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End date: 2009 × Author: Cohen-Or, Daniel × Start date: 2000 ×

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    A Part-aware Surface Metric for Shape Analysis
    (The Eurographics Association and Blackwell Publishing Ltd, 2009) Liu, Rong; Zhang, Hao; Shamir, Ariel; Cohen-Or, Daniel
    The notion of parts in a shape plays an important role in many geometry problems, including segmentation, correspondence, recognition, editing, and animation. As the fundamental geometric representation of 3D objects in computer graphics is surface-based, solutions of many such problems utilize a surface metric, a distance function defined over pairs of points on the surface, to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts: shape parts and surface metric. Specifically, we develop a surface metric that is part-aware. To encode part information at a point on a shape, we model its volumetric context - called the volumetric shape image (VSI) - inside the shape s enclosed volume, to capture relevant visibility information. We then define the part-aware metric by combining an appropriate VSI distance with geodesic distance and normal variation. We show how the volumetric view on part separation addresses certain limitations of the surface view, which relies on concavity measures over a surface as implied by the well-known minima rule. We demonstrate how the new metric can be effectively utilized in various applications including mesh segmentation, shape registration, part-aware sampling and shape retrieval.
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    Selecting Effective Occluders for Visibility Culling
    (Eurographics Association, 2000) Koltun, Vladlen; Cohen-Or, Daniel
    This paper deals with the problem of identifying effective occluders for visibility culling. The solid-angle metric is commonly used for measuring the potential significance of occluders from a single viewpoint. In this paper, we show that it does not extend properly to from-region occlusion calculations. We propose to measure the effectiveness of an occluder by means of the size of its umbra. We first present an analytic object-space algorithm to accurately compute this measure. We then define an approximation which reflects the effectiveness of an occluder, and introduce a hardware-assisted algorithm to rapidly compute it.
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    Warped Textures for UV Mapping Encoding
    (Eurographics Association, 2001) Sorkine, Olga; Cohen-Or, Daniel
    This paper introduces an implicit representation of the u; v texture mapping. Instead of using the traditional explicit u; v mapping coordinates, a non-distorted piecewise embedding of the triangular mesh is created, on which the original texture is remapped, yielding warped textures. This creates an effective atlas of the mapped triangles and provides a compact encoding of the texture mapping.