Small layout changes for Power_test_3's doc entry

(cherry picked from commit fdb4959b3e06c4c3fe4dd17d4420664a5d140486)
This commit is contained in:
Mael Rouxel-Labbé 2014-07-15 11:00:44 +02:00 committed by Laurent Rineau
parent 26861f733d
commit 7cc8f59898
1 changed files with 14 additions and 7 deletions

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@ -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$)),
- `ON_POSITIVE_SIDE` if `t` lies inside this oriented sphere.
`ON_POSITIVE_SIDE` if `t` lies inside this oriented sphere.
\pre `p, q, r, s` are not coplanar.
Note that with this definition, if all the points have a weight equal
to 0, then
`power_test_3(p,q,r,s,t)` = `side_of_oriented_sphere(p,q,r,s,t)`.
<HR WIDTH=50%>
`Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 t)`,
which has an
which has a
definition analogous to the previous method, for coplanar points,
with the power circle \f$ {z(p,q,r)}^{(w)}\f$.
\pre `p, q, r` are not collinear and `p, q, r, t` are coplanar.
If all the points have a weight equal to 0, then
`power_test_3(p,q,r,t)` = `side_of_oriented_circle(p,q,r,t)`.
<HR WIDTH=50%>
`Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 t)`,
which is the same for collinear points, where \f$ {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`.
<HR WIDTH=50%>
`Oriented_side operator()( Weighted_point_3 p, Weighted_point_3 q)`,
which is the same for equal points, that is when `p` and `q`