songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Fix typos

This commit is contained in:
Clement Jamin 2017-01-04 17:44:46 +01:00
parent ebc4605d3e
commit a1a60e9921
2 changed files with 7 additions and 7 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
Triangulation/doc/Triangulation/CGAL/Triangulation.h
View File

@ -214,7 +214,8 @@ type (a signed integral type)
typedef TriangulationDataStructure_::difference_type difference_type;
/*!
\enum used by `Triangulation` to specify which case occurs when locating a point in the triangulation
\enum Locate_type
\brief Used by `Triangulation` to specify which case occurs when locating a point in the triangulation.
*/
enum Locate_type { ON_VERTEX=0, /*!< when the located point coincides with a vertex of the triangulation */
IN_FACE, /*!< when the point is in the interior of a face of dimension equal or less than `maximal_dimension()` - 2 */

11
Triangulation/doc/Triangulation/Triangulation.txt
View File

@ -117,7 +117,7 @@ triangulation data structure and can then be obtained using the method `tds.maxi
A triangulation data structure also knows the <I>current dimension</I> of its full cells,
which can be obtained using `tds.current_dimension()`. In the sequel, let
us denote the maximal dimension with \f$ D \f$ and the current dimension with \f$ d \f$.
The inequalities \f$ -2 \leq d \leq D\f$ and \f$ 0 \le D\f$ always hold.
The inequalities \f$ -2 \leq d \leq D\f$ and \f$ 0 < D\f$ always hold.
The special meaning of negative values for \f$d\f$ is explained below.
## The Set of Faces ##
@ -453,22 +453,21 @@ Let \f$ {S}^{(w)}\f$ be a set of weighted points in \f$ \mathbb{R}^D\f$. Let
\f$ {p}^{(w)}=(p,w_p), p\in\mathbb{R}^D, w_p\in\mathbb{R}\f$ and
\f$ {z}^{(w)}=(z,w_z), z\in\mathbb{R}^D, w_z\in\mathbb{R}\f$
be two weighted points.
If all weights are positive, a weighted point
\f$ {p}^{(w)}=(p,w_p)\f$ can also be seen as a sphere of center \f$ p\f$ and
radius \f$ \sqrt{w_p}\f$.
A weighted point \f$ {p}^{(w)}=(p,w_p)\f$ can also be seen as a sphere of
center \f$ p\f$ and radius \f$ \sqrt{w_p}\f$.
The <I>power product</I> (or <I>power distance</I> )
between \f$ {p}^{(w)}\f$ and \f$ {z}^{(w)}\f$ is
defined as
\f[ \Pi({p}^{(w)},{z}^{(w)}) = {\|{p-z}\|^2-w_p-w_z} \f]
where \f$ \|{p-z}\|\f$ is the Euclidean distance between \f$ p\f$ and \f$ z\f$.
\f$ {p}^{(w)}\f$ and \f$ {z}^{(w)}\f$
are said to be <I>orthogonal</I> if \f$ \Pi{({p}^{(w)}-{z}^{(w)})}
are said to be <I>orthogonal</I> if \f$ \Pi({p}^{(w)},{z}^{(w)})
= 0\f$.
\f$D + 1\f$ weighted points have a unique common orthogonal weighted point
called the <I>power sphere</I>. A sphere \f$ {z}^{(w)}\f$ is said to be
<I>regular</I> if \f$ \forall {p}^{(w)}\in{S}^{(w)},
\Pi{({p}^{(w)}-{z}^{(w)})}\geq 0\f$.
\Pi({p}^{(w)},{z}^{(w)})\geq 0\f$.
A triangulation of \f$ {S}^{(w)}\f$ is <I>regular</I> if the power spheres
of all simplices are regular.