diff --git a/Triangulation_3/doc/Triangulation_3/Concepts/RegularTriangulationTraits_3.h b/Triangulation_3/doc/Triangulation_3/Concepts/RegularTriangulationTraits_3.h index e77f278f11b..ff76c06fdfd 100644 --- a/Triangulation_3/doc/Triangulation_3/Concepts/RegularTriangulationTraits_3.h +++ b/Triangulation_3/doc/Triangulation_3/Concepts/RegularTriangulationTraits_3.h @@ -75,28 +75,33 @@ which performs the following: Let \f$ {z(p,q,r,s)}^{(w)}\f$ be the power sphere of the weighted points \f$ (p,q,r,s)\f$. Returns -`ON_ORIENTED_BOUNDARY` if `t` is orthogonal to -\f$ {z(p,q,r,s)}^{(w)}\f$, +- `ON_ORIENTED_BOUNDARY` if `t` is orthogonal to + \f$ {z(p,q,r,s)}^{(w)}\f$, -`ON_NEGATIVE_SIDE` if `t` lies outside the oriented sphere of -center \f$ z(p,q,r,s)\f$ and radius \f$ \sqrt{ w_{z(p,q,r,s)}^2 + w_t^2 }\f$ -(which is equivalent to \f$ \Pi({t}^{(w)},{z(p,q,r,s)}^{(w)} >0\f$)), +- `ON_NEGATIVE_SIDE` if `t` lies outside the oriented sphere of + center \f$ z(p,q,r,s)\f$ and radius \f$ \sqrt{ w_{z(p,q,r,s)}^2 + w_t^2 }\f$ + (which is equivalent to \f$ \Pi({t}^{(w)},{z(p,q,r,s)}^{(w)} >0\f$)), + +- `ON_POSITIVE_SIDE` if `t` lies inside this oriented sphere. -`ON_POSITIVE_SIDE` if `t` lies inside this oriented sphere. \pre `p, q, r, s` are not coplanar. Note that with this definition, if all the points have a weight equal to 0, then `power_test_3(p,q,r,s,t)` = `side_of_oriented_sphere(p,q,r,s,t)`. +
+ `Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 t)`, -which has an +which has a definition analogous to the previous method, for coplanar points, with the power circle \f$ {z(p,q,r)}^{(w)}\f$. \pre `p, q, r` are not collinear and `p, q, r, t` are coplanar. If all the points have a weight equal to 0, then `power_test_3(p,q,r,t)` = `side_of_oriented_circle(p,q,r,t)`. +
+ `Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 t)`, which is the same for collinear points, where \f$ {z(p,q)}^{(w)}\f$ is the @@ -107,6 +112,8 @@ If all points have a weight equal to 0, then `s(p,q).has_on(t)` would give, where `s(p,q)` denotes the segment with endpoints `p` and `q`. +
+ `Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q)`, which is the same for equal points, that is when `p` and `q`