mirror of https://github.com/CGAL/cgal
renamed from 'Min_circle_2_traits.tex'
This commit is contained in:
Sven Schönherr
parent
4e36b28dbe
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% -*- latex -*-
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% =============================================================================
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% The CGAL Reference Manual
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% Chapter: Geometric Optimisation
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% Concept: MinCircle2Traits
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% -----------------------------------------------------------------------------
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% file : doc_tex/basic/Optimisation/Optimisation_ref/MinCircle2Traits.tex
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% package: Min_circle_2
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% author : Sven Schönherr <sven@inf.ethz.ch>
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% -----------------------------------------------------------------------------
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% $Revision$
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% $Date$
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% =============================================================================
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\begin{ccRefConcept}{MinCircle2Traits}
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% -----------------------------------------------------------------------------
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\ccDefinition
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This concept defines the requirements for traits classes of
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\ccGlobalScope\ccc{Min_circle_2<Traits>}.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{
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The point type must provide default and copy constructor,
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assignment and equality test.}
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\ccNestedType{Circle}{
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The circle type must fulfill the requirements listed below
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in the next section.}
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% -----------------------------------------------------------------------------
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\ccHeading{Variables}
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\ccVariable{ Circle circle;}{
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The current circle. This variable is maintained by the algorithm,
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the user should neither access nor modify it directly.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{traits}
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Only default and copy constructor are required.
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\ccConstructor{ MinCircle2Traits( );}{}
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\ccConstructor{ MinCircle2Traits( const MinCircle2Traits&);}{}
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% -----------------------------------------------------------------------------
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\ccOperations
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The following predicate is only needed, if the member function
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\ccc{is_valid} of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ CGAL::Orientation
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orientation( const Point& p,
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const Point& q,
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const Point& r) const;}{
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returns constants \ccGlobalScope\ccc{LEFTTURN},
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\ccGlobalScope\ccc{COLLINEAR}, or
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\ccGlobalScope\ccc{RIGHTTURN} iff \ccc{r} lies properly to the
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left of, on, or properly to the right of the oriented line
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through \ccc{p} and \ccc{q}, resp.}
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% -----------------------------------------------------------------------------
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\ccHasModels
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\ccRefIdfierPage{CGAL::Min_circle_2_traits_2<K>}
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccIndexTraitsClassRequirements[C]{Min_circle_2}
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\ccRefIdfierPage{CGAL::Min_circle_2<Traits>}
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% -----------------------------------------------------------------------------
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\end{ccRefConcept}
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% =============================================================================
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\ccAutoIndexingOff
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\ccHtmlNoClassToc
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\ccHtmlNoClassLinks
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\ccHtmlNoClassIndex
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\begin{ccClass}{Circle}
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\subsection*{Circle Type (\ccClassTemplateName)}
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\ccSaveThreeColumns
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\ccSetThreeColumns{Distance}{}{returns
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\ccGlobalScope\ccc{ON_BOUNDED_SIDE}, \ccGlobalScope\ccc{ON_BOUNDARY},}
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\ccPropagateThreeToTwoColumns
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% -----------------------------------------------------------------------------
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\ccDefinition
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An object of the class \ccClassName\ is a circle in two-dimensional
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Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$
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has no bounded side, its boundary is $\{p\}$, and its unbounded side
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equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{Point type.}
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The following type is only needed, if the member function \ccc{is_valid}
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of \ccc{Min_circle_2} is used.
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\ccNestedType{Distance}{
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Distance type. The function \ccc{squared_radius} (see below)
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returns an object of this type.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{circle}
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\ccMemberFunction{ void set( );}{
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sets \ccVar\ to the empty circle.}
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\ccMemberFunction{ void set( const Point& p);}{
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sets \ccVar\ to the circle containing exactly $\{\mbox{\ccc{p}}\}$.}
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\ccMemberFunction{ void set( const Point& p,
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const Point& q);}{
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sets \ccVar\ to the circle with diameter equal to the segment
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connecting \ccc{p} and \ccc{q}. The algorithm guarantees that
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\ccc{set} is never called with two equal points.}
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\ccMemberFunction{ void set( const Point& p,
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const Point& q,
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const Point& r);}{
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sets \ccVar\ to the circle through \ccc{p},\ccc{q},\ccc{r}.
