mirror of https://github.com/CGAL/cgal
fix doc
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@ -536,9 +536,10 @@ f_{0,0,1} ^{2}}}
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\section{Software Design}
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%%%%%%%%%%%%%%%%%%%%%%%
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Following \cgal's best practices in geometric software development,
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the package developed in fully generic in the C++ sense ---and is
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templated by three classes.
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We now explain the API and the output of the package, and the role of
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template parameters. Following \cgal's best practices in geometric
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software development, the package developed in fully generic in the
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C++ sense ---and is templated by three classes.
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\subsection{Options and Interface Specifications}
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%%%%%%%%%%%%%%%%%%%%%
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@ -617,29 +618,37 @@ The following picture illustrates the template dependencies.
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More details are given in the reference manual.
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\subsubsection{Template class \ccc{Data_Kernel}}
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\subsubsection{Template parameter \ccc{Data_Kernel}}
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%%%%%%%%%%%
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This class provides the types for the input sample points, together
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with $3d$ vectors and a number type. It is used as template for the
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\ccc{Monge_form}. Typically, one can use \ccc{CGAL::Cartesian<double>}.
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classes
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\ccc{Monge_form<DataKernel>} and
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\ccc{Monge_via_jet_fitting<DataKernel, LocalKernel = Cartesian<double>, LinAlgTraits = Lapack>}
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. Typically, one can use \ccc{CGAL::Cartesian<double>}.
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\subsubsection{Template class \ccc{Local_Kernel}}
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\subsubsection{Template parameter \ccc{Local_Kernel}}
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%%%%%%%%%%%
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This is a parameter of the classes
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\ccc{Monge_via_jet_fitting<DataKernel, LocalKernel = Cartesian<double>, LinAlgTraits = Lapack>}
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and \ccc{Monge_form_condition_numbers<LocalKernel = Cartesian<double> >}
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This class defines the vector and number types used (i)\ for local
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computations (ii)\ to store the Monge\_form\_condition\_numbers class members. Input
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points of type \ccc{Data_Kernel::Point_3} are converted to
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computations (ii)\ to store the Monge\_form\_condition\_numbers class
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members. Input points of type \ccc{Data_Kernel::Point_3} are converted
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to
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\ccc{Local_Kernel::Point_3}. For output of the \ccc{Monge_form} class, these
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types are converted back to \ccc{Data_Kernel} ones. Typically, one can use
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\ccc{CGAL::Cartesian<double>}.
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\ccc{CGAL::Cartesian<double>} which is the default.
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\subsubsection{Template class \ccc{Linalg_traits.}}
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\subsubsection{Template parameter \ccc{Linalg_traits.}}
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%%%%%%%%%%%
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This class provides the matrix algebra operations required by the
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fitting method. These are an eigen method for symmetric mtrices and
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linear solver using a singular value decomposition.
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fitting method in
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\ccc{Monge_via_jet_fitting<DataKernel, LocalKernel = Cartesian<double>, LinAlgTraits = Lapack>}
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. That is a linear solver using a singular value decomposition.
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\subsubsection{Compatibility requirements}
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@ -686,6 +695,7 @@ another text file which may be visualised with the demo program
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introspect-qt displaying the Monge basis at each vertex of the mesh.
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\end{itemize}
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Following are some illustrations featuring principal directions of curvature.
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\begin{figure}[!ht]
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\begin{ccTexOnly}
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@ -39,7 +39,7 @@ basis) and the coefficients of the Monge form in this system.}
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\ccSeeAlso
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\ccc{Monge_form_condition_numbers}
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\ccc{Monge_form_condition_numbers}\\
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\ccc{Monge_form}
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\end{ccRefFunction}
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@ -44,8 +44,8 @@ solution is stored in B.}
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\ccSeeAlso
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\ccc{LinAlgTraits},
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\ccc{Lapack_matrix}.
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\ccc{LinAlgTraits}\\
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\ccc{Lapack_matrix}
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%\ccc{some_other_function}.
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\end{ccRefClass}
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@ -54,8 +54,8 @@ ordered)}
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\ccSeeAlso
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\ccc{LinAlgTraits},
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\ccc{Lapack}.
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\ccc{LinAlgTraits}\\
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\ccc{Lapack}
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%\ccc{some_other_function}.
