Geometrical, topological and perceptual analysis of 3D meshes

Geometry

Regular Centroidal Voronoi tessellations

We advocate the use of a regularity criterion to evaluate the quality of Centroidal Voronoi tessellations (CVTs). We propose a hierarchical algorithm that constructs more regular 3D CVTs than related work. We also propose an algorithm to compute CVTs from implicit volumetric forms and show that the resulting CVTs better approximate the input shape than voxel grids bounded with Marching Cubes or Delaunay tetrahedrizations, for a variety of criteria.

Mesh repair with interactive topology control

We propose an algorithm to transform any kind of mesh (a triangle soup, for instance) into a 2-manifold, with an interactive control of the topology.

Constriction computation on triangulated surfaces

Constrictions are locally shortest closed curves. Automatic detection of these curves can be of great interest for several applications in the area of surface understanding. I have developed several algorithms to do this. I have also investigated (not very successfully) their relation with the surface's local geometry (e.g., curvatures).

Topology

Computation of the homology of simplicial complexes

We propose an algorithm to compute the homology groups (of any dimension) of simplicial complexes. Our method is based on the theory of constructive homology.

Classification of non-manifold singularities in 3D models

This work aims at classifying possible topological singularities discarding a simplicial complex mesh to be a manifold.

Topological quadrangulation of 3D shapes

We propose a topological decomposition of a 3D shape (represented as a triangular mesh) into quadrangles.

Visual perception

Just-noticeable distortion profile for meshes

We analyse how much vertices of a mesh can move without the human eye to notice.