Study Of Fairing Free Curve And Surface Base On B-spline

Computer Aided Geometric Design of the high technology on today is developed follow navigate, shipbuilding, machine design and manufacture prospered, also is the important branch of applied mathematic. Surface modeling is the important content of the graphics computer and Computer Aided Geometric Design, the main work is studying the surface how to show, design , display and analyses in the computer graphics system.Quality of surface is the crisis for designers. Fairing is the focus of the quality of surface. How to fair curve and surface is an important study subject in Computer Aided Geometric Design. Fairing of cu rves and surface coming down to the esthetical, practicality, easy process, is a difficulty bound problem of aesthetics notion.In the paper after the curves continuity, the main aim is how to fair the curve and surface based on the highlight and curvature (include Gaussian curvature and mean curvature).Firstly study how to fair the B-spline surface based on highlight. Then lucubrate the min-energy curve faring and reverse the ordered control point., an whole method of fairing the B-spline surface is given. Lastly how to redraw the highlight if adjust single control point by Taylor expansion approach is studied. Through the section an idiographic algorithm fairing the B-spline surface based on highlight and a case are given.Secondly study how to fair the B-spline curve and surface based on curvature. For fairing B-spline curve given the algorithm how to fair one point once and two points once. Curvature is also frequently used in assessing the shape of a surface. Commonly used analyzing tools include Gaussian and mean curvatures as well as normal curvature as given field of directions. Curvature is an important tools to asses the quality of surface. How to modify to attain an aim to control shape is a crisis question. As a designer, it took more time to modify the curvature of surface manual. But the result could not confirm after modify. So an algorithm must be provided from curvature to surface. Fairing surface with Gaussian curvature requires solving the following problem: how to modify curvature of interpolate point on surface and how to generate the new surface. The first question is really criterion to fair surface by curvature. The second question is how to generate a surface from the original surface based on modified curvature, and then could attain a new surface from original surface. That should lead to a desired result. By a slight modification, a method how to generate new surface with Gaussian curvature is presented.In the paper some creative question is studied as follow:1) From G t0F is studied, a method how to fair curves could put outbased on the Frenet continuity and try to express more the mechanism of the curves fairing.2) Predigest the energy method of fairing curve, a full method how to fairB-spline surface based on highlight firstly is given. Through modify highlight, then reverse the control point of highlight. In the algorithm put an idea to give the order of the spline energy and spring energy based on the focus of designer. Lastly reverse the control point of full surface and attain the aim of fairing surface.3) Bring forward a method how to fair surface based on curvature firstly. The curvature representation algorithm is given firstly. A new surface is obtained by utilizing the least squares optimization method of Gaussian-Newton. The main work is how to compute the Jacobi Matrix. Representation changes the fairing surface to th* modifying curvature. This method would have brought two changes. Firstly change fairing the surface to confirming the modification matrix, designer should evade from the complicated and detailed work. Then criterions of fairing surface is changed how to modify the Gaussian curvature directly. And it is easy to gain the new surface after modifying curvature. It would make fairing surface to focus on the criterions of curvature modification.