A new method to compute the singularities of offsets to rational plane curves

[摘要] Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Maple, showing the efficiency of the algorithm for moderate degrees. (C) 2015 Elsevier B.V. All rights reserved.

[发布日期] 2015-12-15

[关键词] Offset curves;Planar rational curves;Offset self-intersections;Offset singularities;Offset trimming;Symbolic-numeric algorithms