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\end{ccRefClass}
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@ -45,7 +45,7 @@ The \ccc{DataKernel} template parameter must be the
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same for the classes \ccc{Monge_form} and
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\ccc{Monge_via_jet_fitting}. The \ccc{LocalKernel} template parameter
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must be the same for the classes \ccc{Monge_form_condition_numbers} and
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\ccc{Monge_via_jet_fitting} its default value is \ccc{Cartesian<double>}.
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\ccc{Monge_via_jet_fitting}. Its default value is \ccc{Cartesian<double>}.
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\subsection*{Concepts}
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\ccRefConceptPage{DataKernel} \\
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@ -59,16 +59,12 @@ must be the same for the classes \ccc{Monge_form_condition_numbers} and
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\ccRefIdfierPage{CGAL::Lapack_matrix}\\
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\ccRefIdfierPage{CGAL::Lapack}\\
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\subsection*{Global Functions}
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The insert operator is overloaded for the classes \ccc{Monge_form} and
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\ccc{Monge_form_condition_numbers}.
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\ccRefIdfierPage{CGAL::operator<<}\\
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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@ -1,11 +1,11 @@
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%!PS-Adobe-3.0 EPSF-3.0
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%%Creator: Ipelib 60023 (Ipe 6.0 preview 23)
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%%CreationDate: D:20060317155757
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%%CreationDate: D:20060628180511
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%%LanguageLevel: 2
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%%DocumentSuppliedResources: font QEGEHJ+CMR10
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%%+ font ZHNPRT+CMSY10
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%%DocumentSuppliedResources: font GYRBKU+CMR10
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%%+ font ONWWCK+CMSY10
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%%EndComments
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%%BeginProlog
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%%BeginResource: procset ipe 6.0 60023
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@ -53,7 +53,7 @@ end
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%%EndProlog
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%%BeginSetup
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ipe begin
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%%BeginResource: font QEGEHJ+CMR10
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%%BeginResource: font GYRBKU+CMR10
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%!PS-AdobeFont-1.1: CMR10 1.00B
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%%CreationDate: 1992 Feb 19 19:54:52
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% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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@ -67,7 +67,7 @@ ipe begin
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/ItalicAngle 0 def
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/isFixedPitch false def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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@ -79,7 +79,6 @@ dup 58 /colon put
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dup 61 /equal put
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dup 65 /A put
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dup 67 /C put
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dup 68 /D put
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dup 70 /F put