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The algorithm guarantees that \ccc{set} is never called with
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three collinear points.}
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% -----------------------------------------------------------------------------
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\ccPredicates
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\ccMemberFunction{ bool has_on_unbounded_side( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly outside of \ccVar.}
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Each of the following predicates is only needed, if the corresponding
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predicate of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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\ccGlobalScope\ccc{ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
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on the boundary, or properly outside of \ccVar, resp.}
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\ccMemberFunction{ bool has_on_bounded_side( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly inside \ccVar.}
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\ccMemberFunction{ bool has_on_boundary( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies on the boundary
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of \ccVar.}
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\ccMemberFunction{ bool is_empty( ) const;}{
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returns \ccc{true}, iff \ccVar\ is empty (this implies
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degeneracy).}
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if
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\ccVar\ is empty or equal to a single point.}
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% -----------------------------------------------------------------------------
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\ccHeading{Additional Operations for Checking}
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The following operations are only needed, if the member function
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\ccc{is_valid} of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ bool operator == ( const Circle& circle2) const;}{
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returns \ccc{true}, iff \ccVar\ and \ccc{circle2} are equal.}
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\ccMemberFunction{ Point center( ) const;}{
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returns the center of \ccVar.}
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\ccMemberFunction{ Distance squared_radius( ) const;}{
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returns the squared radius of \ccVar.}
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% -----------------------------------------------------------------------------
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\ccHeading{I/O}
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The following I/O operators are only needed, if the corresponding I/O
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operators of \ccc{Min_circle_2} are used.
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\ccHtmlNoIndex
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\ccFunction{ std::ostream&
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operator << ( std::ostream& os, const Circle& circle);}{
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writes \ccVar\ to output stream \ccc{os}.}
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\ccHtmlNoIndex
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\ccFunction{ CGAL::Window_stream&
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operator << ( CGAL::Window_stream& ws,
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const Circle& circle);}{
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writes \ccVar\ to window stream \ccc{ws}.}
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% -----------------------------------------------------------------------------
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\ccRestoreThreeColumns
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\end{ccClass}
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\ccAutoIndexingOn
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% ===== EOF ===================================================================
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@ -0,0 +1,211 @@
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% -*- latex -*-
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% =============================================================================
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% The CGAL Reference Manual
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% Chapter: Geometric Optimisation
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% Concept: MinCircle2Traits
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% -----------------------------------------------------------------------------
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% file : doc_tex/basic/Optimisation/Optimisation_ref/MinCircle2Traits.tex
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% package: Min_circle_2
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% author : Sven Schönherr <sven@inf.ethz.ch>
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% -----------------------------------------------------------------------------
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% $Revision$
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% $Date$
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% =============================================================================
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\begin{ccRefConcept}{MinCircle2Traits}
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% -----------------------------------------------------------------------------
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\ccDefinition
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This concept defines the requirements for traits classes of
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\ccGlobalScope\ccc{Min_circle_2<Traits>}.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{
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The point type must provide default and copy constructor,
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assignment and equality test.}
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\ccNestedType{Circle}{
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The circle type must fulfill the requirements listed below
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in the next section.}
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% -----------------------------------------------------------------------------
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\ccHeading{Variables}
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\ccVariable{ Circle circle;}{
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The current circle. This variable is maintained by the algorithm,
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the user should neither access nor modify it directly.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{traits}
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Only default and copy constructor are required.
