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.
