Construction of smooth closed surfaces by ball functions on a cube

• Main Authors: Diana Sirmayunie Mohd Nasir,, Abd Rahni Mt Piah,
• Format: Article
• Language: English
• Published: Universiti Kebangsaan Malaysia 2010
• Online Access: http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf; http://journalarticle.ukm.my/7386/; http://www.ukm.my/jsm/english_journals/vol39num4_2010/contentsVol39num4_2010.html

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.