Geometric Design and Shape Adjustment for Developable B-Spline Surfaces with Multiple Shape Parameters

To solve the problems in adjusting and controlling shapes of developable surfaces,two explicit and efficient methods of computer-aided design for developable surfaces with multiple local shape parameters are proposed.A class of novel quasi-B-spline basis functions with two shape parameters is presented to construct Bspline curves with multiple shape parameters,which is an extension of the classical cubic uniform B-splinc basis functions.Following the idea of duality between points and planes in 3D projective space,the corresponding developable quasi-B-spline surfaces with multiple shape parameters are represented using control planes with quasi-B-spline basis functions.The developable quasi-B-spline surfaces inherit the outstanding properties of the B-spline surfaces,with good performance in adjusting the local shapes by changing the two shape parameters. In the particular case where shape parameters are both equal to 1,the developable quasi-B-spline surface is a developable B-spline surface.In addition,some properties of the developable quasi-B-spline surfaces and applications in developable surfaces design are discussed.Modeling examples illustrate that the developable quasi-B-spline surfaces provide two valuable ways for the design of developable surfaces.