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Adaptive geometry compression based on four-point interpolatory subdivision schemes with labels

Hui Zhang 1 Jun-Hai Yong 1 Jean-Claude Paul 1
1 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : We propose an adaptive geometry compression method with labels based on four-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a four-point subdivision curve with a subdivision step. Labels are recorded in data compression to facilitate merging the segments in data decompression. We provide high-speed four-point interpolatory subdivision curve generation methods for efficiently decompressing the compressed data. For an arbitrary positive integer k, formulae for the number of resultant control points of a four-point subdivision curve after k subdivision steps are provided. Some formulae for calculating points at the kth subdivision step are also presented. The time complexity of the new approaches is O(n), where n is the number of points in the given digital curve. Examples are provided to illustrate the efficiency of the proposed approaches.
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Submitted on : Thursday, January 3, 2008 - 12:28:33 PM
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Hui Zhang, Jun-Hai Yong, Jean-Claude Paul. Adaptive geometry compression based on four-point interpolatory subdivision schemes with labels. International Journal of Computer Mathematics, Taylor & Francis, 2007, 84 (9), pp.1353-1365. ⟨10.1080/00207160701242276⟩. ⟨inria-00201857⟩



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