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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universiti Kebangsaan Malaysia
2010
|
| Online Access: | http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf |
| _version_ | 1848811465305227264 |
|---|---|
| author | Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah, |
| author_facet | Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah, |
| author_sort | Diana Sirmayunie Mohd Nasir, |
| building | UKM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T23:46:50Z |
| format | Article |
| id | oai:generic.eprints.org:7386 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T23:46:50Z |
| publishDate | 2010 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org: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 |
| spellingShingle | Diana Sirmayunie Mohd Nasir, Abd Rahni Mt Piah, Construction of smooth closed surfaces by ball functions on a cube |
| title | 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_short | Construction of smooth closed surfaces by ball functions on a cube |
| title_sort | construction of smooth closed surfaces by ball functions on a cube |
| url | http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/ http://journalarticle.ukm.my/7386/1/01_Md_Yeaminhossain.pdf |