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ACM Transactions on Graphics (TOG), Volume 13 Issue 1, Jan. 1994

Distance approximations for rasterizing implicit curves
Gabriel Taubin
Pages: 3-42
DOI: 10.1145/174462.174531
In this article we present new algorithms for rasterizing implicit curves, i.e., curves represented as level sets of functions of two variables. Considering the pixels as square regions of the plane, a “correct” algorithm should...

Three-dimensional alpha shapes
Herbert Edelsbrunner, Ernst P. Mücke
Pages: 43-72
DOI: 10.1145/174462.156635
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose, this article introduces the...

Algorithms for intersecting parametric and algebraic curves I: simple intersections
Dinesh Manocha, James Demmel
Pages: 73-100
DOI: 10.1145/174462.174617
The problem of computing the intersection of parametric and algebraic curves arises in many applications of computer graphics and geometric and solid modeling. Previous algorithms are based on techniques from elimination theory or subdivision...