Developable B-Spline Surfaces with Multiple Shape Parameters

To solve the problems in adjusting and controlling shapes of developable surfaces, a direct explicit and efficient methods of computer-aided design for developable surfaces with multiple local shape parameters are proposed. Firstly, a class of novel λμ-B-spline basis functions with two shape parameters is presented. And then, following the important idea of duality between points and planes in 3D projective space, the corresponding developable λμ-B-spline surfaces with multiple shape parameters are represented using control planes with λμ-B-spline basis functions. The developable λμ-B-spline surfaces inherit the outstanding properties of the B-spline surfaces, with a good performance on adjusting their local shapes by changing the two shape parameters. In addition, some properties of the developable λμ-B-spline surfaces and applications in developable surfaces design are discussed. The modeling examples illustrate that the developable λμ-B-spline surfaces provide a valuable ways for the design of developable surfaces.