Geodesic Remeshing Using Front Propagation [PDF]
Gabriel Peyré and Laurent Cohen
Proc. VLSM'03, Sept. 2003

Remaillage géodésique par propagation de fronts [PDF]
Gabriel Peyré and Laurent Cohen
Proc. RFIA'04, Jan. 2004

Abstract: In this paper, we present a method for remeshing triangulated manifolds by using geodesic path calculations and distance maps. Our work builds on the Fast Marching algorithm which has been extended to arbitrary meshes by Sethian and Kimmel. First, a set of points that are evenly spaced across the surface is automatically found. A geodesic Delaunay triangulation of the set of points is then created, using a Voronoi diagram construction based on Fast Marching. At last, we use the distance information to find a simple parameterization of the manifold. Marching algorithm makes this method computationally inexpensive, and gives very good results. Examples are shown for synthetic and real surfaces.

Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization [Web]
Progress in Nonlinear Differential Equations and Their Applications, Vol. 63, 157–171, 2005
Gabriel Peyré and Laurent Cohen

Abstract: In this paper, we propose a fast and accurate algorithm to flatten a genus-0 triangulated manifold. This method naturally fits into a framework for 3D geometry modelling and processing that uses only fast geodesic computations. These techniques are gathered and extended from classical areas such as image processing or statistical perceptual learning. Using the FastMarching algorithm, we are able to recast these powerful tools in the language of mesh processing. Thanks to some classical geodesic-based building blocks, we are able to derive a flattening method that exhibit a conservation of local structures of the surface.
On large meshes (more than 500,000 vertices), our techniques speed up computation by over one order of magnitude in comparison to classical remeshing and parameterization methods. Our methods are easy to implement and do not need multilevel solvers to handle complex models that may contain poorly shaped triangles.

Surface Segmentation Using Geodesic Centroidal Tesselation [PDF]
Gabriel Peyré and Laurent Cohen
Proc. 3DPVT'04

Abstract: In this paper, we solve the problem of mesh partition using intrinsic computations on the 3D surface. The key concept is the notion of centroidal tesselation that is widely used in an eucidan settings. Using the Fast Marching algorithm, we are able to recast this powerful tool in the language of mesh processing. This method naturally fits into a framework for 3D geometry modelling and processing that uses only fast geodesic computations. With the use of classical geodesic-based building blocks, we are able to take into account any available information or requirement such as a 2D texture or the curvature of the surface.

Démo of geodesic computations [ZIP].
This demo shows the Fast Marching algorithm, and its application to the computation of geodesic paths.
You must also download models.zip.

Démo of remeshing [ZIP].
This demo shows the greedy "farthest point" sampling algorihtm, and its application to adaptive remeshing.
You must also download models.zip.

3D models [ZIP].
You must unzip the demo file under the same directory as models.zip.
You should have 3 sub-directories test_geodesic/, test_remeshing/ and models/.
The David is not included because it is copyrighted.

Geowave library
This library contains source code to perform geodesic computation on 3D meshes.
Please use the CVS anonymous access to retrieve the cource code.