Convex Hulls of Algebraic Curves

David J. Kriegman, Erliang Yeh, and Jean Ponce


Abstract


A new algorithm based on curve tracing and decomposition techniques is presented for computing the convex hull of an algebraic curve defined implicitly by f(x,y)=0; the curve may have multiple components as well as singular points. The output is an ordered collection of line segments and sections of the curve represented by a sample point and interval bounds; this representation is suitable for rendering the convex hull by classical curve tracing techniques. Additionally, we present a point classification function for the convex hull based on Sturm sequences. Progress toward extending these results to algebraic surfaces is briefly discussed.