Construction Of B-spline Surfaces Interpolating Curvature And Feature Curves

Given a 3D curve network(wireframe model),it is a basic problem in geometric modeling that constructing a surface to interpolate the curve network.In addition,the line of curvature is a type of the very important curve on the surface,and is a kind of the internal geometry of the surface with good geometrical features,which can guide surface analysis,and is widely used in geometric design,shape recognition and render-ing.In this paper,based on the basic problem of constructing surface interpolating the input curve network model and the good properties of curvature lines,a B-spline surface construction method is proposed to interpolate curvature and feature curves.With such method,generated surfaces always have high orders of smoothness and is a local con-struction method.Besides,there is no need of extra patching or trimming operations which increase computational cost and result in low orders of smoothness compared with traditional geometric modeling techniques.In chapter two,we give a brief depict of B-spline curve and surface,the product of two B-spline functions,G1 continuous and curvature line,which provides theoret-ical support for subsequent research work.However,the calculation of curvature line of surface is to solve nonlinear differential equation,which is complicated and compu-tationally large.Therefore,the curvature line constraints of B-spline surface is given by using Weingarten mapping,which is only relational expression about basic form of surface,avoiding the complex process of solving nonlinear differential equation.In chapter three,a new method that is local structural format is proposed to interpo-late the curve network which is called as construction of B-spline surfaces interpolating curvature and feature curves.Firstly,we obtain the required boundary curve network by B-spline curve fitting for the input 3D curve network.Then,revised the boundary curve network and determined all constraints,including G1 continuous splicing con-dition about vertex,G1 continuous splicing condition about edge and curvature line condition and converted the constraints to the corresponding B-spline surface control points constraints.Finally,solved the thin-plate-spline energy model for each patch to get the final surface.Based on the above process,the problem about construction of sur-face interpolating given 3D curve network is transformed into a quadratic programming problem with constraint conditions.Finally,In chapter four we make a conclusion on the research work of this thesis and point out the advantages and a little defects for our new method.Besides,we also give the future work.