Constrained Design, Streamline Modeling, Automatic Fairing and Automatic Joining Techniques for Non-Uniform Rational B-Spline (NURBS) Surfaces

本研究提出发展先进的非均匀有理B样条（NURBS）曲面造型技术，以解决四个计算机辅助设计（CAD）问题：（1）受约束的曲面设计，（2）使用流线造型方法的曲面设计，（3）自动曲面光顺，（4）曲面的自动连接。目标是开发新的和有效的技术，能够（1）创建连续的一阶导数光滑表面（或切线方向）和规定的形状属性（例如规定的形状范围、凸度和有界曲率），（2）通过操纵切向量而不是控制点来执行实时表面设计，（3）自动检测并去除给定表面的光顺模型上的表面不规则;（4）执行平滑的自动n边间接或直接连接，其中n大于或等于2。 第一个主题的结果将提供广泛的设计和建模社区的形状生成技术，不仅可以控制的形状范围，但也凸度和曲率分布，因此，提供了一个机会，以解决在表面开发阶段的可制造性问题。 第二个主题的结果将提供一个交互式的表面设计技术，允许直接操纵表面曲率和曲率的变化设计工程师。第三和第四个主题的结果将显着缩短曲面光顺和连接过程，因此，使CAD更积极和有效的产品开发过程。总的来说，这项研究的结果将有助于减少产品开发过程的成本和周期时间。

The research proposes to develop advanced Non-Uniform Rational B-Spline (NURBS) surface modeling techniques to solve four computer aided design (CAD) problems: (1) constrained surface design, (2) surface design using the streamline modeling methodology, (3) automatic surface fairing, and (4) automatic joining of surfaces. The goal is aiming at developing new and efficient techniques that are capable of (1) creating smooth surfaces with continuous first derivative (or tangent direction) and prescribed shape properties (such as prescribed shape ranges, convexity, and bounded curvature), (2) performing real-time surface design by manipulating tangent vectors instead of control points, (3) detecting and removing surface irregularities on a fairness model of the given surface automatically, and (4) performing smooth, automatic n-sided indirect or direct joining with n bigger than or equal to 2. Results on the first topic will provide the broad design and modeling community a shape generation technique that can be controlled not only in shape ranges, but also convexity and curvature distribution and, hence, provide an opportunity to address the manufacturability issues in the surface development stage. Results on the second topic will provide design engineers with an interactive surface design technique that allows direct manipulation of surface curvature and variation of curvature. Results on the third and forth topics will significantly shorten the surface fairing and joining processes and, consequently, make CAD more proactive and effective in the product development process. Overall, results of this research will help reduce both the cost and cycle time of the product development process.