Abstract:

 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-spline 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.

Key words: B-spline curve, shape parameter, developable surface, duality, control plane