Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves

Details Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves

2011-02-27

arxiv.org/abs/1102.5463v1

Computer Science

Computational Geometry

Scientific paper

Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive epsilon, we want to compute an epsilon-isotopic polygonal approximation to the restriction of the curve S=f^{-1}(0)={p in R^2: f(p)=0} to B_0. We focus on subdivision algorithms because of their adaptive complexity and ease of implementation. Plantinga and Vegter gave a numerical subdivision algorithm that is exact when the curve S is bounded and non-singular. They used a computational model that relied only on function evaluation and interval arithmetic. We generalize their algorithm to any bounded (but possibly non-simply connected) region that does not contain singularities of S. With this generalization as a subroutine, we provide a method to detect isolated algebraic singularities and their branching degree. This appears to be the first complete purely numerical method to compute isotopic approximations of algebraic curves with isolated singularities.

Affiliated with

Also associated with

No associations

Rating

Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-53784