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\ccConstructor{ MinCircle2Traits( );}{}
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\ccConstructor{ MinCircle2Traits( const MinCircle2Traits&);}{}
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% -----------------------------------------------------------------------------
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\ccOperations
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The following predicate is only needed, if the member function
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\ccc{is_valid} of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ CGAL::Orientation
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orientation( const Point& p,
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const Point& q,
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const Point& r) const;}{
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returns constants \ccGlobalScope\ccc{LEFTTURN},
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\ccGlobalScope\ccc{COLLINEAR}, or
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\ccGlobalScope\ccc{RIGHTTURN} iff \ccc{r} lies properly to the
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left of, on, or properly to the right of the oriented line
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through \ccc{p} and \ccc{q}, resp.}
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% -----------------------------------------------------------------------------
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\ccHasModels
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\ccRefIdfierPage{CGAL::Min_circle_2_traits_2<K>}
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% -----------------------------------------------------------------------------
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\ccSeeAlso
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\ccIndexTraitsClassRequirements[C]{Min_circle_2}
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\ccRefIdfierPage{CGAL::Min_circle_2<Traits>}
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% -----------------------------------------------------------------------------
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\end{ccRefConcept}
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% =============================================================================
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\ccAutoIndexingOff
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\ccHtmlNoClassToc
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\ccHtmlNoClassLinks
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\ccHtmlNoClassIndex
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\begin{ccClass}{Circle}
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\subsection*{Circle Type (\ccClassTemplateName)}
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\ccSaveThreeColumns
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\ccSetThreeColumns{Distance}{}{returns
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\ccGlobalScope\ccc{ON_BOUNDED_SIDE}, \ccGlobalScope\ccc{ON_BOUNDARY},}
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\ccPropagateThreeToTwoColumns
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% -----------------------------------------------------------------------------
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\ccDefinition
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An object of the class \ccClassName\ is a circle in two-dimensional
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Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$
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has no bounded side, its boundary is $\{p\}$, and its unbounded side
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equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{Point type.}
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The following type is only needed, if the member function \ccc{is_valid}
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of \ccc{Min_circle_2} is used.
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\ccNestedType{Distance}{
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Distance type. The function \ccc{squared_radius} (see below)
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returns an object of this type.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{circle}
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\ccMemberFunction{ void set( );}{
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sets \ccVar\ to the empty circle.}
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\ccMemberFunction{ void set( const Point& p);}{
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sets \ccVar\ to the circle containing exactly $\{\mbox{\ccc{p}}\}$.}
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\ccMemberFunction{ void set( const Point& p,
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const Point& q);}{
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sets \ccVar\ to the circle with diameter equal to the segment
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connecting \ccc{p} and \ccc{q}. The algorithm guarantees that
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\ccc{set} is never called with two equal points.}
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\ccMemberFunction{ void set( const Point& p,
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const Point& q,
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const Point& r);}{
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sets \ccVar\ to the circle through \ccc{p},\ccc{q},\ccc{r}.
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The algorithm guarantees that \ccc{set} is never called with
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three collinear points.}
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% -----------------------------------------------------------------------------
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\ccPredicates
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\ccMemberFunction{ bool has_on_unbounded_side( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly outside of \ccVar.}
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Each of the following predicates is only needed, if the corresponding
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predicate of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
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\ccGlobalScope\ccc{ON_BOUNDARY}, or
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\ccGlobalScope\ccc{ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
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on the boundary, or properly outside of \ccVar, resp.}
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\ccMemberFunction{ bool has_on_bounded_side( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly inside \ccVar.}
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\ccMemberFunction{ bool has_on_boundary( const Point& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies on the boundary
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of \ccVar.}
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\ccMemberFunction{ bool is_empty( ) const;}{
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returns \ccc{true}, iff \ccVar\ is empty (this implies
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degeneracy).}
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if
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\ccVar\ is empty or equal to a single point.}
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% -----------------------------------------------------------------------------
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\ccHeading{Additional Operations for Checking}
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The following operations are only needed, if the member function
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\ccc{is_valid} of \ccc{Min_circle_2} is used.
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\ccMemberFunction{ bool operator == ( const Circle& circle2) const;}{
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returns \ccc{true}, iff \ccVar\ and \ccc{circle2} are equal.}
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\ccMemberFunction{ Point center( ) const;}{
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returns the center of \ccVar.}
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\ccMemberFunction{ Distance squared_radius( ) const;}{
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returns the squared radius of \ccVar.}
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% -----------------------------------------------------------------------------
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\ccHeading{I/O}
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The following I/O operators are only needed, if the corresponding I/O
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operators of \ccc{Min_circle_2} are used.
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\ccHtmlNoIndex
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\ccFunction{ std::ostream&
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operator << ( std::ostream& os, const Circle& circle);}{
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writes \ccVar\ to output stream \ccc{os}.}
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\ccHtmlNoIndex
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\ccFunction{ CGAL::Window_stream&
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operator << ( CGAL::Window_stream& ws,
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const Circle& circle);}{
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writes \ccVar\ to window stream \ccc{ws}.}
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% -----------------------------------------------------------------------------
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\ccRestoreThreeColumns
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\end{ccClass}
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\ccAutoIndexingOn
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% ===== EOF ===================================================================
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