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. 655659. ISSN 01266039

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Official URL: http://www.ukm.my/jsm/english_journals/vol39num4_2...
Abstract
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 freeform 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 Bspline 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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