Documentation changes in Seam_mesh / SMP

This commit is contained in:
Mael Rouxel-Labbé 2017-01-23 14:34:13 +01:00
parent 6308f2a94a
commit 4702f3ca36
18 changed files with 944 additions and 63 deletions

View File

@ -460,7 +460,7 @@ When we circulate in the seam graph we will traverse `h7`, `h1`, `h3*`, and we a
When we start at `h3`, we will traverse `h3`, `h5`, `h7*`, and we are back at `h3`.
\cgalFigureBegin{fig_Seam_mesh_1, Seam_mesh_1.png}
\cgalFigureBegin{fig_Seam_mesh_1, seam_mesh_1.svg}
A seam mesh with two seam edges `(2,3)` and `(6,7)`.
\cgalFigureEnd

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@ -0,0 +1,643 @@
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@ -47,14 +47,14 @@ public:
/// the vertices of the mesh. Mark them as <I>parameterized</I>.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -63,7 +63,6 @@ public:
/// \param vimap an instanciation of the class `VertexIndexMap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (`vimap` must be initialized)
///

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@ -115,9 +115,9 @@ using the `Surface_mesh` built-in property mechanism.
\section secSurfaceParameterizationMethods Surface Parameterization Methods
This \cgal package implements surface parameterization methods, such
as Least Squares Conformal Maps, Discrete Conformal Map, Discrete
Authalic Parameterization, Floater Mean Value Coordinates or Tutte
Barycentric Mapping. These methods are provided as models of the
as As Rigid as Possible, Least Squares Conformal Maps, Discrete Conformal Map,
Discrete Authalic Parameterization, Floater Mean Value Coordinates or Tutte
Barycentric and Orbifold Mappings. These methods are provided as models of the
`Parameterizer_3` concept.
\subsection Surface_mesh_parameterizationFixedBorder Fixed Border Surface Parameterizations
@ -271,7 +271,7 @@ Least squares conformal maps.
`Surface_mesh_parameterization::ARAP_parameterizer_3<TriangleMesh, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
An as rigid as possible parameterization was introduced by Liu et al. \cgalCite{liu2008local}.
An as-rigid-as-possible parameterization was introduced by Liu et al. \cgalCite{liu2008local}.
It is a shape-preserving method based on an iterative energy minimization process.
Each step alternates a local optimization technique to find the best local mapping
and a global stitching technique equivalent to the resolution of a linear system
@ -282,6 +282,14 @@ coefficient &lambda; that allows the user to choose to give importance to angle
preservation (conforming parameterization) when &lambda; = 0, to shape preservation (as rigid as
possible) when &lambda; goes to infinity, or a balance of both.
\cgalFigureAnchor{Surface_mesh_parameterizationfigARAP}
<center>
<img src="ARAP.png" style="width:800px"/>
</center>
\cgalFigureCaptionBegin{Surface_mesh_parameterizationfigARAP}
As Rigid As Possible parameterization (the cut is traced in red).
\cgalFigureCaptionEnd
\subsection secBorderParameterizationsforFreeMethods Border Parameterizations for Free Methods
Parameterization methods for borders are used as traits classes modifying
@ -300,7 +308,7 @@ in the current version of this package.
</UL>
\subsection Surface_mesh_parameterizationBorderless Borderless Parameterizations
\subsection Surface_mesh_parameterizationBorderless Borderless Surface Parameterizations
\subsubsection Surface_mesh_parameterizationOrbi Orbifold Tutte Embedding
@ -321,6 +329,15 @@ The parameterization process intrinsically requires the uses of seams, but whose
have no influence on the result. The `Seam_mesh` structure (see also next Section)
is used for this purpose.
\cgalFigureAnchor{Surface_mesh_parameterizationfigOrbifold}
<center>
<img src="orbifold.png" style="width:800px"/>
</center>
\cgalFigureCaptionBegin{Surface_mesh_parameterizationfigOrbifold}
Type IV Orbifold Tutte Embedding. The (four) base cones are shown in green and the
virtual cut is shown in red.
\cgalFigureCaptionEnd
\section secCuttingaMesh Cutting a Mesh
The surface parameterization methods proposed in this package only
@ -406,7 +423,7 @@ who worked as an engineer at Inria Sophia-Antipolis.
For CGAL 4.10 the package has undergone a major rewrite by Andreas Fabri.
The algorithms are the same, but they are now based on the `FaceGraph` API.
Additionally, the class `Seam_mesh` got introduced, which is also a model of
Additionally, the class `Seam_mesh` was introduced, which is also a model of
a `FaceGraph`, and replaces a wrapper which had a more complicated API.
*/

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@ -1,6 +1,7 @@
/*!
\example Surface_mesh_parameterization/discrete_authalic.cpp
\example Surface_mesh_parameterization/lscm.cpp
\example Surface_mesh_parameterization/orbifold.cpp
\example Surface_mesh_parameterization/seam_Polyhedron_3.cpp
\example Surface_mesh_parameterization/simple_parameterization.cpp
\example Surface_mesh_parameterization/square_border_parameterizer.cpp

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@ -91,8 +91,8 @@ namespace Surface_mesh_parameterization {
/// When &lambda; is non-null, the border does not need to be parameterized and
/// a random vertex is pinned.
///
/// If flips are present in the parameterization, a post-processing step is applied
/// using `CGAL::Surface_mesh_parameterization::MVC_post_processor_3<TriangleMesh, SparseLinearAlgebraTraits_d>`
/// If flips are present in the initial parameterization, a post-processing step
/// is applied using `CGAL::Surface_mesh_parameterization::MVC_post_processor_3<TriangleMesh, SparseLinearAlgebraTraits_d>`
/// to attempt to obtain a valid final embedding.
///
/// A one-to-one mapping is *not* guaranteed.
@ -1194,14 +1194,14 @@ public:
/// The result is the (u,v) pair image of each vertex of the 3D surface.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -1210,7 +1210,6 @@ public:
/// \param vimap an instanciation of the class `VertexIndexMap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (vimap must be initialized).
///

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@ -110,14 +110,14 @@ public:
/// `compute_edge_length()`.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -125,8 +125,8 @@ public:
/// \param uvmap an instanciation of the class `VertexUVmap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (vimap must be initialized).
///
template <typename VertexUVmap,
typename VertexIndexMap,

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@ -146,14 +146,14 @@ public:
/// The result is the (u,v) pair image of each vertex of the 3D surface.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -162,7 +162,6 @@ public:
/// \param vimap an instanciation of the class `VertexIndexMap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The mesh border must be mapped onto a convex polygon.
/// \pre The vertices must be indexed (`vimap` must be initialized)
@ -276,11 +275,11 @@ protected:
/// "u = constant" and "v = constant".
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
///
/// \param A the matrix in both linear system

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@ -163,14 +163,14 @@ public:
/// The result is the (u,v) pair image of each vertex of the 3D surface.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -179,7 +179,6 @@ public:
/// \param vimap an instanciation of the class `VertexIndexMap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (`vimap` must be initialized).
///

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@ -727,11 +727,11 @@ public:
/// that is not necessarily embedded to a piece of the 2D space.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
///
/// \param mesh a triangulated surface.

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@ -88,10 +88,19 @@ enum Weight_type
///
/// This is a borderless parameterization. A one-to-one mapping is guaranteed.
///
/// The main function of the class `Orbifold_Tutte_parameterizer_3` is `parameterize()`,
/// to which the user provides a `Seam_mesh` with marked edges (the seams)
/// and a set of vertices of the mesh (the cones). The choice of cones influences
/// the resulting parameterization, but not the choice of the seam path between these cones.
///
/// The example \ref Surface_mesh_parameterization/orbifold.cpp "orbifold.cpp"
/// shows how to select cones on the input mesh and automatically construct
/// the seams and the cones on the `Seam_mesh`.
///
/// \cgalModels `Parameterizer_3`
///
/// \tparam SeamMesh must be a `Seam_mesh`, with underlying mesh any model of `FaceGraph`
/// \tparam SparseLinearAlgebraTraits_d Traits class to solve a sparse linear system. <br>
/// \tparam SparseLinearAlgebraTraits_d Traits class to solve a sparse linear system
///
/// \sa `CGAL::Surface_mesh_parameterization::ARAP_parameterizer_3<TriangleMesh, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
/// \sa `CGAL::Surface_mesh_parameterization::Barycentric_mapping_parameterizer_3<TriangleMesh, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
@ -627,26 +636,39 @@ public:
/// The mapping is piecewise linear (linear in each triangle).
/// The result is the (u,v) pair image of each vertex of the 3D surface.
///
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// `boost::graph_traits<Seam_mesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `Seam_mesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<Seam_mesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<Seam_mesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a model of the `FaceGraph` concept
/// \param mesh a `Seam_mesh` parameterized by any model of a `FaceGraph`
/// \param bhd a halfedge on the border of the seam mesh
/// \param cmap a mapping of 4 (or 6) `vertex_descriptor`s that are cones
/// \param cmap a mapping of the `vertex_descriptor`s of `mesh` that are cones
/// to their respective `Cone_type`.
/// \param uvmap an instanciation of the class `VertexUVmap`.
/// \param vimap an instanciation of the class `VertexIndexMap`.
///
/// \pre cones and seams must be valid.
/// \pre `mesh` must be a triangular mesh.
/// \pre The underlying mesh of `mesh` is a topological ball.
/// \pre The vertices must be indexed (vimap must be initialized).
/// \pre The cones are vertices of `mesh` and their number is adapted to
/// the orbifold type (4 for types I, II or III and 6 for type IV).
/// \pre The seam edges form a set of segments that contains the different cones,
/// and starts and ends at two different cones.
/// \pre The seam edges form a set of segments that is homotopic to a
/// line. Specifically, the paths between cones should not self intersect
/// or intersect other paths (see Figure below).
///
/// \cgalFigureBegin{Surface_mesh_parameterizationfigorbifold, orbifold_path.svg}
/// Bad (left) and good (right) seam paths. The seam edges are shown in dark red.
/// Cones are marked in yellow and blue.
/// \cgalFigureEnd
template<typename ConeMap,
typename VertexIndexMap,
typename VertexUVMap>

