U.S.-Venezuela Cooperative Research: Implicit Curves for Geometric Modeling

这个美洲计划奖将支持理查德 印第安纳州大学的帕特森与 与中央大学的Marco Paluszny合作， 委内瑞拉 研究人员打算合作 在算法的发展上， 计算机辅助的隐式定义的三次曲线 几何设计 基本上有两种方法来描述曲线 在平面中：使用参数化或 隐式方程中使用的参数化 计算机辅助设计的定义是 多项式或有理函数，它们 提供了几个优点，包括易于 图表和各种方法的存在， 控制他们。 然而， 通过使用隐式方程， 计算机辅助几何建模，包括 参考点的定位 曲线 此外，隐式曲线的使用是 与参数化相比， 曲线，因此，还有很多工作要做。 在这个问题上做。 合作者带来了 主题补充方法和专业知识， 这项工作有可能成为 重要贡献，特别是在 数值/计算建模。

This Americas Program award will support Richard Patterson of Indiana University in collaboration with Marco Paluszny of the Universidad Central de Venezuela. The researchers intend to collaborate on the development of algorithms to use implicitly defined cubic curves in computer-aided geometric design. There are essentially two ways to describe curves in the plane: with a parametrization or an implicit equation. The parametrizations used in computer-aided design are defined either by polynomials or by rational functions and they offer several advantages, including ease of graphing and the existence of various methods to control them. However, there is much to be gained by the use of implicit equations in computer-aided geometric modeling, including the localization of points with reference to the curve. Moreover, the use of implicit curves is in its infancy in comparison with parametric curves and, consequently, much work remains to be done on the subject. The collaborators bring to the topic complementary approaches and expertise, and the work has the potential to make an important contribution, particularly in the area of numerical/computational modeling.