_H


 #endif // CGAL_DETERMINANT_H

det2x2_by_formula
CGAL_BEGIN_NAMESPACE FT det2x2_by_formula(const FT &a00, const FT &a01, const FT &a10, const FT &a11)
Definition: determinant.h:59

det3x3_by_formula
CGAL_KERNEL_MEDIUM_INLINE FT det3x3_by_formula(const FT &a00, const FT &a01, const FT &a02, const FT &a10, const FT &a11, const FT &a12, const FT &a20, const FT &a21, const FT &a22)
Definition: determinant.h:71

det5x5_by_formula
CGAL_KERNEL_LARGE_INLINE FT det5x5_by_formula(const FT &a00, const FT &a01, const FT &a02, const FT &a03, const FT &a04, const FT &a10, const FT &a11, const FT &a12, const FT &a13, const FT &a14, const FT &a20, const FT &a21, const FT &a22, const FT &a23, const FT &a24, const FT &a30, const FT &a31, const FT &a32, const FT &a33, const FT &a34, const FT &a40, const FT &a41, const FT &a42, const FT &a43, const FT &a44)
Definition: determinant.h:114

det6x6_by_formula
FT det6x6_by_formula(const FT &a00, const FT &a01, const FT &a02, const FT &a03, const FT &a04, const FT &a05, const FT &a10, const FT &a11, const FT &a12, const FT &a13, const FT &a14, const FT &a15, const FT &a20, const FT &a21, const FT &a22, const FT &a23, const FT &a24, const FT &a25, const FT &a30, const FT &a31, const FT &a32, const FT &a33, const FT &a34, const FT &a35, const FT &a40, const FT &a41, const FT &a42, const FT &a43, const FT &a44, const FT &a45, const FT &a50, const FT &a51, const FT &a52, const FT &a53, const FT &a54, const FT &a55)
Definition: determinant.h:156

CGAL_KERNEL_MEDIUM_INLINE
#define CGAL_KERNEL_MEDIUM_INLINE
Definition: kernel_basic.h:55

det4x4_by_formula
CGAL_KERNEL_LARGE_INLINE FT det4x4_by_formula(const FT &a00, const FT &a01, const FT &a02, const FT &a03, const FT &a10, const FT &a11, const FT &a12, const FT &a13, const FT &a20, const FT &a21, const FT &a22, const FT &a23, const FT &a30, const FT &a31, const FT &a32, const FT &a33)
Definition: determinant.h:88

CGAL_KERNEL_LARGE_INLINE
#define CGAL_KERNEL_LARGE_INLINE
Definition: kernel_basic.h:56

CGAL_BEGIN_NAMESPACE
#define CGAL_BEGIN_NAMESPACE
Definition: kdtree_d.h:86

sign_of_determinant.h

CGAL_END_NAMESPACE
#define CGAL_END_NAMESPACE
Definition: kdtree_d.h:87