Toward the Effective Use of Geometrically Continuous Techniques

这项研究涉及计算和基础 数学，曲线和曲面的属性， 几何连续性而不是参数连续性。 几何 连续实体可以通过各种启发式“形状”来控制 功能”，并可能被证明更适合计算机辅助设计 而不是参数连续实体。 计算知识 建立和保持几何连续性的技术， 稀疏，主要局限于三次Beta样条曲线。 这 研究将集中在Beta样条曲线和三角Beta样条 表面的任意多项式阶，并将寻求（1）发展 评估算法，以及（2）对形状函数进行编目和分类， 在CAD中使用

This research deals with the computational, and underlying mathematical, properties of curves and surfaces that exhibit geometrical rather than parametric continuity. Geometrically continuous entites are controllable through various heuristic "shape functions" and may prove to be more suitable for computer-aided design than parametrically continuous entities. Knowledge about computational techniques for establishing and preserving geometric continuity is sparse, and is confined mainly to cubic Beta-spline curves. This research will focus on Beta-spline curves and triangular Beta-spline surfaces of arbitrary polynomial order, and will seek to (1) develop evaluation algorithms, and (2) catalog and classify shape functions for use in CAD.