Research On Algorithm For Curvature Lines Of Surface In CAGD

The topic of this paper is to make an investigation on arithmetic for curvature lines of surface in CAGD.The opening chapter gives a general overview of history of the development of the NURBS surface, awaken to the necessity of compute on geodesic and curvature lines of surface.We summarize the actuality of compute on geodesic and curvature lines, described in the second chapter. It consists of integral of geodesic on NURBS surface, algorithm of the shortest path on discrete meshes, evaluating the principal direction in vertex on meshes, judgement of umbilical point, feature process, track algorithm and optimization of space.In the third chapter, the essential part of this thesis, author presents a systemic formula for computing the integral curvature lines on NURBS surfaces. The discrete normal is used to simplify the calculation of the second fundamental form of the surface largely, which accelerate the Euler iteration process in solving the differential equation of curvature line. The discrete points on the curvature line are then obtained and approximated by a B-spline curve on the NURBS surface within some tolerance based on singular mixed interpolation.The fourth chapter, the last chapter, gives an introduction to rough results and ideas of algorithm of discrete principal curvature on mesh.