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

这一美洲项目奖将支持印第安纳大学的理查德·帕特森与委内瑞拉中央大学的马尔科·帕鲁兹尼合作。研究人员打算合作开发算法，在计算机辅助几何设计中使用隐式定义的三次曲线。基本上有两种方法来描述平面中的曲线：使用参数化或隐式方程。计算机辅助设计中使用的参数化用多项式或有理函数来定义，它们提供了几个优点，包括易于作图和存在各种控制它们的方法。然而，在计算机辅助几何建模中使用隐式方程可以获得很多东西，包括参照曲线定位点。此外，与参数曲线相比，隐式曲线的使用还处于初级阶段，因此，在这一问题上仍有许多工作要做。合作者为这一主题带来了互补的方法和专门知识，这项工作有可能做出重要贡献，特别是在数值/计算建模领域。

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.