An alternative method for constructing interpolatory subdivision from approximating subdivision
This paper presents a new perspective for constructing interpolatory subdivision from primal approximating subdivision. The basic idea is constructing the subdivision rule for new inserted vertices of a new interpolatory subdivision scheme based on an approximating subdivision algorithm applied to a...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/84490 http://hdl.handle.net/10220/13101 |
| _version_ | 1826124755116228608 |
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| author | Li, Xin. Zheng, Jianmin. |
| author2 | School of Computer Engineering |
| author_facet | School of Computer Engineering Li, Xin. Zheng, Jianmin. |
| author_sort | Li, Xin. |
| collection | NTU |
| description | This paper presents a new perspective for constructing interpolatory subdivision from primal approximating subdivision. The basic idea is constructing the subdivision rule for new inserted vertices of a new interpolatory subdivision scheme based on an approximating subdivision algorithm applied to a local configuration of the mesh with one vertex updated for interpolation of the vertex. This idea is demonstrated by presenting two new interpolatory subdivision schemes based on Catmull–Clark subdivision for an arbitrary polygonal mesh and Loop subdivision for a triangular mesh, respectively. These algorithms are simple and have a small stencil for computing new points. The new perspective also shows a link between those classic approximating and interpolatory subdivision algorithms such as cubic B-spline curve subdivision and the four-point interpolatory subdivision, Catmull–Clark subdivision and Kobbeltʼs interpolatory scheme, and Loop subdivision and the butterfly algorithm. |
| first_indexed | 2024-10-01T06:25:52Z |
| format | Journal Article |
| id | ntu-10356/84490 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:25:52Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/844902020-05-28T07:17:16Z An alternative method for constructing interpolatory subdivision from approximating subdivision Li, Xin. Zheng, Jianmin. School of Computer Engineering DRNTU::Engineering::Computer science and engineering This paper presents a new perspective for constructing interpolatory subdivision from primal approximating subdivision. The basic idea is constructing the subdivision rule for new inserted vertices of a new interpolatory subdivision scheme based on an approximating subdivision algorithm applied to a local configuration of the mesh with one vertex updated for interpolation of the vertex. This idea is demonstrated by presenting two new interpolatory subdivision schemes based on Catmull–Clark subdivision for an arbitrary polygonal mesh and Loop subdivision for a triangular mesh, respectively. These algorithms are simple and have a small stencil for computing new points. The new perspective also shows a link between those classic approximating and interpolatory subdivision algorithms such as cubic B-spline curve subdivision and the four-point interpolatory subdivision, Catmull–Clark subdivision and Kobbeltʼs interpolatory scheme, and Loop subdivision and the butterfly algorithm. 2013-08-15T06:22:04Z 2019-12-06T15:46:03Z 2013-08-15T06:22:04Z 2019-12-06T15:46:03Z 2012 2012 Journal Article Li, X.,& Zheng, J. (2012). An alternative method for constructing interpolatory subdivision from approximating subdivision. Computer Aided Geometric Design, 29(7), 474-484. https://hdl.handle.net/10356/84490 http://hdl.handle.net/10220/13101 10.1016/j.cagd.2012.03.008 en Computer aided geometric design |
| spellingShingle | DRNTU::Engineering::Computer science and engineering Li, Xin. Zheng, Jianmin. An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title | An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title_full | An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title_fullStr | An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title_full_unstemmed | An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title_short | An alternative method for constructing interpolatory subdivision from approximating subdivision |
| title_sort | alternative method for constructing interpolatory subdivision from approximating subdivision |
| topic | DRNTU::Engineering::Computer science and engineering |
| url | https://hdl.handle.net/10356/84490 http://hdl.handle.net/10220/13101 |
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