Smoothing of curves and surfaces

Using BCrier-techniques or B-spline-techniques for lntrrpolation or approximation of cur\es or wrfaces inflection pants or changes of sign of the Gaussian curvature occaaionallq occur. Inflection polnth or changer of sign of Gaussian curvature are ur&vwd in some applications. notably the fairlng of ship liner or the fairlng of car body surfaces. In the present contribution we mtroduce ~1 simple criterion for detecting buch undwrcd domains by usmg the k-orrho~onws. The X-orthotomics are wellknown in optics [Bruce et al. ‘X4]. Such undesired domains can be smoothed intcractivelq or by using a procedure bnsrd on :I method from .~lgcbraic geometry. the so called B&out-method [Salmon 1885. Goldman et al. ‘X5]. Kqwords. BCzier-curbes, Bezier-surfaces. inflection pants. GaussIan curvature. orthotomics, B&out-mrthod.