曲面形状调配与形式化简的算法研究

Based on this research, in the aspect of shape blending, a geometric continuity-preserving method in shape blending for parametric curves is given. Some characteristics of developable Bézier function surfaces are detected. Affine arithmetic is introduced into algebraic curve drawing so that its effect and efficiency are better than interval arithmetic. Above three mathematical models for shape blending give some new tools for CAD. In the aspect of surface form simplification, we have put forward the idea to convert Bézier surface into Wang-Ball surface for evaluating, thus a very troubled problem for computing in systems can be solved；we have made a theoretical breakthrough, i.e., multi-degree reduction and corners interpolation for surfaces can be implemented at the same time, and the precision of degree reduction is very high；Also, applying Liu-hui's cutting circle method we have reduced the degree of offset approximated curves so that degree of that one by former methods is three times than degree of this one；Furthermore, we made high order H-interpolation for PH curves by using complex analysis, have invented new algorithms for the boundary of interval Bézier curves and for the approximated interval Bézier surfaces, and have given the relationship between the H & h approximations of rational surfaces, have obtained their convergence conditions. All above results will extensively apply to data commutation and data transition, and obviously elevate the speed, the quality and the efficiency of CAD systems.

研究基于活动局部球面坐标插值的一整套曲面形状调配算法，包括调配曲面几何连续条件，自交防范，模块集成和对于带尖点尖边的多种形式的细分曲面调配算法；同时，研究对有理参数曲面及其求导求积的降阶逼近、多项式逼近、隐式逼近以及对任意拓扑网格的细分逼近中的优化算法、收敛条件、误差估计，把我国动画制作和工业造型提到更新更高的水平。