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dup 71 /G put
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dup 75 /K put
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@ -104,10 +103,8 @@ dup 113 /q put
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dup 114 /r put
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dup 115 /s put
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dup 116 /t put
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dup 118 /v put
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currentdict end
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||||
ET
|
||||
Q
|
||||
q 1 0 0 1 432 304 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.192 cm
|
||||
1 0 0 1 0 -785.1922 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.192 Td[(FT)]TJ
|
||||
/F8 9.9626 Tf 0 785.1922 Td[(FT)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 336.5 315.27 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -788.345 cm
|
||||
1 0 0 1 0 -788.3449 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 788.345 Td[(=)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 163.205 316.61 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.872 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.872 Td[(cas)-1(t)]TJ
|
||||
/F8 9.9626 Tf 0 788.3449 Td[(=)]TJ
|
||||
ET
|
||||
Q
|
||||
q np
|
||||
|
|
@ -576,165 +528,135 @@ h q f* Q S
|
|||
Q
|
||||
Q
|
||||
q 1 0 0 1 247.62 362.167 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.081 cm
|
||||
1 0 0 1 0 -785.0815 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.081 Td[(CGAL::)1(A\013)]TJ
|
||||
/F8 9.9626 Tf 0 785.0815 Td[(CGAL::A\013)]TJ
|
||||
ET
|
||||
1 0 0 1 48.128 785.081 cm
|
||||
1 0 0 1 48.1279 785.0815 cm
|
||||
q
|
||||
[]0 d
|
||||
0 J
|
||||
0.398 w
|
||||
0 0.199 m
|
||||
2.989 0.199 l
|
||||
0.3985 w
|
||||
0 0.1992 m
|
||||
2.9888 0.1992 l
|
||||
S
|
||||
Q
|
||||
1 0 0 1 -48.128 -785.081 cm
|
||||
1 0 0 1 -48.1279 -785.0815 cm
|
||||
BT
|
||||
/F8 9.963 Tf 51.117 785.081 Td[(tra)1(nfor)1(m)-1(at)1(ion)]TJ
|
||||
/F8 9.9626 Tf 51.1168 785.0815 Td[(tran)1(for)1(m)-1(ati)1(on)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 245.386 245.88 cm 1 0 0 1 0 0 cm 1 0 0 1 0 32.766 cm
|
||||
0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -792 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.081 Td[(CGAL::)1(Linear)]TJ
|
||||
/F8 9.9626 Tf 0 785.0815 Td[(CGAL::Li)1(near)]TJ
|
||||
ET
|
||||
1 0 0 1 62.684 785.081 cm
|
||||
1 0 0 1 62.6845 785.0815 cm
|
||||
q
|
||||
[]0 d
|
||||
0 J
|
||||
0.398 w
|
||||
0 0.199 m
|
||||
2.989 0.199 l
|
||||
0.3985 w
|
||||
0 0.1992 m
|
||||
2.9888 0.1992 l
|
||||
S
|
||||
Q
|
||||
1 0 0 1 -62.684 -785.081 cm
|
||||
1 0 0 1 -62.6845 -785.0815 cm
|
||||
BT
|
||||
/F8 9.963 Tf 65.673 785.081 Td[(Algebr)1(aC)-1(d)]TJ -65.673 -11.955 Td[(CGAL::)1(Sqr)1(t)]TJ 0 -11.955 Td[(CGAL::)1(s)-1(ign)]TJ
|
||||
/F8 9.9626 Tf 65.6733 785.0815 Td[(Algebr)1(aC)-1(d)]TJ -65.6733 -11.9552 Td[(CGAL::S)1(qrt)]TJ 0 -11.9551 Td[(CGAL::sign)]TJ
|
||||
ET
|
||||
1 0 0 1 52.058 761.171 cm
|
||||
1 0 0 1 52.0576 761.1712 cm
|
||||
q
|
||||
[]0 d
|
||||
0 J
|
||||
0.398 w
|
||||
0 0.199 m
|
||||
2.989 0.199 l
|
||||
0.3985 w
|
||||
0 0.1992 m
|
||||
2.9888 0.1992 l
|
||||
S
|
||||
Q
|
||||
1 0 0 1 -52.058 -761.171 cm
|
||||
1 0 0 1 -52.0576 -761.1712 cm
|
||||
BT
|
||||
/F8 9.963 Tf 55.046 761.171 Td[(of)]TJ
|
||||
/F8 9.9626 Tf 55.0465 761.1712 Td[(of)]TJ
|
||||
ET
|
||||
1 0 0 1 63.67 761.171 cm
|
||||
1 0 0 1 63.6697 761.1712 cm
|
||||
q
|
||||
[]0 d
|
||||
0 J
|
||||
0.398 w
|
||||
0 0.199 m
|
||||
2.989 0.199 l
|
||||
0.3985 w
|
||||
0 0.1992 m
|
||||
2.9888 0.1992 l
|
||||
S
|
||||
Q
|
||||
1 0 0 1 -63.67 -761.171 cm
|
||||
1 0 0 1 -63.6697 -761.1712 cm
|
||||
BT
|
||||
/F8 9.963 Tf 66.659 761.171 Td[(d)1(e)-1(termin)1(an)28(t3)]TJ/F14 9.963 Tf 57.866 0 Td[(\002)]TJ/F8 9.963 Tf 7.749 0 Td[(3)]TJ
|
||||
/F8 9.9626 Tf 66.6585 761.1712 Td[(determinan)29(t3)]TJ/F14 9.9626 Tf 57.8665 0 Td[(\002)]TJ/F8 9.9626 Tf 7.7487 0 Td[(3)]TJ
|
||||
ET
|
||||
1 0 0 1 0 759.234 cm
|
||||
0 g 0 G
|
||||
Q
|
||||
q np
|
||||
88.1705 225.049 m
|
||||
132.834 225.049 l
|
||||
74.3833 305.475 m
|
||||
