A Global Fairing Algorithm for B-spline Surfaces Using Non-linear Programming

비선형 계획법을 이용한 B-스플라인 곡면의 순정 알고리듬

In the reverse engineering, surfaces are modeled for new products by interpolating the digitized data points obtained by measuring the existing shapes. However, many measuring or deviation errors are happened during the measuring process. If these errors are ignored, designers could get undesirable results. Therefore, it is important to handle such errors and fairing procedure with the esthetics criteria is needed during surface modeling process. This paper presents algorithms for the fairing of B-spline surfaces. The algorithms are based on automatic repositioning of control points for B-spline surfaces. New positions of the control points are determined by solving a non-linear programming of which the objective functions are derived variously using derived surfaces and constraints are established by distance measures between the original and the modified control points. Changes in surface shapes are analyzed by illustrations of their shapes and continuous plotting of gaussian and mean curvatures.