Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Degree reduction of B-spline curves
Computer Aided Geometric Design
Approximate Boolean operations on free-form solids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
CIM algorithm for approximating three-dimensional polygonal curves
Journal of Computer Science and Technology
Octree-based Animated Geometry Compression
DCC '04 Proceedings of the Conference on Data Compression
Adaptive geometry compression based on 4-point interpolatory subdivision schemes
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
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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.