Geometric Design and Adjustment of Shape for Developable Quartic λBézier Surfaces with Shape Parameters

Abstract

Abstract: To solve the problems in adjusting and controlling shapes of developable surfaces, two direct explicit and efficient methods of computeraided 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 λBézier surfaces with shape parameters were represented using control planes with quartic λBézier basis functions. The developable quartic λBézier 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 λBézier surface is a developable Bézie surface. And then, the conditions of G2 continuity and C2 continuity between two adjacent developable quartic λBézier surfaces were presented. Finally, some properties of the developable quartic λBézier surfaces and applications in developable surfaces design were discussed. The modeling examples illustrate that the developable quartic λBézier surfaces provide two valuable ways for the design of developable surfaces.

Key words: Bézier curve, shape parameter, developable surface, duality, control plane, continuity conditionBézier

CLC Number:

HU Gang-a, b , JI Xiao-Min-b, c , QIN Xin-Qiang-a, SHEN Xiao-Qin-a. Geometric Design and Adjustment of Shape for Developable Quartic λBézier Surfaces with Shape Parameters[J]. Journal of Shanghai Jiaotong University, 2012, 46(04): 601-606.

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[1]	HU Gang,DAI Fang,QIN Xinqiang,ZHANG Suxia . On Continuity Conditions for Quartic Bézier Curves and Surfaces with Shape Parameters [J]. Journal of Shanghai Jiaotong University, 2010, 44(11): 1481-1485.
[2]	QIN Xinqiang，YUE Li，HU Gang，LI Kai . Approximate Merging of a Pair of Cubic Uniform Bspline Curves with Shape Parameters [J]. Journal of Shanghai Jiaotong University, 2010, 44(08): 1084-1088.