119.047 305.475 l
|
||||
0.4 w S
|
||||
q np
|
||||
132.834 225.049 m
|
||||
125.834 227.382 l
|
||||
125.834 222.716 l
|
||||
119.047 305.475 m
|
||||
112.047 307.808 l
|
||||
112.047 303.141 l
|
||||
h q f* Q S
|
||||
Q
|
||||
q np
|
||||
88.1705 225.049 m
|
||||
95.1705 222.716 l
|
||||
95.1705 227.382 l
|
||||
74.3833 305.475 m
|
||||
81.3833 303.141 l
|
||||
81.3833 307.808 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q np
|
||||
88.6172 206.29 m
|
||||
128.814 206.29 l
|
||||
78.021 280.787 m
|
||||
115.092 280.34 l
|
||||
0.4 w S
|
||||
q np
|
||||
128.814 206.29 m
|
||||
121.814 208.623 l
|
||||
121.814 203.957 l
|
||||
h q f* Q S
|
||||
Q
|
||||
q np
|
||||
88.6172 206.29 m
|
||||
95.6172 203.957 l
|
||||
95.6172 208.623 l
|
||||
115.092 280.34 m
|
||||
108.12 282.757 l
|
||||
108.064 278.091 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q np
|
||||
89.5104 188.872 m
|
||||
126.581 188.425 l
|
||||
0.4 w S
|
||||
q np
|
||||
126.581 188.425 m
|
||||
119.61 190.843 l
|
||||
119.553 186.176 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q 1 0 0 1 106.036 230.409 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -788.345 cm
|
||||
q 1 0 0 1 93.0147 310.069 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -788.3449 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 788.345 Td[(=)]TJ
|
||||
/F8 9.9626 Tf 0 788.3449 Td[(=)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 100.23 210.757 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.872 cm
|
||||
q 1 0 0 1 130.086 304.263 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.0815 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.872 Td[(cas)-1(t)]TJ
|
||||
/F8 9.9626 Tf 0 785.0815 Td[(is)-334(t)1(he)-334(sam)-1(e)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 143.107 224.603 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.081 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.081 Td[(is)-334(t)1(he)-334(same)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 139.534 206.29 cm 1 0 0 1 0 0 cm 0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.081 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.081 Td[(cas)-1(t)-333(is)-334(a)28(v)56(aila)1(ble)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 139.087 187.978 cm 1 0 0 1 0 0 cm 1 0 0 1 0 1.937 cm
|
||||
q 1 0 0 1 124.534 278.361 cm 1 0 0 1 0 0 cm 1 0 0 1 0 1.9372 cm
|
||||
0 0 0 rg 0 0 0 RG
|
||||
1 0 0 1 0 -785.081 cm
|
||||
1 0 0 1 0 -785.0815 cm
|
||||
BT
|
||||
/F8 9.963 Tf 0 785.081 Td[(is)-334(t)1(e)-1(mpl)1(ate)-334(for)]TJ
|
||||
/F8 9.9626 Tf 0 785.0815 Td[(is)-334(t)1(e)-1(mplat)1(e)-334(for)]TJ
|
||||
ET
|
||||
Q
|
||||
showpage
|
||||
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||||
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||||
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|
||||
|
|
|
|||
Binary file not shown.
|
Before Width: | Height: | Size: 26 KiB After Width: | Height: | Size: 20 KiB |
Binary file not shown.
|
|
@ -44,7 +44,8 @@ public:
|
|||
class Lapack{
|
||||
public:
|
||||
typedef Lapack_matrix Matrix;
|
||||
//solve MX=B using SVD and give the condition number of M
|
||||
//solve MX=B using SVD and give the condition number of M
|
||||
//The solution is stored in B
|
||||
static
|
||||
void solve_ls_svd_algo(Matrix& M, double* B, double &cond_nb);
|
||||
};
|
||||
|
|
|
|||
|
|
@ -153,7 +153,7 @@ dump_4ogl(std::ostream& out_stream, const FT scale)
|
|||
|
||||
template <class DataKernel>
|
||||
std::ostream&
|
||||
operator<<(std::ostream& out_stream, Monge_form<DataKernel>& monge)
|
||||
operator<<(std::ostream& out_stream, const Monge_form<DataKernel>& monge)
|
||||
{
|
||||
monge.dump_verbose(out_stream);
|
||||
return out_stream;
|
||||
|
|
@ -190,7 +190,7 @@ public:
|
|||
|
||||
template <class LocalKernel>
|
||||
std::ostream&
|
||||
operator<<(std::ostream& out_stream, Monge_form_condition_numbers<LocalKernel>& monge)
|
||||
operator<<(std::ostream& out_stream, const Monge_form_condition_numbers<LocalKernel>& monge)
|
||||
{
|
||||
out_stream << "cond_nb : " << monge.cond_nb() << std::endl
|
||||
<< "pca_eigen_vals " << monge.pca_eigen_vals()[0]
|
||||
|
|
|
|||
Loading…
Reference in New Issue