Abstract
Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bezier-like basis called AHT Bezier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0, α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bezier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD modelling systems.
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