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Title: G1 scattered data interpolation with minimized sum of squares of principal curvatures
Authors: Azizan, Saaban
Abd R Mt Piah
Ahmad, Abdul Majid
Chang Hooi Tuang, Lawrence
Keywords: Computational geometry;Curve fitting;Interpolation;Mesh generation;Surface fitting;Computer programming
Issue Date: Jul-2005
Publisher: Institute of Electrical and Electronics Engineering (IEEE)
Citation: p.385-390
Series/Report no.: Proceedings of the International Conference on Computer Graphics, Imaging and Vision: New Trends, 2005
Abstract: One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(xi, yi), i=1,...,n} ∈ R2 over a polygonal domain and a corresponding set of real numbers {zi}i=1n, we wish to construct a surface S which has continuous varying tangent plane everywhere (G1) such that S(xi, yi) = zi. Specifically, the polynomial being considered belong to G1 quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G1 continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.
Description: Link to publisher's homepage at http://ieeexplore.ieee.org
URI: http://ieeexplore.ieee.org/xpls/abs_all.jsp?=&arnumber=1521092
ISBN: 0-7695-2392-7
Appears in Collections:Institute of Engineering Mathematics (Articles)

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