From 3787e86753aa6f50c45b9897593715f8bb145c54 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A9bastien=20Loriot?= Date: Wed, 21 Aug 2019 09:10:37 +0200 Subject: [PATCH] doc fix --- .../Arrangement_on_surface_2.txt | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) 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 719b0deceed..6a41f684a19 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 @@ -79,7 +79,7 @@ for an illustration of the various \sc{Dcel} features. For more details on the \sc{Dcel} data structure see \cgalCite{bkos-cgaa-00} Chapter 2. \cgalFigureBegin{arr_figseg_dcel,arr_segs.png} -An arrangement of interior-disjoint line segments with some of the \sc{Dcel} records that represent it. The unbounded face \f$ f_0\f$ has a single connected component that forms a hole inside it, and this hole is comprised if several faces. The half-edge \f$ e\f$ is directed from its source vertex \f$ v_1\f$ to its target vertex \f$ v_2\f$. This edge, together with its twin \f$ e'\f$, correspond to a line segment that connects the points associated with \f$ v_1\f$ and \f$ v_2\f$ and separates the face \f$ f_1\f$ from \f$ f_2\f$. The predecessor \f$ e_{\rm prev}\f$ and successor \f$ e_{\rm next}\f$ of \f$ e\f$ are part of the chain that form the outer boundary of the face \f$ f_2\f$. The face \f$ f_1\f$ has a more complicated structure as it contains two holes in its interior: One hole consists of two adjacent faces \f$ f_3\f$ and \f$ f_4\f$, while the other hole is comprised of two edges. \f$ f_1\f$ also contains two isolated vertices \f$ u_1\f$ and \f$ u_2\f$ in its interior. +An arrangement of interior-disjoint line segments with some of the \sc{Dcel} records that represent it. The unbounded face \f$ f_0\f$ has a single connected component that forms a hole inside it, and this hole is comprised of several faces. The half-edge \f$ e\f$ is directed from its source vertex \f$ v_1\f$ to its target vertex \f$ v_2\f$. This edge, together with its twin \f$ e'\f$, correspond to a line segment that connects the points associated with \f$ v_1\f$ and \f$ v_2\f$ and separates the face \f$ f_1\f$ from \f$ f_2\f$. The predecessor \f$ e_{\rm prev}\f$ and successor \f$ e_{\rm next}\f$ of \f$ e\f$ are part of the chain that form the outer boundary of the face \f$ f_2\f$. The face \f$ f_1\f$ has a more complicated structure as it contains two holes in its interior: One hole consists of two adjacent faces \f$ f_3\f$ and \f$ f_4\f$, while the other hole is comprised of two edges. \f$ f_1\f$ also contains two isolated vertices \f$ u_1\f$ and \f$ u_2\f$ in its interior. \cgalFigureEnd The \f$ x\f$-monotone curves of an arrangement are embedded in an @@ -559,8 +559,8 @@ The arrangement of the line segments \f$ s_1, \ldots, s_5\f$ constructed in `edg The following program demonstrates the usage of the four insertion functions. It creates an arrangement of five line segments, as -depicted in \cgalFigureRef{arr_figex_1}.\cgalFootnote{Notice that in all figures in the rest of this chapter the coordinate axes are drawn only for illustrative purposes and are not part of the arrangement.} As the arrangement is very -simple, we use the simple Cartesian kernel of \cgal with integer +depicted in \cgalFigureRef{arr_figex_2} \cgalFootnote{Notice that in all figures in the rest of this chapter the coordinate axes are drawn only for illustrative purposes and are not part of the arrangement.}. As the arrangement is very +simple, we use the simple %Cartesian kernel of \cgal with integer coordinates for the segment endpoints. We also use the `Arr_segment_traits_2` class that enables the efficient maintenance of arrangements of line segments; see more details on @@ -668,7 +668,7 @@ In case the Gmp library is not installed (as indicat the `CGAL_USE_GMP` flag defined in `CGAL/basic.h`), we use `MP_Float`, a number-type included in \cgal's support library that is capable of storing floating-point numbers with -unbounded mantissa. We also use the standard Cartesian +unbounded mantissa. We also use the standard %Cartesian kernel of \cgal as our kernel. This is recommended when the kernel is instantiated with a more complex number type, as we demonstrate in other examples in this chapter. @@ -1439,7 +1439,7 @@ of the edge, it is removed as well. \image latex h_shape.png The following example demonstrates the usage of the free removal -functions. In creates an arrangement of four line segment forming +functions. It creates an arrangement of four line segment forming an H-shape with a double horizontal line. Then it removes the two horizontal edges and clears all redundant vertices, such that the final arrangement consists of just two edges associated with the @@ -2668,7 +2668,7 @@ of arbitrary degree (in general, a sequence of \f$ n+1\f$ control points define Bézier curve of degree \f$ n\f$). The template parameters are the same ones used by the `Arr_conic_traits_2` class template, and here it is also recommended to use the `CORE_algebraic_number_traits` class, with -Cartesian kernels instantiated with the `Rational` and `Algebraic` +%Cartesian kernels instantiated with the `Rational` and `Algebraic` number-types defined by this class. As mentioned above, we assume that the coordinates of all control