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...
Saved in:
Main Authors: | , |
---|---|
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 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
my-ukm.journal.7386 |
---|---|
record_format |
eprints |
spelling |
my-ukm.journal.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 |
institution |
Universiti Kebangsaan Malaysia |
building |
Perpustakaan Tun Sri Lanang Library |
collection |
Institutional Repository |
continent |
Asia |
country |
Malaysia |
content_provider |
Universiti Kebangsaan Malaysia |
content_source |
UKM Journal Article Repository |
url_provider |
http://journalarticle.ukm.my/ |
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/7386/1/01_Md_Yeaminhossain.pdf http://journalarticle.ukm.my/7386/ http://www.ukm.my/jsm/english_journals/vol39num4_2010/contentsVol39num4_2010.html |
_version_ |
1643737109643657216 |
score |
13.18916 |