Symbolic and Numeric Computation in Curve Interrogation

Abstract

The control of shape of curves is of great importance in computer aided geometric design. Determination of planar curves convexity, the detection of infection points, coincident regions, and self intersection points, the enclosed area of a closed curve, and the locations of extreme curvature are importantfeatures of curves that can affect the design, in modelling environments.In this paper, we investigate the ability to robustly answer the above queries and related questions using an approach which exploits both symbolic computation and numeric analysis.