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simplify reconstruction description

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Sébastien Loriot 2014-10-24 13:59:57 +02:00
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Scale_space_reconstruction_3/doc/Scale_space_reconstruction_3/Scale_space_reconstruction_3.txt
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@ -89,7 +89,7 @@ The neighborhood size is estimated using `Orthogonal_k_neighbor_search`. The poi
The scale-space is constructed at the original scale of the points. An iteration of increasing the the scale is computed using a weighted PCA procedure. By default we use the efficient \ref thirdpartyEigen libraries for this procedure. It is also possible to provide your own model for the `WeightedApproximation_3` concept and provide it as a template parameter. The PCA procedure is performed locally per point, so it can performed with parallel computing if both Intel TBB is linked and the `Ct` template parameter is set to `Parallel_tag`. The scale-space is constructed at the original scale of the points. An iteration of increasing the the scale is computed using a weighted PCA procedure. By default we use the efficient \ref thirdpartyEigen libraries for this procedure. It is also possible to provide your own model for the `WeightedApproximation_3` concept and provide it as a template parameter. The PCA procedure is performed locally per point, so it can performed with parallel computing if both Intel TBB is linked and the `Ct` template parameter is set to `Parallel_tag`.
The mesh reconstruction is performed by filtering an `Alpha_shape_3` or `Fixed_alpha_shape_3` of the point set at a fixed scale. Which shape is used is captured in the `FS` template parameter of `Scale_space_surface_reconstruction_3`. This filtering constructs a triangle for each regular facet of the \f$ \alpha \f$-shape; each singular facet results in two triangles facing opposite directions. If the `Sh` is set to `Tag_true`, these triangles are ordered per oriented connected component. The mesh reconstruction is performed by filtering a \ref Chapter_3D_Alpha_Shapes "3D alpha-shape" of the point set at a fixed scale. This filtering constructs a triangle for each regular facet; each singular facet results in two triangles facing opposite directions. If the `Sh` is set to `Tag_true`, these triangles are ordered per oriented connected component.
The resulting surface is stored as a collection of triples. Each triple contains three indices to the point set. The scale iterations do not change the order of the points. This means these indices can be applied on the point set at its original scale to get an interpolating surface, called \em reverting the scale of the surface. The indices may also be applied to the point set at the current scale to get a smoothed surface. This smoothed surface will generally have shrunk somewhat compared to the reverted surface. The resulting surface is stored as a collection of triples. Each triple contains three indices to the point set. The scale iterations do not change the order of the points. This means these indices can be applied on the point set at its original scale to get an interpolating surface, called \em reverting the scale of the surface. The indices may also be applied to the point set at the current scale to get a smoothed surface. This smoothed surface will generally have shrunk somewhat compared to the reverted surface.