From 1733a29deadae6d41d94a417ebf2a4f144d46cdd Mon Sep 17 00:00:00 2001 From: Efi Fogel Date: Wed, 12 May 2021 20:03:12 +0300 Subject: [PATCH] Added more information about construction of great circle arcs. --- .../Arrangement_on_surface_2.txt | 28 ++++++++++++++++++ .../Arr_geodesic_arc_on_sphere_traits_2.h | 15 ++++++++-- .../fig/right_hand_rule.png | Bin 0 -> 96703 bytes 3 files changed, 40 insertions(+), 3 deletions(-) create mode 100644 Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig/right_hand_rule.png diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt index 4585d9fd3b3..c4249afaa67 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt @@ -5407,6 +5407,34 @@ identification curve is drawn as a gray tube. \cgalExample{Arrangement_on_surface_2/spherical_insert.cpp} +Use the `Arr_geodesic_arc_on_sphere_traits_2::Construct_point_2`, +`Arr_geodesic_arc_on_sphere_traits_2::Construct_x_monotone_curve_2`, +and `Arr_geodesic_arc_on_sphere_traits_2::Construct_curve_2` functors +to construct a point, an \f$X\f$-monotone curve and a curve objects, +respectively. Observe that an \f$X\f$-monotone curve cannot intersect +the identification curve in its interior. A curve can be constructed +from either (i) two endpoints, (ii) two endpoints and a normal, or +(iii) a normal. The two endpoints determine the plane. The normal +determines the orientation of the plane and the final arc (whether it +is the minor arc or the major arc). If the normal is not provided, the +minor arc is constructed. If a curve is constructed and only the +normal is provided a full great circle is constructed. If an +\f$X\f$-monotone curve is constructed and only the normal is provided +an arc that resembles a full circle is constructed; this arc has one +endpoint that lies on the identification curve; this point is +considered both the source and target (and also the left and right) +point of the arc. See \cgalFigureRef{aos_fig-right_hand_rule} for an +illustration of the right-hand rule, which depicts the relation +between the arc and the normal. + + +\cgalFigureBegin{aos_fig-right_hand_rule,right_hand_rule.png} +To use the right hand rule, point your right thumb in the direction of +the normal and curl your fingers in the direction of the arc starting +with source pendpoint and endding at the target endpoint. +\cgalFigureEnd + + \subsection arr_ssecmeta_tr Traits-Class Decorators diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h index e375b142e38..4f599f66a41 100644 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h @@ -359,20 +359,29 @@ namespace CGAL { * \param[in] q the second endpoint. * \pre p and q must not coincide. * \pre p and q cannot be antipodal. + * \pre The constructed minor arc does not intersect the identification + * curve in its interior. */ X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q); /*! Construct a full great circle from a normal to a plane. + * Observe that the constrcted arc has one endpoint that lies on + * the identification curve. This point is considered both the source and + * target (and also the left and right) point of the arc. * \param normal the normal to the plane containing the great circle. * \pre the plane is not vertical. */ X_monotone_curve_2 operator()(const Direction_3& normal); - /*! Construct a geodesic arc from two endpoints contained in a plane. + /*! Construct a geodesic arc from two endpoints and a normal to the plane + * containing the arc. The two endpoints determine the plane. The normal + * determines the orientation of the plane and the final arc (whether its + * the minor arc or the major arc). The right-hand rule can be used + * to select the appropriate normal. * \param[in] p the first endpoint. * \param[in] q the second endpoint. - * \param[in] normal the normal to the plane containing the arc. - * \pre Both endpoints lie on the given plane. + * \param[in] normal the normal to the oriented plane containing the arc. + * \pre Both endpoints lie on the given oriented plane. */ X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q, const Direction_3& normal); diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig/right_hand_rule.png b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig/right_hand_rule.png new file mode 100644 index 0000000000000000000000000000000000000000..3beebbf7b193043491007da35047fc37719e8cf9 GIT binary patch literal 96703 zcmX_H1yEaC*Ttb|f){tU;I6@;6f17Qt+=}f2-X&NikG6r-HW?B6o*2gNYS77y}o~# z3^R8oIkwN*Yp=a-^xHS`Sm-3^aBy%~iV9#2I5-3#92~qd8p_KP8}oIFmwzY_WqB~% z^FM!i?Ij;yp1g8a&~t->!@&FJ0}q#xMf~y*)m>3l7IhaH6Ci{d{`CtN92^y#B3Mex 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