mirror of https://github.com/CGAL/cgal
polynomial concepts
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Monique Teillaud
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2299b9a550
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c702d80914
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@ -32,11 +32,11 @@ of degree up to~1.}
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polynomials of degree up to~2 that can store equations of spheres.}
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\ccNestedType{Polynomials_for_lines_3}{A model of
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\ccc{AlgebraicKernelForSpheres::Polynomials_for_lines_3}, for systems of
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\ccc{AlgebraicKernelForSpheres::PolynomialsForLines_3}, for systems of
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polynomials that can store equations of lines in 3D.}
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\ccGlue
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\ccNestedType{Polynomials_for_circles_3}{A model of
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\ccc{AlgebraicKernelForSpheres::Polynomials_for_circles_3}, for systems of
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\ccc{AlgebraicKernelForSpheres::PolynomialsForCircles_3}, for systems of
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polynomials that can store equations of circles in 3D.}
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\ccNestedType{Root_of_2}{A model of
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@ -0,0 +1,46 @@
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\begin{ccRefConcept}{AlgebraicKernelForSpheres::PolynomialForSpheres_2_3}
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\ccDefinition
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Concept to represent
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bivariate polynomials of degree up to~2 capable of storing equations
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of spheres, whose center's coordinates, as well as the square of the radius,
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are of a type that is a model of the concept
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\ccc{FieldNumberType}.
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%\footnote{Of course the name looks bad since it mixes geometry with algebra.
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%suggestions welcome}
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\ccRefines
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CopyConstructible, Assignable, DefaultConstructible
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\ccCreation
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\ccCreationVariable{pol}
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%\ccConstructor{PolynomialForSpheres_2_2(const FT & a, const FT & b, const FT & rsq);}{Constructs polynomial \ccc{(x-a)^2 + (y-b)^2 - rsq}.}
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%\ccAccessFunctions
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%\ccMethod{const FT & a();}{\ccc{x}-coordinate of the center of the sphere.}
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%\ccGlue
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%\ccMethod{const FT & b();}{\ccc{y}-coordinate of the center of the sphere.}
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%\ccGlue
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%\ccMethod{const FT & r_sq();}{Square radius of the center of the sphere.}
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\ccOperations
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The comparison operator \ccc{==} must be provided.
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\ccFunction{bool operator ==
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(AlgebraicKernelForSpheres::const PolynomialForSpheres_2_3 & p,
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const AlgebraicKernelForSpheres::PolynomialForSpheres_2_3 & q);}{}
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\ccHasModels
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\ccc{CGAL::Polynomial_for_spheres_2_3}
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicKernelForSpheres}
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\end{ccRefConcept}
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@ -0,0 +1,31 @@
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\begin{ccRefConcept}{AlgebraicKernelForSpheres::Polynomial_1_3}
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\ccDefinition
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Concept to represent bivariate polynomials of degree 1 whose
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coefficients are of a type that is a model of the concept
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\ccc{RingNumberType}.
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\ccRefines
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CopyConstructible, Assignable, DefaultConstructible
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%\ccAccessFunctions
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%\ccFunction{const RT & a() const;}{}
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%\ccGlue
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%\ccOperations
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%The comparison operator \ccc{==} must be provided.
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% also proportional polynomials
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\ccHasModels
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\ccc{CGAL::Polynomial_1_3}
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicKernelForSpheres}
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\end{ccRefConcept}
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@ -0,0 +1,30 @@
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\begin{ccRefConcept}{AlgebraicKernelForSpheres::PolynomialsForCircles_3}
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\ccDefinition
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Concept to represent a system of polynomials on \ccc{FieldNumberType},
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capable of storing equations of circles.
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\ccRefines
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CopyConstructible, Assignable, DefaultConstructible
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%\ccAccessFunctions
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%\ccFunction{const RT & a() const;}{}
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%\ccGlue
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%\ccOperations
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%The comparison operator \ccc{==} must be provided.
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% also proportional polynomials
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\ccHasModels
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\ccc{CGAL::Polynomials_for_circles_3}
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicKernelForSpheres}
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\end{ccRefConcept}
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@ -0,0 +1,30 @@
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\begin{ccRefConcept}{AlgebraicKernelForSpheres::PolynomialsForLines_3}
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\ccDefinition
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Concept to represent a system of polynomials on \ccc{FieldNumberType},
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capable of storing equations of lines.
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\ccRefines
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CopyConstructible, Assignable, DefaultConstructible
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%\ccAccessFunctions
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%\ccFunction{const RT & a() const;}{}
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%\ccGlue
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%\ccOperations
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%The comparison operator \ccc{==} must be provided.
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% also proportional polynomials
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\ccHasModels
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\ccc{CGAL::Polynomials_for_lines_3}
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicKernelForSpheres}
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\end{ccRefConcept}
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@ -33,6 +33,26 @@
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\subsubsection*{Functors}
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\ccRefConceptPage{AlgebraicKernelForCircles::ConstructPolynomial_1_3}\\
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\ccRefConceptPage{AlgebraicKernelForCircles::ConstructPolynomialForSpheres_2_3}
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\ccRefConceptPage{AlgebraicKernelForCircles::ConstructPolynomials_for_lines_3}\\
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\ccRefConceptPage{AlgebraicKernelForCircles::ConstructPolynomialsForCircles_2}
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\ccRefConceptPage{AlgebraicKernelForSpheres::CompareX}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::CompareY}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::CompareZ}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::CompareXY}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::CompareXYZ}
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\ccRefConceptPage{AlgebraicKernelForSpheres::SignAt}
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\ccRefConceptPage{AlgebraicKernelForSpheres::XCriticalPoints}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::YCriticalPoints}\\
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\ccRefConceptPage{AlgebraicKernelForSpheres::ZCriticalPoints}
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\ccRefConceptPage{AlgebraicKernelForSpheres::Solve}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Geometric Kernels and Classes}
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@ -49,6 +69,19 @@
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\subsubsection*{Kernel}
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\ccRefIdfierPage{CGAL::Algebraic_kernel_for_spheres_2_3<RT>}
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\subsubsection*{Polynomials}
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\ccRefIdfierPage{CGAL::Polynomial_1_3<FT>}\\
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\ccRefIdfierPage{CGAL::Polynomial_for_spheres_2_3<FT>}
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\ccRefIdfierPage{CGAL::Polynomials_for_lines_3<FT>}\\
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\ccRefIdfierPage{CGAL::Polynomials_for_circles_3<FT>}
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\subsubsection*{Roots of Polynomials}
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\ccRefIdfierPage{CGAL::Root_of_2<RT>}\\
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\ccRefIdfierPage{CGAL::Root_for_spheres_2_3<RT>}
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\ccRefIdfierPage{CGAL::Root_of_traits_2<RT>}
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@ -26,5 +26,13 @@
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% algebraic objects
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\input{Circular_kernel_3_ref/Polynomial_1}
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\input{Circular_kernel_3_ref/PolynomialForSpheres_2_3}
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\input{Circular_kernel_3_ref/PolynomialsForLines_3}
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\input{Circular_kernel_3_ref/PolynomialsForCircles_3}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% algebraic functors
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