Presidential Young Investigator Award: Loop Detection in Surface Patch Intersections

这位总统青年研究员在几何学方面的研究 建模集中在四个方面：曲面片相交，立方体 代数曲面片，局部曲面隐式化， 代数曲线的近似参数化 对于曲面片 交叉口，他计划继续计算曲线的工作， 两个参数曲面片的交集。 他已经 找到了一种方法来确定是否有任何封闭的循环， 交叉曲线和平面图制定一般交叉口 算法，利用这个循环测试。 在三次代数曲面片中，他计划研究 三阶代数曲面片建模方法。 以前的工作证明，它们可以用C1拼接在一起 连续性，并且可以对其施加合理的参数化 他们 他正致力于创造计算机环境， 塑造他们。 局部表面隐式化的问题涉及发现 一个参数曲面片可以被一个 提出了一种低次隐式曲面生成算法， 计算这些表面。 例如，双三次曲面片通常具有 一个18次的隐式方程，但希望大多数双三次方程 可以用四度或五度表面来近似贴片。 最后，可以找到一个精确的隐式方程， 参数曲线，但反之则不然。 塞德伯格教授 正致力于开发一种算法， 有理三次曲线到代数曲线。

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.