DESBRUN M.: Anisotropic polygonal remeshing

Figure 1: From an input triangulated geometry, the curvature tensor eld is estimated, then smoothed, and its umbilics are deduced (colored dots). Lines of curvatures (following the principal directions) are then traced on the surface, with a local density guided by the principal curvatures, while usual point-sampling is used near umbilic points (spherical regions). The nal mesh is nally extracted by subsampling, and conforming-edge insertion. The result is an anisotropic mesh, with elongated quads aligned to the original principal directions, and triangles in isotropic regions. Such an anisotropy-based placement of the edges and cells makes for a very efcient and high-quality description of the geometry. A smooth surface can be obtained by quad/triangle subdivision of the newly generated model. In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of nat-ural or man-made geometry. In particular, we use curvature direc-tions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. Af-ter extracting and smoothing the curvature tensor eld 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 point-sampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly com-posed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the exibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted