Paper Info
Title
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
Abstract
For an irreducible algebraic space curve C that is implicitly defined as the intersection of two algebraic surfaces, f (x, y, z) = 0 and g (x, y, z) = 0, there always exists a birational correspondence between the points of C and the points of an irreducible plane curve P, whose genus is the same as that of C. Thus C is rational if the genus of P is zero. Given an irreducible space curve C = (f ∩ g), with f and g not tangent along C, we present a method of obtaining a projected irreducible plane curve P together with birational maps between the points of P and C. Together with [4], this method yields an algorithm to compute the genus of C, and if the genus is zero, the rational parametric equations for C. As a biproduct, this method also yields the implicit and parametric equations of a rational surface S containing the space curve C.The birational mappings of implicitly defined space curves find numerous applications in geometric modeling and computer graphics since they provide an efficient way of manipulating curves in space by processing curves in the plane. Additionally, having rational surfaces containing C yields a simple way of generating related families of rational space curves.
Year
DOI
Venue
1989
10.1145/77269.77273
ACM Trans. Graph.
Keywords
DocType
Volume
irreducible space curve,space curve C.The birational,projected irreducible plane curve,birational correspondence,additional key words and phrases: computer-aided design,irreducible plane curve,space curve,rational parametric equation,rational curve,irreducible algebraic space curve,rational surface,parametric curves,surfaces IV,rational space curve,automatic parameterization
Journal
8
Issue
ISSN
Citations 
4
0730-0301
23
PageRank 
References 
Authors
1.79
8
2
Name
Order
Citations
PageRank
S. S. Abhyankar17714.33
C. J. Bajaj2231.79