From d409ffdd7fc986221f35591730c7afec4d495338 Mon Sep 17 00:00:00 2001 From: Andreas Fabri Date: Mon, 20 Aug 2012 18:06:50 +0000 Subject: [PATCH] Fix nesting of
; Capitalize headings --- Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt b/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt index 789a806c007..985da4dcf55 100644 --- a/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt +++ b/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt @@ -77,7 +77,7 @@ of the alpha complex where singular faces are removed \anchor figgenregex \image html gen-reg-ex.png -
Comparison of general and regularized alpha-shape. Left: Some points are taken on the surface of a torus, three points being taken relatively far from the surface of the torus; Middle: The general alpha-shape (for a large enough alpha value) contains the singular triangle facet of the three isolated points; Right: The regularized version (for the same value of alpha) does not contains any singular facet.
+
Comparison of general and regularized alpha-shape. Left: Some points are taken on the surface of a torus, three points being taken relatively far from the surface of the torus; Middle: The general alpha-shape (for a large enough alpha value) contains the singular triangle facet of the three isolated points; Right: The regularized version (for the same value of alpha) does not contains any singular facet.
The alpha shapes of a set of points @@ -119,7 +119,7 @@ regularized versions. \section I1_SectAlpha_Shape_3 Functionality -## Family of alpha shapes ## +## Family of Alpha Shapes ## The class `CGAL::Alpha_shape_3` represents the whole family of alpha shapes for a given set of points. @@ -143,15 +143,15 @@ Finally, it provides a function to determine the smallest value \f$ \alpha\f$ such that the alpha shape satisfies the following two properties -(ii) all data points are either on the boundary or in the interior +(i) all data points are either on the boundary or in the interior of the regularized version of the alpha shape (no singular faces). -(i) The number of components is equal or less than a given number .
+(ii) The number of components is equal or less than a given number .
The current implementation is static, that is after its construction points cannot be inserted or removed. -## Alpha shape for a fixed alpha ## +## Alpha Shape for a Fixed Alpha ## Given a value of alpha, the class `CGAL::Fixed_alpha_shape_3
` represents one alpha shape for a given set of points. @@ -162,7 +162,7 @@ a classification type.
The current implementation of this class is dynamic, that is after its construction points can be inserted or removed. -## Classification and iterators ## +## Classification and Iterators ## Both classes provide member functions to classify for a (given) value of \f$ alpha\f$ the different faces of the triangulation as