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Adaptive geometry compression based on 4-point interpolatory subdivision schemes with labels

Hui Zhang 1 Jun-Hai Yong 1 Jean-Claude Paul 2
2 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 4-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 di®erent compression levels. Each segment is a 4-point subdivision curve with a subdivision step. Labels are recorded in data compression to facilitate merging those segments in data decompression. In the meantime, we provide high-speed 4-point interpolatory subdivision curve generation methods for e±ciently decompressing the compressed data. For an arbitrary positive integer k, formulae of the number of the resultant control points of a 4-point subdivision curve after k subdivision steps are provided. Some formulae for calculating points at the kth ubdivision step are presented as well. The time complexity of the new approaches is O(n), where n is the number of the points in the given digital curve. Examples are provided as well to illustrate the efficiency of the proposed approaches.
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Hui Zhang, Jun-Hai Yong, Jean-Claude Paul. Adaptive geometry compression based on 4-point interpolatory subdivision schemes with labels. International Journal of Computer Mathematics, Taylor & Francis, 2007, 16p. ⟨inria-00515531⟩

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