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

作者：Zhang Hui^*; Yong Jun Hai; Paul Jean Claude

来源：International Journal of Computer Mathematics, 2007, 84(9): 1353-1365.

DOI：10.1080/00207160701242276

• geometry compression
• Subdivision scheme
• four-point subdivision
• interpolatory subdivision
• high-speed curve generation

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.

• 出版日期2007
• 单位清华大学