Local shape of offsets to algebraic curves

Authors:
Juan Gerardo Alcazar;Juan Rafael Sendra
Affiliations:
Departamento de Matemáticas, Universidad de Alcalá, E-28871-Madrid, Spain;Departamento de Matemáticas, Universidad de Alcalá, E-28871-Madrid, Spain
Venue:
Journal of Symbolic Computation
Year:
2007

Citing 9
Cited 7

Analytic properties of plane offset curves

Computer Aided Geometric Design
Algebraic properties of plane offset curves

Computer Aided Geometric Design
Rational curves and surfaces with rational offsets

Computer Aided Geometric Design
Offset-rational parametric plane curves

Computer Aided Geometric Design
Parametric generalized offsets to hypersurfaces

Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
A Laguerre geometric approach to rational offsets

Computer Aided Geometric Design
Algorithms for rational real algebraic curves

Fundamenta Informaticae - Special issue on symbolic computation and artificial intelligence
Normal parameterizations of algebraic plane curves

Journal of Symbolic Computation
Degree formulae for offset curves

Journal of Pure And Applied Algebra

Good global behavior of offsets to plane algebraic curves

Journal of Symbolic Computation
Good local behavior of offsets to rational regular algebraic surfaces

Journal of Symbolic Computation
Parameterizing surfaces with certain special support functions, including offsets of quadrics and rationally supported surfaces

Journal of Symbolic Computation
On convolutions of algebraic curves

Journal of Symbolic Computation
Topology of 2D and 3D rational curves

Computer Aided Geometric Design
Local shape of generalized offsets to algebraic curves

Journal of Symbolic Computation
The shape of conchoids to plane algebraic curves

Proceedings of the 7th international conference on Curves and Surfaces

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we introduce the notion of local shape to describe the behavior of a real place of an algebraic curve around its center. We analyze how the local shape is affected by the offsetting process, and we relate this phenomenon to the curvature of the curve. Furthermore, we characterize the situations when the offsetting process behaves locally well, so that the local shape is preserved.