基于细分的几何图形算法

Subdivision surface is an important surface and method within the fields of computer graphics and geometric modeling. We have developed new rules for subdivision surface generation by extending the NURBS method, and the properties and the convergence analysis are also presented. Since subdivision surface is a kind of powerful geometric modeling tool, we present new algorithm for complex surface reconstruction by subdivsion surface. It can help to compress the data and display the surface in a multi-resolution manner. A step estimation formula is also presented to subdivide a rational curve or a rational surface. Besides for subdivision methods, new theories of mu-basis for rational curves and rational ruled surfaces are presented.

本项目研究非均匀细分算法在几何造型和图形学中的理论和实践问题。主要内容为发展各种特殊的细分规则，分析细分算法的连续性，产生高质量的细分曲面，探索细分算法与立体退型技术的集成。主要目标是发展有效、多层次、自适应的细分曲面表示与算法以支持各种实际应用的需要。它的完成将促进我国高科技的发展，也推动成国在这一领域的研究水平。