Characterizing degrees of freedom for geometric design of developable composite Bézier surfaces

Chu, Chih-Hsing; Chen, Jang-Ting

doi:10.1016/j.rcim.2005.12.003

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…The construction of developable surfaces has always been an important research field in CAD, for which a mass of results have been presented. Fernández-Jambrina [4] derived an algorithm for constructing B-spline control nets for spline developable surfaces of arbitrary degree and number of pieces; using the de Casteljaus algorithm, Aumann et al [5][6][7] constructed Bézier developable patches through a Bézier boundary; for the construction of developable surfaces interpolating two given space curves defining a strip, Chu [8][9][10][11][12], Wang [1,13,14] and their cooperators carried out very detailed studies and proposed some algorithms for designing low degree Bézier developable patches.…”

Section: Introductionmentioning

confidence: 99%

Design of Rational Bezier Developable Surface Pencil Through A Common Isogeodesic

Liu¹,

Wang²

2012

JDCTA

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This paper studies the problem of designing a rational Bézier developable surface pencil with a common isogeodesic, and provides an algorithm for the representation of complicated geometric models in industrial applications which need to satisfy that the shape surface can be developed and a given curve is geodesic. By employing the local Frenet orthonormal frame, the explicit expression of the rational Bézier developable surface pencil is derived. Furthermore, the order of the rational Bézier developable surface pencil interpolating a planar or non-planar curve as its geodesic is discussed. The formulae of the control net vertices for the derived surface are presented. Finally, the effectiveness and correctness of the algorithm are verified by examples of the rational Bézier developable surface pencil through a degree 2 or 3 Bézier curve as a common geodesic.

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