Developable B-spline Surface And The Research Of Convexity

When designing the shapes of industrial products,we will encount with the design problem of developable surface. About this Aumann[8] has provided some methods,connecting lines between two boundary curves,shaping ruled surface, and adding some developable conditions to ruled surface.Helmut Pottmann [2][3] has studied developable rational Bezier surface and rational B-spline surface.On the basis of Aumann,Meng Ya-qin and Ye Zheng-lin[13],Cuan-ying and Xue Ji-jun[16] have gained some conditions about characteristic polygon of the ruled surface,they used two Bezier curves in paralled plane as boundary curves to get ruled surface.In this paper,the B-spline curve is supposed as boundary curves,when they are in two paralled plane and two arbitrary plane,the condition about the control vertex of characteristic polygon when the ruled surface is developable are gained,solved the designing problem of (n,n+l) degree and (n,n) degree B-spline curve .Throughing (2,3) degree and (2,2) degree B-spline ,we haveproved the validity and utility of this method.The convexity of surface is a important measuring parameter of sur-face.Though the analysis of the convexity of the front surface, this paper gained some terse and practical results.We can control the shape of developable surface through adjusting corresponding plane curves.