Tailor: understanding 3D shapes using curvature

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression, and simplification of 3D shapes. Different features, such as flats, limbs, tips, pits, and various blending shapes that transition between them may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in the surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. For example, for a thin limb, that intersection will start simply connected and will rapidly split into two components. For a point on the tip of a limb, that intersection will usually simply remain connected, but the ratio of its length to the radius of the bubble will be decreasing. For a point on a blend, that ratio will exceed 2p. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated f i lters, that may capture the needs of a particular application