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@ -73,8 +73,10 @@ The implementation within \cgal is generic in the sense that it can process any
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that consists of hexahedral cells.
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that consists of hexahedral cells.
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In case of a conforming grid, the Marching Cubes algorithm generates
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In case of a conforming grid, the Marching Cubes algorithm generates
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as output a surface triangle mesh that is 2-manifold in most scenarios.
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as output a surface triangle mesh that is 2-manifold in most scenarios.
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[@todo PA: reformulate, as it is either strict or not - precise in which cases it is not, and say
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whether you talk about just combinatorially 2-manifold, or truly 2-manifold with 3D embedding taken into account]
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@todo PA: reformulate, as it is either strict or not - precise in which cases it is not, and say
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whether you talk about just combinatorially 2-manifold, or truly 2-manifold with 3D embedding taken into account
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If the mesh is 2-manifold and the isosurface does not intersect the domain boundary, then the output mesh is watertight.
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If the mesh is 2-manifold and the isosurface does not intersect the domain boundary, then the output mesh is watertight.
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As the Marching Cubes algorithm uses linear interpolation of the sampled scalar field along the grid edges,
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As the Marching Cubes algorithm uses linear interpolation of the sampled scalar field along the grid edges,
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it can miss details or components that are not captured by the sampling of the scalar field.
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it can miss details or components that are not captured by the sampling of the scalar field.
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@ -84,7 +86,7 @@ MC often generates more triangles, and more skinny triangles with small or large
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@todo PA: The statement is too strong - I would largely reformulate it as this depends too much on the parameters. I recommend to add instead a figure with different parameters and methods,
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@todo PA: The statement is too strong - I would largely reformulate it as this depends too much on the parameters. I recommend to add instead a figure with different parameters and methods,
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depicting the mesh edges in black in addition to the shaded facets.
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depicting the mesh edges in black in addition to the shaded facets.
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MC does not preserve the sharp features present in the isovalue of the input scalar field
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Furthermore, MC does not preserve the sharp features present in the isovalue of the input scalar field
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(see \cgalFigureRef{IsosurfacingMCDC}).
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(see \cgalFigureRef{IsosurfacingMCDC}).
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\subsection SubSecTMC Topologically Correct Marching Cubes (TMC)
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\subsection SubSecTMC Topologically Correct Marching Cubes (TMC)
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@ -220,7 +222,7 @@ Both these domain models are equipped with template parameters enabling the user
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A few classes are provided by default, such as `CGAL::Isosurfacing::Value_function_3` and
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A few classes are provided by default, such as `CGAL::Isosurfacing::Value_function_3` and
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`CGAL::Isosurfacing::Interpolated_discrete_values_3`. Users can provide their own value class,
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`CGAL::Isosurfacing::Interpolated_discrete_values_3`. Users can provide their own value class,
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provided it meets the requirements described by the concept `IsosurfacingValueField_3`.
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provided it meets the requirements described by the concept `IsosurfacingValueField_3`.
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- <b>GradientField (`Dual_contouring_domain_3` only):</b> this must be a class that provides the gradient
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- <b>GradientField:</b> (`CGAL::Isosurfacing::Dual_contouring_domain_3` only) this must be a class that provides the gradient
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of the scalar field at the vertices of the partition.
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of the scalar field at the vertices of the partition.
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A few classes are provided by default, such as
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A few classes are provided by default, such as
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`CGAL::Isosurfacing::Finite_difference_gradient_3` and
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`CGAL::Isosurfacing::Finite_difference_gradient_3` and
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@ -29,7 +29,7 @@ namespace Isosurfacing {
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* \brief A domain that can be used as input in the %Dual Contouring algorithm.
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* \brief A domain that can be used as input in the %Dual Contouring algorithm.
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*
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*
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* \details This class is essentially a wrapper around the different bricks provided by its
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* \details This class is essentially a wrapper around the different bricks provided by its
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* template parameters: `Partition` provides the spacial partitioning, `ValueField` and `GradientField`
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* template parameters: `Partition` provides the spatial partitioning, `ValueField` and `GradientField`
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* the values and gradients that define the isosurface. The optional template parameter
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* the values and gradients that define the isosurface. The optional template parameter
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* `EdgeIntersectionOracle` gives control over the method used to compute edge-isosurface intersection points.
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* `EdgeIntersectionOracle` gives control over the method used to compute edge-isosurface intersection points.
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*
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*
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@ -29,7 +29,7 @@ namespace Isosurfacing {
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* \brief A domain that can be used with the Marching Cubes algorithm.
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* \brief A domain that can be used with the Marching Cubes algorithm.
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*
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*
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* \details This class is essentially wrapper around the different bricks provided by its
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* \details This class is essentially wrapper around the different bricks provided by its
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* template parameters: `Partition` provides the spacial partitioning, `ValueField`
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* template parameters: `Partition` provides the spatial partitioning, `ValueField`
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* the values that define the isosurface. The optional template parameter
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* the values that define the isosurface. The optional template parameter
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* `EdgeIntersectionOracle` gives control over the method used to compute edge-isosurface intersection points.
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* `EdgeIntersectionOracle` gives control over the method used to compute edge-isosurface intersection points.
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*
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*
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@ -37,7 +37,7 @@ namespace Isosurfacing {
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* \tparam ValueField must be a model of `IsosurfacingValueField_3`
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* \tparam ValueField must be a model of `IsosurfacingValueField_3`
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* \tparam EdgeIntersectionOracle must be a model of `IsosurfacingEdgeIntersectionOracle_3`
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* \tparam EdgeIntersectionOracle must be a model of `IsosurfacingEdgeIntersectionOracle_3`
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*
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*
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* \sa `CGAL::Isosurfacing::marching_cubes_3()`
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* \sa `CGAL::Isosurfacing::marching_cubes()`
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* \sa `CGAL::Isosurfacing::Dual_contouring_domain_3`
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* \sa `CGAL::Isosurfacing::Dual_contouring_domain_3`
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*/
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*/
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template <typename Partition,
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template <typename Partition,
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@ -41,7 +41,7 @@ namespace Isosurfacing {
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* and `BackInsertionSequence` whose value type is `std::size_t`.
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* and `BackInsertionSequence` whose value type is `std::size_t`.
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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*
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* \param domain the domain providing the spacial partition and the values and gradient data
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* \param domain the domain providing the spatial partition and the values and gradient data
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* \param isovalue the value defining the isosurface
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* \param isovalue the value defining the isosurface
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* \param points the points of the polygons in the created polygon soup
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* \param points the points of the polygons in the created polygon soup
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* \param polygons each element in the vector describes a polygon using the indices of the points in `points`
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* \param polygons each element in the vector describes a polygon using the indices of the points in `points`
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@ -39,7 +39,7 @@ namespace Isosurfacing {
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* and `BackInsertionSequence` whose value type is `std::size_t`.
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* and `BackInsertionSequence` whose value type is `std::size_t`.
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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* \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
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*
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*
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* \param domain the domain providing the spacial partition and the data
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* \param domain the domain providing the spatial partition and the data
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* \param isovalue the value defining the isosurface
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* \param isovalue the value defining the isosurface
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* \param points the points of the triangles in the created indexed face set
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* \param points the points of the triangles in the created indexed face set
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* \param triangles each element in the vector describes a triangle using the indices of the points in `points`
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* \param triangles each element in the vector describes a triangle using the indices of the points in `points`
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