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Event(s) on August 2007


  • Friday, 3rd August, 2007

    Title: Surface Approximation by MLS – Review and Recent Developments
    Speaker: Prof. David Levin, School of Mathematical Sciences, Tel Aviv University, Israel
    Time/Place: 11:00  -  12:00
    FSC 1217
    Abstract: A basic projection strategy for surface approximation is presented and discussed. The projection is based upon the 'Moving-Least-Squares' (MLS) approach, and the resulting surface is C^∞ smooth. The projection involves a first stage of defining a local reference domain and a second stage of constructing an MLS approximation with respect to the reference domain. The general approach is presented for the problem of approximating a (d - 1)-dimensional manifold in R^d, d ≥ 2. The application for surface approximation in R^3 yields a C^∞ surface, interpolating or smoothing the data, which is mesh-independent. For example, the resulting surface is independent upon the triangulation chosen for its parametrization. In a recent work with Yaron Lipman and Danny Cohen-Or we have consider the problem of approximating surfaces with sharp features. The new method builds on the MLS projection methodology, but introduces a fundamental modification: While the classical MLS uses a fixed approximation space, i.e., polynomials of a certain degree, the new method is data-dependent. For each projected point, it finds a proper local approximation space of piecewise polynomials (splines). The locally constructed spline encapsulates the local singularities which may exist in the data. The optional singularity for this local approximation space is modeled via a Singularity Indicator Field (SIF) which is computed over the input data points. The effectiveness of the method is demonstrated by reconstructing surfaces from real scanned 3D data, while being faithful to their most delicate features.