Physical Sciences and Mathematics Commons^™

The Algebra And Geometry Of Curve And Surface Inversion, Thomas W. Sederberg, Eng-Wee Chionh, Kent Ridge

Faculty Publications

An inversion equation takes the Cartesian coordinates of a point on a parametric curve or surface and returns the parameter value(s) of that point. A 2-D curve inversion equation has the form t = f(x,y)/g(x,y). This paper shows that practical insight into inversion can be obtained by studying the geometry of the implicit curves f(x,y) = 0 and g(x,y) = 0. For example, the relationship between the singular locus of the parametric curve and the lowest possible degree of an inversion equation can be understood in this way. Also, insight is given into what parameter value will be returned if …