Construct Control Meshes of Helicoids over Trapezium Domain
Received:July 04, 2009  Revised:December 30, 2009  Download PDF
Wenyu Chen,Gang Xu,Guozhao Wang. Construct Control Meshes of Helicoids over Trapezium Domain. International Journal of Software and Informatics, 2009,3(4):501~511
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Fund:This effort is sponsored by the National Natural Science Foundation of China under Grant Nos. 60473130, 60773179; the National Basic Research Program (973) of China under Grant No.2004CB318000; the Natural Science Foundation of Zhejiang Province under Grant No. Y1090718.
Abstract:In this paper, we present a geometric construction of control meshes of helicoids over trapezium domain. We first introduce the quasi-Bézier basis in the space spanned by {1;t;cos t;sin t;t sin t;t cos t}; with t [0;α];α [0;2π). We denote the curves ex-pressed by the quasi-Bézier basis as algebraic-trigonometric Bézier curves, for short AT-Bézier curves. Then we find out the transform matrices between the quasi-Bézier basis and {1;t;cos t; sin t;t sin t; tcos t}. Finally, we present the control mesh representation of the heli-coids and the geometric construction of the control mesh. In detail, we construct the controlpolygon of the planar Archimedean solenoid, which is also expressed with the quasi-Bézier basis, and then generate the mesh vertices by translating points of the control polygon.
keywords:helicoids  Archimedean solenoid  minimal surface  AT-Bézier surfaces  control mesh representation  CAGD/CAM
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