A Research On Shape Modification Of B-spline Curve And Surface Via Constrained Optimization

Computer Aided Geometric Design mainly researches on free curve and surface. Changing shape of curves and surfaces and approximate merging two adjacent curves and surfaces are both hot topics in CAGD. The B-spline curve is widely used in Computer Aided Geometric Design and Computer Graphics. It has much better properties for shape design than some other curves. Developing more convenient techniques for designing and modifying B-spline curves is an important problem, and isalso an important research issue in CAD/CAM and NC Technology fields.In the first section, the development history of curve and surface constructing modelling is reviewed. For the shape adjusting, we get the main idea of this paper: This presents a new method based on changing the control points of the curves via constrained optimization. By this method, the authors modify control points of the original B-spline curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.In the second section, according to the special properties of B-spline curves, we change the control points of the curves via Constrained Optimization for the single point and the Multi-Target point case respectively. This problem is come down to minimization problem of Constrained Optimization. Practical examples are also given.In the third section, we first introduce the definition of the B-spline surface, and we also modify the B-spline surface by Constrained Optimization. Practical examples are also given.In the fourth section, firstly the main conclusions of this thesis are induced;then the work in the future is mentioned.