Construction of smooth closed surfaces by ball functions on a cube

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-f...

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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/ http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf

id	ukm-7386
recordtype	eprints
spelling	ukm-73862016-12-14T06:43:55Z http://journalarticle.ukm.my/7386/ Construction of smooth closed surfaces by ball functions on a cube Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah, 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. Universiti Kebangsaan Malaysia 2010-08 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf 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 http://www.ukm.my/jsm/english_journals/vol39num4_2010/contentsVol39num4_2010.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	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.
format	Article
author	Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah,
spellingShingle	Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah, Construction of smooth closed surfaces by ball functions on a cube
author_facet	Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah,
author_sort	Diana Sirmayunie Mohd Nasir,
title	Construction of smooth closed surfaces by ball functions on a cube
title_short	Construction of smooth closed surfaces by ball functions on a cube
title_full	Construction of smooth closed surfaces by ball functions on a cube
title_fullStr	Construction of smooth closed surfaces by ball functions on a cube
title_full_unstemmed	Construction of smooth closed surfaces by ball functions on a cube
title_sort	construction of smooth closed surfaces by ball functions on a cube
publisher	Universiti Kebangsaan Malaysia
publishDate	2010
url	http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf
first_indexed	2023-09-18T19:49:33Z
last_indexed	2023-09-18T19:49:33Z
_version_	1777406127856680960

Construction of smooth closed surfaces by ball functions on a cube

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