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@ -151,7 +151,7 @@ void output_arrangement_to_off(const Arrangement& arr,
out << std::endl;
}
/// A type to regroup all the info and avoid having to pass it all in each function.
// A type to regroup all the info and avoid having to pass it all in each function.
template<typename SeamMesh_,
typename ConeMap_,
typename VertexIndexMap_,
@ -184,7 +184,7 @@ public:
{ }
};
/// Affine transformation to express A = T*B + V
// Affine transformation to express A = T*B + V
// @fixme transf needs a translation component too (for orb type IV)
template<typename Kernel>
class Affine_transformation
@ -253,8 +253,8 @@ public:
}
};
/// halfedge that carries a transformation that is used to compute the coordinates
/// of the incident faces in the tiled space.
// halfedge that carries a transformation that is used to compute the coordinates
// of the incident faces in the tiled space.
template<typename SeamMesh>
class halfedge_with_transformation
{
@ -280,6 +280,7 @@ public:
} // namespace internal
template<typename Arrangement,
typename EmbeddedMesh>
class Orbifold_sphere_mapper

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@ -259,14 +259,14 @@ public:
/// (i.e.\ a (u,v) pair) on the border's shape. Mark them as <i>parameterized</i>.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -274,8 +274,8 @@ public:
/// \param uvmap an instanciation of the class `VertexUVmap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (vimap must be initialized).
///
template<typename VertexUVMap,
typename VertexIndexMap,

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@ -275,14 +275,14 @@ public:
/// Map two extreme vertices of the 3D mesh and mark them as <i>parameterized</i>.
///
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
/// \tparam VertexIndexMap must be a model of `ReadablePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a unique integer as value type.
/// \tparam VertexParameterizedMap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// a Boolean as value type.
///
/// \param mesh a triangulated surface.
@ -291,8 +291,8 @@ public:
/// \param vimap an instanciation of the class `VertexIndexMap`.
/// \param vpmap an instanciation of the class `VertexParameterizedMap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (vimap must be initialized).
///
template <typename VertexUVmap,
typename VertexIndexMap,

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@ -37,7 +37,7 @@
#include <utility>
#include <vector>
/// \file Orbifold_cone_helper.h
/// \file orbifold_cone_helper.h
namespace CGAL {

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@ -70,10 +70,8 @@ void output_shortest_paths_to_selection_file(const TriangleMesh& mesh,
os << std::endl;
}
/// Visitor to stop Dijkstra when a target turns 'BLACK' (the point has been examined
/// through all its edges)
///
/// \tparam TriangleMesh
// Visitor to stop Dijkstra when a target turns 'BLACK' (the point has been examined
// through all its edges)
template<typename TriangleMesh>
class Stop_at_target_Dijkstra_visitor : boost::default_dijkstra_visitor
{

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@ -56,7 +56,7 @@ namespace Surface_mesh_parameterization {
/// \tparam HD must be the halfedge_descriptor type corresponding to the graph
/// traits of TriangleMesh.
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
///
@ -65,10 +65,11 @@ namespace Surface_mesh_parameterization {
/// \param bhd a halfedge descriptor on the boundary of `mesh`.
/// \param uvm an instanciation of the class `VertexUVmap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The mesh border must be mapped onto a convex polygon
/// (for fixed border parameterizations).
/// \pre The vertices must be indexed (vimap must be initialized).
///
template <class TriangleMesh, class Parameterizer, class HD, class VertexUVmap>
Error_code parameterize(TriangleMesh& mesh,
Parameterizer parameterizer,
@ -105,7 +106,7 @@ Error_code parameterize(TriangleMesh& mesh,
/// \tparam HD must be the halfedge_descriptor type corresponding to the graph
/// traits of TriangleMesh.
/// \tparam VertexUVmap must be a model of `ReadWritePropertyMap` with
/// `boost::graph_traits<TM>::%vertex_descriptor` as key type and
/// `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key type and
/// %Point_2 (type deduced from `TriangleMesh` using `Kernel_traits`)
/// as value type.
///
@ -113,8 +114,9 @@ Error_code parameterize(TriangleMesh& mesh,
/// \param bhd a halfedge descriptor on the boundary of `mesh`.
/// \param uvm an instanciation of the class `VertexUVmap`.
///
/// \pre `mesh` must be a surface with one connected component.
/// \pre `mesh` must be a triangular mesh.
/// \pre The vertices must be indexed (vimap must be initialized).
///
template <class TriangleMesh, class HD, class VertexUVmap>
Error_code parameterize(TriangleMesh& mesh,
HD bhd,