mirror of https://github.com/CGAL/cgal
124 lines
4.3 KiB
TeX
124 lines
4.3 KiB
TeX
\begin{ccRefClass}{Circle_3<Kernel>}
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\ccDefinition
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An object of type \ccRefName\ is a circle in the
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three-dimensional Euclidean space $\E^3$. Note that the
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circle can be degenerate, i.e.\ the squared radius may be zero.
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{c}
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\ccHidden
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\ccConstructor{ Circle_3( );}{
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introduces an uninitialized variable \ccVar\ of type
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\ccClassTemplateName.}
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\ccConstructor{Circle_3(Point_3<Kernel> const& center,
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Kernel::FT const& sq_r,
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Plane_3<Kernel> const& plane);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle of center \ccc{center} and
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squared radius \ccc{sq_r} in plane \ccc{plane}.
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\ccPrecond{\ccc{center} lies in \ccc{plane} and
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\ccc{sq_r} $\geq$ 0.}}
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\ccConstructor{Circle_3(Point_3<Kernel> const& center,
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Kernel::FT const& sq_r,
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Vector_3<Kernel> const& n);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle of center \ccc{center} and
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squared radius \ccc{sq_r} in a plane normal to
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the vector \ccc{n}.
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\ccPrecond{\ccc{sq_r} $\geq$ 0.}}
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\ccConstructor{Circle_3(Point_3<Kernel> const& p,
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Point_3<Kernel> const& q, Point_3<Kernel> const& r);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle passing through the three points.
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\ccPrecond{The three points are not collinear.}}
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\ccConstructor{Circle_3(Sphere_3<Kernel> const& sphere1,
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Sphere_3<Kernel> const& sphere2);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle along which the two spheres intersect.
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\ccPrecond{The two spheres intersect along a circle.}}
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\ccConstructor{Circle_3(Sphere_3<Kernel> const& sphere,
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Plane_3<Kernel> const& plane);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle along which the sphere and the
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plane intersect.
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\ccPrecond{The sphere and the plane intersect along a circle.}}
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\ccConstructor{Circle_3(Plane_3<Kernel> const& plane,
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Sphere_3<Kernel> const& sphere);}
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{introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to the circle along which the sphere and the
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plane intersect.
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\ccPrecond{The sphere and the plane intersect along a circle.}}
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\ccHidden
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\ccConstructor{ Circle_3( Circle_3<Kernel> const&);}{
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copy constructor.}
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\ccHidden
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\ccMemberFunction{ Circle_3<Kernel>& operator = ( Circle_3<Kernel> const&);}{
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assignment.}
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% -----------------------------------------------------------------------------
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\ccAccessFunctions
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\ccMemberFunction{Point_3<Kernel> const& center( ) const;}{
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returns the center of \ccVar.}
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\ccGlue
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\ccMemberFunction{Kernel::FT const& squared_radius( ) const;}{
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returns the squared radius of \ccVar.}
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\ccGlue
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\ccMemberFunction{Plane_3<Kernel> const& supporting_plane( ) const;}{
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returns the supporting plane of \ccVar.}
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\ccGlue
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\ccMemberFunction{Sphere_3<Kernel> const& diametral_sphere( ) const;}{
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returns the diametral sphere of \ccVar.}
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\ccMemberFunction{Kernel::FT const& area_divided_by_pi( ) const;}{
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returns the area of \ccVar, divided by $\pi$. }
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\ccGlue
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\ccMemberFunction{double const& approximate_area( ) const;}{
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returns an approximation of the area of \ccVar. }
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\ccGlue
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\ccMemberFunction{Kernel::FT const& squared_length_divided_by_pi_square( ) const;}{
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returns the squared length of \ccVar, divided by $\pi^2$. }
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\ccGlue
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\ccMemberFunction{double const& approximate_squared_length( ) const;}{
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returns an approximation of the squared length (i.e. perimeter) of \ccVar. }
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\ccPredicates
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\ccMethod{bool has_on(Point_3<Kernel> const& p) const;}
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{}
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\ccOperations
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\ccFunction{ bool operator == (Circle_3<Kernel> const& c1,
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Circle_3<Kernel> const& c2);}
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{returns \ccc{true}, iff \ccc{c1} and \ccc{c2} are equal,
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i.e.\ if they have the same center, the same squared radius
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and the same supporting plane.}
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\ccFunction{ bool operator != (Circle_3<Kernel> const& c1,
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Circle_3<Kernel> const& c2);}
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{}
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\ccMemberFunction{ Bbox_3 bbox() const;}{
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returns a bounding box containing \ccVar.}
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\ccSeeAlso
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\ccRefConceptPage{Kernel::Circle_3}
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\end{ccRefClass}
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