In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus-0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.

In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus-0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.

This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library Cgal.

Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or "nearly manifold". We propose here a progressive geometry compression scheme which can handle manifold models as well as "triangle soups" and 3D tetrahedral meshes. The method is lossless when the decompression is complete which is extremely important in some domains such as medical or finite element.While most existing methods enumerate the vertices of the mesh in an order depending on the connectivity, we use a kd-tree technique [8] which does not depend on the connectivity. Then we compute a compatible sequence of meshes which can be encoded using edge expansion [14] and vertex split [24]. 0 INRIA, BP 93, 06902 Sophia Antipolis cedex, France. E-mail: Firstname.Lastname@sophia.inria.fr . 1The main contributions of this paper are: the idea of using the kd-tree encoding of the geometry to drive the construction of a sequence of meshes, an improved coding of the edge expansion and vertex split since the vertices to split are implicitly defined, a prediction scheme which reduces the code for simplices incident to the split vertex, and a new generalization of the edge expansion operation to tetrahedral meshes.

Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or "nearly manifold". We propose here a progressive geometry compression scheme which can handle manifold models as well as "triangle soups" and 3D tetrahedral meshes. The method is lossless when the decompression is complete which is extremely important in some domains such as medical or finite element. While most existing methods enumerate the vertices of the mesh in an order depending on the connectivity, we use a kd-tree technique [Devillers and Gandoin 2000] which does not depend on the connectivity. Then we compute a compatible sequence of meshes which can be encoded using edge expansion [Hoppe et al. 1993] and vertex split [Popović and Hoppe 1997].The main contributions of this paper are: the idea of using the kd-tree encoding of the geometry to drive the construction of a sequence of meshes, an improved coding of the edge expansion and vertex split since the vertices to split are implicitly defined, a prediction scheme which reduces the code for simplices incident to the split vertex, and a new generalization of the edge expansion operation to tetrahedral meshes.