mirror of https://github.com/CGAL/cgal
111 lines
4.2 KiB
TeX
111 lines
4.2 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: GradientFittingTraits.tex
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% +------------------------------------------------------------------------+
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% | 06.04.2000 Author
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% | Package: Package
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% |
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\RCSdef{\RCSGradientFittingTraitsRev}{$Id$}
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\RCSdefDate{\RCSGradientFittingTraitsDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefConcept}{GradientFittingTraits}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[concept]{} %% add further index entries
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\ccDefinition
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The function \ccc{sibson_gradient_fitting} is parameterized by a
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traits class that defines the primitives used by the algorithm. The
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concept \ccRefName\ defines this common set of requirements.
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\ccTypes
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\ccNestedType{FT}{The number type must follow the model
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\ccc{FieldNumberType}.}
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\ccNestedType{Point_d}{The point type on
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which the function is defined and interpolated.}
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\ccNestedType{Vector_d}{The corresponding vector type.}
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\ccNestedType{Aff_transformation_d}{defines a
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matrix type.
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Must provide the following member functions~: \\
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\ccc{Aff_transformation tr.inverse ()} which gives the inverse
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transformation, and \\
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\ccc{Aff_transformation tr.transform( Vector v)} which returns the
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multiplication of \ccc{tr} with \ccc{v}.
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}
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%%% FUNCTION TYPES:
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%VECTOR:
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\ccNestedType{Construct_vector_d} {A constructor object for
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\ccc{Vector_d}.
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Provides~: \\
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\ccc{Vector_d operator() (Point_d a, Point_d b)} which produces the
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vector \ccc{b -
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a} and \\
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\ccc{Vector_d operator() (Null_vector NULL_VECTOR)} which introduces
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the null vector.}
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\ccNestedType{Construct_scaled_vector_d}{Constructor object for
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\ccc{Vector_d}.
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Provides~: \\
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\ccc{Vector_d operator() (Vector_d v,FT scale)} which produces the
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vector \ccc{v} scaled by a factor \ccc{scale}.}
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%AFF_TRANSFORMATION:
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\ccNestedType{Construct_null_matrix_d}{Constructor object for
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\ccc{Aff_transformation_d}. Provides~: \\
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\ccc{Aff_transformation_d operator()()} which introduces an affine
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transformation whose matrix has only zero entries.}
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\ccNestedType{Construct_scaling_matrix_d}{Constructor object for
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\ccc{Aff_transformation_d}. Provides~: \\
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\ccc{Aff_transformation_d operator()(FT scale)} which introduces a
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scaling by a scale factor \ccc{scale}.}
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\ccNestedType{Construct_sum_matrix_d}{Constructor object for
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\ccc{Aff_transformation_d}. Provides~: \\
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\ccc{Aff_transformation_d operator()(Aff_transformation_d tr1,
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Aff_transformation_d tr2)} which returns the sum of the two matrices
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representing \ccc{tr1} and \ccc{tr2}.}
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\ccNestedType{Construct_outer_product_d} {Constructor object for
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\ccc{Aff_transformation_d}. Provides~: \\
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\ccc{Aff_transformation_d operator()(Vector v)} which returns the
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outerproduct, i.e.~the quadratic matrix \ccc{v}$^t$\ccc{v}.}
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\ccCreation
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\ccCreationVariable{traits} %%
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\ccConstructor{GradientFittingTraits();}{default constructor.}
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\ccOperations The following functions that create instances of the
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above constructor object types must exist.
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\ccMethod{Construct_vector_d construct_vector_d_object();}{} \ccGlue
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\ccMethod{Construct_scaled_vector_d
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construct_scaled_vector_d_object();}{} \ccGlue
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\ccMethod{Construct_null_matrix_d construct_null_matrix_d_object();}{}
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\ccGlue \ccMethod{Construct_sum_matrix_d
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construct_sum_matrix_d_object();}{} \ccGlue
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\ccMethod{Construct_outer_product_d
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construct_outer_product_d_object();}{}
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\ccHasModels
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\ccc{CGAL::Interpolation_gradient_fitting_traits_2<K>} \\
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\ccSeeAlso
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\ccRefConceptPage{InterpolationTraits}\\
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\ccRefIdfierPage{CGAL::Interpolation_traits_2<K>} \\
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\ccRefIdfierPage{CGAL::sibson_gradient_fitting} \\
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\ccRefIdfierPage{CGAL::sibson_c1_interpolation} \\
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\ccRefIdfierPage{CGAL::farin_c1_interpolation} \\
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\ccRefIdfierPage{CGAL::quadratic_interpolation} \\
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%\ccRefIdfierPage{CGAL::natural_neighbor_coordinates_2}\\
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%\ccRefIdfierPage{CGAL::regular_neighbor_coordinates_2} \\
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%\ccRefIdfierPage{CGAL::surface_neighbor_coordinates_3}\\
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\end{ccRefConcept}
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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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% +------------------------------------------------------------------------+
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