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 correspo...
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my.unimap-307842013-12-23T07:35:55Z G1 scattered data interpolation with minimized sum of squares of principal curvatures Saaban, A. Piah, A.R.M. Majid, A.A. Chang, L.H.T. Interpolation Data acquisition 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=1 n we wish to construct a surface S which has continuous varying tangent plane everywhere (G1) such that S(x iyi) = zi. Specifically, the polynomial being considered belong to G1 quartic Bézier 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 Bézier 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. 2013-12-23T07:35:55Z 2013-12-23T07:35:55Z 2005-07-30 Technical Report Saaban, A., Piah, A.R.M., Majid, A.A., Chang, L.H.T. G1 scattered data interpolation with minimized sum of squares of principal curvatures (2005) Proceedings of the Conference on Computer Graphics, Imaging and Vision: New Trends 2005, 2005, art. no. 1521092, pp. 385-390. http://hdl.handle.net/123456789/30784 en Proceedings of the Conference on Computer Graphics, Imaging and Vision: New Trends;2005 Institute of Engineering Mathematics |
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Interpolation Data acquisition Saaban, A. Piah, A.R.M. Majid, A.A. Chang, L.H.T. G1 scattered data interpolation with minimized sum of squares of principal curvatures |
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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=1 n we wish to construct a surface S which has continuous varying tangent plane everywhere (G1) such that S(x iyi) = zi. Specifically, the polynomial being considered belong to G1 quartic Bézier 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 Bézier 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. |
format |
Technical Report |
author |
Saaban, A. Piah, A.R.M. Majid, A.A. Chang, L.H.T. |
author_facet |
Saaban, A. Piah, A.R.M. Majid, A.A. Chang, L.H.T. |
author_sort |
Saaban, A. |
title |
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_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_sort |
g1 scattered data interpolation with minimized sum of squares of principal curvatures |
publisher |
Institute of Engineering Mathematics |
publishDate |
2013 |
url |
http://dspace.unimap.edu.my/xmlui/handle/123456789/30784 |
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1643796382140596224 |
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13.209306 |