Tracing surface intersections

被引：135

作者：

Bajaj, C.L. ^{[1
]}

Hoffmann, C.M. ^{[1
]}

Lynch, R.E. ^{[1
]}

Hopcroft, J.E.H. ^{[1
]}

机构：

[1] Purdue Univ, United States

来源：

Computer Aided Geometric Design | 1988年 / 5卷 / 04期

基金：

美国国家科学基金会;

关键词：

Computer Graphics - Mathematical Techniques - Geometry - Surfaces;

D O I：

10.1016/0167-8396(88)90010-6

中图分类号：

学科分类号：

摘要：

We consider the problem of tracing the intersection of surfaces given either implicitly or parametrically. We give a numerical tracing procedure in which a third-order Taylor approximant is constructed for taking steps of variable length, and the points so found are improved by Newton iteration. We show how this construction relates to local parameterizations of the curve at singularities, and discuss our experience with the method. For plane curves, given implicitly, we show how desingularization techniques can be incorporated to trace correctly through all types of singularities. An implementation of this method is also discussed.

引用

页码：285 / 307