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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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Main Authors: Saaban, A., Piah, A.R.M., Majid, A.A., Chang, L.H.T.
Format: Technical Report
Language:English
Published: Institute of Engineering Mathematics 2013
Subjects:
Interpolation
Data acquisition
Online Access:http://dspace.unimap.edu.my/xmlui/handle/123456789/30784
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spelling 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
institution Universiti Malaysia Perlis
building UniMAP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Perlis
content_source UniMAP Library Digital Repository
url_provider http://dspace.unimap.edu.my/
language English
topic Interpolation
Data acquisition
spellingShingle 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
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=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
_version_ 1643796382140596224
score 13.222552

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