# 平面可展曲面

planar developable 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 degree and degree B-spline curve .Throughing (2,3) degree and (2,2) degree B-spline ,we haveproved the validity and utility of this method.

In this manner, a developable surface was designed using control planes with Bézier and B-spline basis functions.

Based on the important idea of duality between plane and point geometries,two direct explicit methods of computer-aided design for developable surface s were proposed,the developable surface s were represented using control planes with appropriate basis functions.

It order to overcome the difficulties in representation of developable surface s utilizing traditional approaches,based the concept of duality between points and planes in 3D projective space, a direct explicit method of computer-aided design for developable surface s was presented.

First, this paper, in the field of intrinsic geometry, studies the geometric problems on garment design, as well as applies the frame and semi-geodesic coordinates to prove the fundamental theorem of being a developable surface.

In wire-cutting manufacturing of the top and bottom different curve,accomplishing cutting way of ellipse bias changing curved surface which between two plane curve into developable surface in order to calculate NC program of four axis ganging.

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.

It shows that some of the geometric construction algorithms that exist for curves can be also generalized to the design of developable surfaces.

To solve the problems in adjusting and controlling shapes of developable surfaces, following the important idea of duality between points and planes in 3D projective space, two direct explicit and efficient methods of computer aided design for developable surfaces are proposed.

planar developable surface：平面可展曲面

plan of experiment 实验计划 | planar developable surface 平面可展曲面 | planar graph 平面图

plan of experiment：实验计划

place value 位值 | plan of experiment 实验计划 | planar developable surface 平面可展曲面