New Computation Techniques for Shape Modeling and Design

9400823程造型和设计技术将得到拓展和提高。将开发将内插法和近似法结合为单一过程(称为邻近法)的计算技术。这里将考虑的曲线和曲面表示包括B样条线、NURBS、Beta样条线和有理Beta样条线。本课程将研究构造多项式(积分)和有理B-样条曲线曲面的不同方法，以及它们作为数字滤波器时的性质。建立了设计和造型过程中参数曲面相交形成的尖角和尖边自动光顺的通用模型。这项工作还将包括用n3的n边面片填充n边孔。将开发一个通用的模型，用于不相交的参数曲面的自动光滑连接。形状建模和设计的计算技术正在迅速成为现代工业设计和制造的重要工具。计算机模型正在取代物理模型。它们的构建成本更低，更改更容易，分析也更简单。计算机生成的图像可以在设计过程中实现快速准确的可视化，从而提高工作效率。应用包括设计和制造汽车车身、船体、飞机机翼和机械部件以及各种管道、混合物和圆角。许多重要的开放的理论和实践问题需要探索，为工业设计提供有效的工具。

9400823 Cheng The techniques of shape modeling and design will be broadened and improved. Computation techniques that combine interpolation and approximation into a single process (called interproximation) will be developed. The curve and surface representations that will be considered here include B-splines, NURBS, Beta-splines and rational Beta-splines. Different ways of building polynomial (integral) and rational B-spline curves and surfaces as well as their properties when viewed as digital filters will be studied. A general model for the automatic smoothing of sharp corners and edges formed by intersecting parametric surfaces in the design and modeling process will be built. This work will also include filling an n-sided hole with an n-sided patch with n 3. A general model will be developed for the automatic smooth connection of disjoint parametric surfaces. Computational techniques for shape modeling and design are rapidly becoming important tools for modern industrial design and manufacture. Computer models are replacing physical models. They are cheaper to construct, easier to change, and simpler to analyze. Computer-generated images increase productivity by allowing rapid and accurate visualization during design. Applications include the design and manufacture of car bodies, ship hulls, airplane wings, and mechanical parts as well as a large variety of ducts, blends, and fillets. Many important open theoretical and practical issues need to be explored to provide effective tools for industrial design.