Presidential Young Investigator Award: Loop Detection in Surface Patch Intersections

点击翻译按钮获取中文摘要

This Presidential Young Investigator's research in geometric modeling focuses on four areas: surface patch intersections, cubic algebraic surface patches, local surface implicitization, and approximate parametrization of algebraic curves. For surface patch intersections, he plans to continue work on computing the curve of intersection of two parametric surface patches. He has already found a method to determine if there are any closed loops in an intersection curve and plans to develop a general intersection algorithm which takes advantage of this loop test. In cubic algebraic surface patches, he plans to investigate methods of modelling with third order algebraic surface patches. Previous work proves that they can be pieced together with C1 continuity and that a rational parametrization can be imposed on them. He is working on creating the computer environment for modelling them. The problem of local surface implicitization involves finding how closely a parametric surface patch can be approximated by an implicit surface of low degree and developing an algorithm for computing such surfaces. For example, a bicubic patch generally has an implicit equation of degree 18, but it is hoped that most bicubic patches can be approximated with a degree four or five surface. Finally, an exact implicit equation can be found for any parametric curve, but the reverse is not true. Professor Sederberg is working on developing an algorithm for fitting a piecewise rational cubic curve to an algebraic curve.