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Merge pull request #4169 from sloriot/Argt-doc_fixes 

User manual fixes
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Sebastien Loriot 2019-08-27 06:18:16 +02:00 committed by GitHub
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Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt
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@ -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 <I>not</I> 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 <I>not</I> 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 <span class="textsc">Gmp</span> 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
B&eacute;zier 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