GSoC2023 - ACVD for Simplification & Remeshing

[hoskillua]

Release Management

• Affected package(s): PMP (to be separated)
• Issue: Approximated (Discrete) Centroidal Voronoi Diagrams for Simplification & Remeshing #7852
• Feature/Small Feature (if any): link Approximated Centroidal Voronoi Diagrams for Simplification & Remeshing(GSoC2023-WIP)
• current version of the doc

TODO

• remove commit introducing interpolated_corrected_curvatures.h after the merge of the gsoc2022 branch
• remove qem_metrics.h and types.h from history (for @sloriot)
• check branch size (for @sloriot)
• handle interpolated curvature update (for @sloriot)
• debug the QEM minimization implementation (for @hoskillua)
• test the other versions as possibly some cases produce bad results (for @hoskillua)
• code cleanup (especially the logic for computing energy difference on edge and moving an element for @hoskillua )
• recompute the energy after each convergence (for @hoskillua)
• add concurrency flag (optional @sloriot)
• better initialisation
• get rid of duplicated implementation (keep only qem one)

[afabri]

That means that the dependency on Eigen in the CMakeLists.txt can be removed.

[MaelRL]

Suggested change

	This method is a vertex clustering based remeshing algorithm. It is based on
	\cgalCite{cgal:vc-acvdupmc-04} and extended in \cgalCite{cgal:audette2011approach} and \cgalCite{cgal:vcp-grtmmdvd-08}.
	The function `CGAL::Polygon_mesh_processing::approximated_centroidal_Voronoi_diagram_remeshing()` takes as input a triangle mesh and
	the expected number of output vertices, and it updates the mesh with the remeshed version.
	The number of vertices in the output mesh might be larger than the input parameters if the input is not closed
	or if the budget of points provided is too low to generate a manifold output mesh.
	Note that providing an initial low number of vertices will affect the uniformity of the output triangles
	in case some extra points are added to make the output manifold. The algorithm is similar to Lloyd's algorithm
	(or k-means) where some random input vertices are picked to initialize clusters of vertices, and then clusters
	are grown to minimize a particular energy, until convergence. Upon convergence, output vertices are computed
	from the vertices of each cluster. If the input mesh contains some sharp features or corners, it is possible
	to use the quadric error metrics to either move output vertices (fast but can produce bad looking triangles),
	of to use the quadric error metrics directly in the energy formulation of each cluster (slower but produces
	better quality triangles). It is also possible to use an adaptive remeshing based on curvature.
	This remeshing algorithm uses clustering on polygonal meshes as to approximate a Centroidal Voronoi Diagram construction.
	It is inspired by the method presented in \cgalCite{cgal:vc-acvdupmc-04} and further developed in \cgalCite{cgal:audette2011approach} and \cgalCite{cgal:vcp-grtmmdvd-08}.
	The algorithm is similar to Lloyd's algorithm (or k-means) where random input vertices are picked to initialize clusters of vertices, which are then grown to minimize a particular energy, until convergence.
	Upon convergence, output vertices are computed from the vertices of each cluster.
	The function `CGAL::Polygon_mesh_processing::approximated_centroidal_Voronoi_diagram_remeshing()` takes as input a triangle mesh and an expected number of output vertices, and updates the mesh with the remeshed version.
	Note that the final vertex count may exceed the input parameter if the input mesh is not closed, or if the specified vertex budget was insufficient to generate a manifold mesh.
	In this case, the uniformity of the output triangles may be affected.
	If the input mesh contains sharp features or corners, it is possible to use quadric error metrics to either move output vertices (fast but can produce bad looking triangles), of to use quadric error metrics directly into the energy formulation of each cluster (slower but produces better quality triangles).
	Additionally, adaptive remeshing based on surface curvature is possible.

[MaelRL]

Seems like the fact that topology can change should be highlighted as it is a significant difference with other methods.

[MaelRL]

Here and at other places, the type should be VPM's value type, not GT::Point_3

[sloriot]

They are the same or I'm missing your point.

[sloriot]

/force-build:v2

[github-actions]

The documentation is built. It will be available, after a few minutes, here: https://cgal.github.io/7837/v2/Manual/index.html