An Investigation on Surface-to-Surface Intersection Problems

本工作的目的是研究一种新的方法， 发现并描述未知代数曲线的所有特征 导致表面与表面相交的情况。 我们 方法涉及曲线方程的符号推导， 使用代数几何技术，及其在 矩形窗口内的伯恩斯坦基，它允许分段 表示，并提供几何意义， 基本系数 新的方法来计算 曲线的特征点，用于保证正确的 拓扑结构，提出。 它们基于符号计算， 大规模系列求和的自适应方法，以增强 精确度和最小化技术。 对曲线的质疑， 基于非均匀自适应细分， 和隐曲线的参数近似， 距离误差，基于伯恩斯坦的性质 代表性，也提出了研究。 的意义 拟议的工作是，它承诺提供一个强大的表面， 表面相交能力，这是必要的， 设计、分析和制造的自动化模式 藏物 我们的技术的许多元素也是可并行的 这是真实的时间大尺度的一个重要属性 应用.

The objective of this work is to investigate a new method to discover and describe all features of an unknown algebraic curve resulting in the context of surface to surface intersections. Our method involves symbolic derivation of the equation of the curve, using algebraic geometry techniques, and its representation in the Bernstein basis within a rectangular window, which allows piecewise representation and provides geometrical significance to the underlying coefficients. Novel methods to compute the characteristic points of the curve, useful in guaranteeing correct topology, are proposed. These are based on symbolic computation, adaptive methods for large scale series summation, to enhance accuracy, and minimization techniques. Interrogation of the curve, based on non-uniform adaptive subdivision, and derivation of point and parametric approximations of the implicit curve, with prescribed distance errors, based on the properties of the Bernstein representation, are also proposed for study. The significance of the proposed work is that it promises to provide a robust surface to surface intersection capability, which is necessary in a more automated mode of design, analysis and manufacturing of complex artifacts. Many elements of our technique are also parallelizable which is an important attribute for real time large scale applications.