修剪曲面在相交边界处的水密化处理
Watertightization of Trimmed Surfaces at Intersection Boundary
AI总结：
本文提出一种针对CAD中修剪曲面的水密化技术，通过重参数化将其转换为标准参数域内的Bezier曲面片并用相交曲线替换边界，消除相交边界处的间隙或重叠，从而弥合CAD与CAE之间的间隙。
摘要：
本文介绍了一种处理CAD中曲面与曲面相交边界表示的水密化技术。曲面在当今的几何设计中扮演着重要角色。非均匀有理B样条曲面（NURBS）的数学模型是主流且为ISO标准。在曲面与曲面相交的情况下，情况有些复杂，因为曲面的某些部分可能被切掉，从而出现所谓的修剪曲面，这是过去几十年CAD学术界和工业界的核心课题。主要问题是修剪曲面的参数域通常不是标准的正方形或矩形，而是典型地由曲线界定，这些曲线基于交点的点逆映射并进行插值。相交边界处间隙或重叠的存在使得CAE和其他下游应用的预处理变得困难。在这种情况下，NURBS难以保持闭合形式。通常，必须附加特殊的相交曲线数据结构以支持下游应用，而整个CAD系统的数据结构并不统一，计算效率也不高。针对作为NURBS特例的Bezier曲面，本文设计了一种重参数化或归一化方法，将修剪曲面转换为一组位于标准参数域[0,1]X[0,1]中的Bezier曲面片。然后，可以用相交曲线替换归一化Bezier曲面片的边界曲线，从而实现沿边界的水密化。通过这种方式，修剪曲面被消除，CAD与CAE之间的“间隙”被弥合。
英文摘要：
This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational B-spline surfaces (NURBS) is the mainstream and ISO standard. In the situation of surface-surface intersection, things are a little complicated, for some parts of surfaces may be cut-off, so called trimmed surfaces occur, which is the central topic in the past decades in CAD community of both academia and industry. The main problem is that the parametric domain of the trimmed surface generally is not the standard square or rectangle, and rather, typically, bounded by curves, based on point inverse of the intersection points and interpolated. The existence of gaps or overlaps at the intersection boundary makes hard the preprocessing of CAE and other downstream applications. The NURBS are in this case hard to keep a closed form. In common, a special data structure of intersection curves must be affiliated to support downstream applications, while the data structure of the whole CAD system is not unified, and the calculation is not efficient. In terms of Bezier surface, a special case of NURBS, this paper designs a reparameterization or normalization to transform the trimmed surface into a group of Bezier surface patches in standard parametric domain [0,1]X[0,1]. And then the boundary curve of normalized Bezier surface patch can be replaced by the intersection curve to realize watertight along the boundary. In this way, the trimmed surface is wiped out, the "gap" between CAD and CAE is closed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
