Computing Approximation Offsets of Non-Self-Intersecting NURBS Curves

Abstract

The NURBS curve is a standard tool in CAGD. The calculation of the offset curve is an important research component in CAGD. The processing of abnormal situations, including self-intersections(or self-intersection loops) and singularities, is a key technology of offset curve calculation. Based on the second-derivative sampling and injectivity of the NURBS curve, an algorithm for computing non-self-intersecting approximate offset curve of the NURBS curve is proposed. First, the maximum offset distance of the non-self-intersecting offset curve of the NURBS curve is proposed and proved. Second, using the injectivity of the NURBS curve as a constraint condition, the non-self-intersecting offset curve of the NURBS curve is computed. Examples of computing non-self-intersecting offset curves of NURBS curves with degrees of 2 and 3 are presented. It is verified through examples that the proposed algorithm can quickly and effectively generate the approximate offset curves of the non-self-intersecting NURBS curve. Furthermore, the proposed algorithm does not depend on the choice of weights, and retains the adjustment of the weights of the NURBS curve to the curve shape.