Convex hulls of algebraic curves

David J. Kriegman; Erliang Yeh; Jean Ponce

doi:10.1117/12.131738

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1 November 1992 Convex hulls of algebraic curves

David J. Kriegman, Erliang Yeh, Jean Ponce

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Proceedings Volume 1830, Curves and Surfaces in Computer Vision and Graphics III; (1992) https://doi.org/10.1117/12.131738
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

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) equals 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.

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David J. Kriegman, Erliang Yeh, and Jean Ponce "Convex hulls of algebraic curves", Proc. SPIE 1830, Curves and Surfaces in Computer Vision and Graphics III, (1 November 1992); https://doi.org/10.1117/12.131738

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