mirror of https://github.com/CGAL/cgal
69 lines
2.3 KiB
TeX
69 lines
2.3 KiB
TeX
% begin cgal manual page
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\begin{ccRefClass}[Nef_polyhedron_S2<Traits>::]{Sphere_circle}
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\ccCreationVariable{c}
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\ccDefinition
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An object \ccc{c} of type \ccc{Sphere_circle} is an oriented great
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circle on the surface of a unit sphere. Such circles correspond to
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the intersection of an oriented plane (that contains the origin) and
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the surface of $S_2$. The orientation of the great circle is that of a
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counterclockwise walk along the circle as seen from the positive
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halfspace of the oriented plane.
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\ccSetOneOfTwoColumns{6.5cm}
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\ccTypes
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\ccNestedType{RT}{ ring type. }
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\ccNestedType{Plane_3}{ plane a \ccc{Sphere_circle} lies in.}
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\ccCreation
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\ccConstructor{Sphere_circle()}{ creates some great circle. }
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\ccConstructor{Sphere_circle(const Sphere_point& p,
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const Sphere_point& q)}{ If $p$ and $q$ are
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opposite of each other, then we create the unique great circle on $S_2$
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which contains p and q. This circle is oriented such
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that a walk along \ccc{c} meets $p$ just before the shorter segment
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between $p$ and $q$. If $p$ and $q$ are opposite of each other then
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we create any great circle that contains $p$ and $q$. }
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\ccConstructor{Sphere_circle(const Plane_3& h)}{ creates the
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circle corresponding to the plane \ccc{h}. \ccPrecond \ccc{h}
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contains the origin. }
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\ccConstructor{Sphere_circle(const RT& x, const RT& y, const RT& z)}
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{ creates the circle orthogonal to the vector $(x,y,z)$. }
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\ccConstructor{Sphere_circle(Sphere_circle c, const Sphere_point&
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p)}{ creates a great circle orthogonal to $c$ that contains $p$.
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\ccPrecond $p$ is not part of $c$. }
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\ccSetTwoOfThreeColumns{2.5cm}{3.8cm}
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\ccOperations
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\ccMethod{Sphere_circle opposite() ;}{ Returns a sphere circle
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in the oppostie direction of \ccc{c}. }
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\ccMethod{bool has_on(const Sphere_point& p) ;}{ returns true iff
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\ccc{c} contains \ccc{p}. }
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\ccMethod{Plane_3 plane() ;}{ returns the plane supporting \ccc{c}. }
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\ccMethod{Sphere_point orthogonal_pole() ;}{ returns the point that
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is the pole of the hemisphere left of \ccc{c}. }
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\ccHeading{Global functions}
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\ccFunction{bool equal_as_sets(
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const Nef_polyhedron_S2<Traits>::Sphere_circle c1,
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const Nef_polyhedron_S2<Traits>::Sphere_circle c2) ;}{
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returns true iff \ccc{c1} and \ccc{c2} are equal as unoriented
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circles. }
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\end{ccRefClass} |