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| Geometric Design and Adjustment of Shape for Developable Quartic λBézier Surfaces with Shape Parameters |
| HU Gang-a, b , JI Xiao-Min-b, c , QIN Xin-Qiang-a, SHEN Xiao-Qin-a |
| (a. School of Science, b. Faculty of Mechanical and Precision Instrument Engineering, c. College of the Arts, Xi’an University of Technology, Xi’an 710048, China) |
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Abstract To solve the problems in adjusting and controlling shapes of developable surfaces, two direct explicit and efficient methods of computeraided design for developable surfaces with local shape parameters were proposed. Firstly, following the important idea of duality between points and planes in 3D projective space, the developable quartic λBézier surfaces with shape parameters were represented using control planes with quartic λBézier basis functions. The developable quartic λBézier surfaces inherit the outstanding properties of the Bézier surfaces, with a good performance on adjusting their local shapes by changing the shape parameters. In the particular case where λ is equal to 0, the developable quartic λBézier surface is a developable Bézie surface. And then, the conditions of G2 continuity and C2 continuity between two adjacent developable quartic λBézier surfaces were presented. Finally, some properties of the developable quartic λBézier surfaces and applications in developable surfaces design were discussed. The modeling examples illustrate that the developable quartic λBézier surfaces provide two valuable ways for the design of developable surfaces.
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Received: 03 May 2011
Published: 28 April 2012
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