Computing Approximation Offsets of Non-Self-Intersecting NURBS Curves

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.