G1 scattered data interpolation with minimized sum of squares of principal curvatures
One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(xi, yi), i=1,...,n} ∈ R2 over a polygonal domain and a corresp...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2005
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/4332/1/A._s.pdf |
| _version_ | 1803624841501212672 |
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| author | Saaban, Azizan Piah, A.R.M. Majid, A.A. Chang, L.H.T. |
| author_facet | Saaban, Azizan Piah, A.R.M. Majid, A.A. Chang, L.H.T. |
| author_sort | Saaban, Azizan |
| collection | UUM |
| description | One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(xi, yi), i=1,...,n} ∈ R2 over a polygonal domain and a corresponding set of real numbers {zi}i=1n, we wish to construct a surface S which has continuous varying tangent plane everywhere (G1) such that S(xi, yi) = zi. Specifically, the polynomial being considered belong to G1 quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G1 continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method. |
| first_indexed | 2024-07-04T05:24:47Z |
| format | Conference or Workshop Item |
| id | uum-4332 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T05:24:47Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | uum-43322011-12-27T01:32:07Z https://repo.uum.edu.my/id/eprint/4332/ G1 scattered data interpolation with minimized sum of squares of principal curvatures Saaban, Azizan Piah, A.R.M. Majid, A.A. Chang, L.H.T. QA76 Computer software One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(xi, yi), i=1,...,n} ∈ R2 over a polygonal domain and a corresponding set of real numbers {zi}i=1n, we wish to construct a surface S which has continuous varying tangent plane everywhere (G1) such that S(xi, yi) = zi. Specifically, the polynomial being considered belong to G1 quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G1 continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method. 2005-07-26 Conference or Workshop Item PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/4332/1/A._s.pdf Saaban, Azizan and Piah, A.R.M. and Majid, A.A. and Chang, L.H.T. (2005) G1 scattered data interpolation with minimized sum of squares of principal curvatures. In: International Conference on Computer Graphics, Imaging and Vision: New Trends, 26-29 July 2005 . http://dx.doi.org/10.1109/CGIV.2005.39 doi:10.1109/CGIV.2005.39 doi:10.1109/CGIV.2005.39 |
| spellingShingle | QA76 Computer software Saaban, Azizan Piah, A.R.M. Majid, A.A. Chang, L.H.T. G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title | G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title_full | G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title_fullStr | G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title_full_unstemmed | G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title_short | G1 scattered data interpolation with minimized sum of squares of principal curvatures |
| title_sort | g1 scattered data interpolation with minimized sum of squares of principal curvatures |
| topic | QA76 Computer software |
| url | https://repo.uum.edu.my/id/eprint/4332/1/A._s.pdf |
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