Construction of smooth closed surfaces by ball functions on a cube

Diana Sirmayunie Mohd Nasir, and Abd Rahni Mt Piah, (2010) Construction of smooth closed surfaces by ball functions on a cube. Sains Malaysiana, 39 (4). pp. 655-659. ISSN 0126-6039


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In Computer Aided Geometric Design (CAGD), surface constructions are basically formed from collections of surface patches, by placing a certain continuity condition between adjacent patches. Even though tensor product BŽzier patches are currently used extensively in most CAGD systems to model free-form surfaces, this method can only be used to generate closed surface of genus one, i.e. a surface which is equivalent to a torus. A surface with tangent plane continuity is known as a first order geometrically smooth surface or a G1 surface. This paper presents a simple G1 surface construction method, i.e. a surface of genus zero, by defining Ball bicubic functions on faces of a cube. The constructed basis functions have small support and sum to one. The functions are useful for designing, approximating and interpolating a simple closed surface of genus zero. This construction method was first introduced by Goodman in 1991 who defined biquadratic generalised B-spline functions on faces of a simple quadrilateral mesh. Several examples of surfaces/objects which are constructed by the proposed method are presented in this paper.

Item Type:Article
Keywords:Approximation; Ball function; closed surface; geometric continuity; interpolation
Journal:Sains Malaysiana
ID Code:7386
Deposited By: Mr Fazli Nafiah -
Deposited On:07 Aug 2014 11:44
Last Modified:14 Dec 2016 06:43

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