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Now showing 1 - 3 of 3
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    Orthogonal Decomposition of Non-Uniform Bspline Spaces using Wavelets
    (Blackwell Publishers Ltd and the Eurographics Association, 1997) Kazinnik, Roman; Elber, Gershon
    We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniform Bspline (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions.Applying Multiresolution decomposition to possibly C1 discontinuous surfaces, one can preserve the general shape on one hand and local features on the other of the free-form models, including geometric discontinuities. The Multiresolution decomposition of the NUB tensor product surface is computed via the symbolic computation of inner products of Bspline basis functions. To find a closed form representation for the inner product of the Bspline basis functions, an equivalent interpolation problem is solved.As an example for the strength of the Multiresolution decomposition, a tool demonstrating the Multiresolution editing capabilities of NUB surfaces was developed and is presented as part of this work, allowing interactive 3D editing of NUB free-form surfaces.
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    Symbolic and Numeric Computation in Curve Interrogation
    (Blackwell Science Ltd and the Eurographics Association, 1995) Elber, Gershon
    The control of shape of curves is of great importance in computer aided geometric design. Determination of planar curves convexity, the detection of infection points, coincident regions, and self intersection points, the enclosed area of a closed curve, and the locations of extreme curvature are importantfeatures of curves that can affect the design, in modelling environments.In this paper, we investigate the ability to robustly answer the above queries and related questions using an approach which exploits both symbolic computation and numeric analysis.
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    Isometric Texture Mapping for Free-form Surfaces
    (Blackwell Publishers Ltd and the Eurographics Association, 1997) Arad, Nur; Elber, Gershon
    Texture mapping is a frequently exploited technique in computer graphics aimed at the emulation of high-resolution details in surfaces. In this paper we present a distance-ratios preservation method for bivariate raster texture mapping to free-form surfaces in an arbitrarily precise manner. The proposed method reduces the original general problem of computing the inverse of a three-dimensional parametric surface mapping into a problem of two-dimensional image warping. Several examples that demonstrate the proposed approach are also provided.