C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation

Nowadays, scientific visualization is an important branch in computer graphics to graphically visualize the scientific data from three dimensional phenomena. The construction of a surface usually involves generating a set of surface patches that smoothly connected together and the surface should inh...

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Main Author:	Yeong, Yee Yon
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA1-939 Mathematics
Online Access:	http://eprints.usm.my/48367/1/Thesis%28YEONG%20YEE%20YON%29%20cut.pdf
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id	my-usm-ep.48367
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spelling	my-usm-ep.483672021-02-21T07:40:53Z C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation 2019-05 Yeong, Yee Yon QA1-939 Mathematics Nowadays, scientific visualization is an important branch in computer graphics to graphically visualize the scientific data from three dimensional phenomena. The construction of a surface usually involves generating a set of surface patches that smoothly connected together and the surface should inherit certain shape property of the data like non-negativity. The construction of non-negativity preserving 1C interpolation surface to scattered data is considered. The given data is triangulated using Delaunay triangulation. The interpolating surface to scattered data is piecewise with Bézier triangular patches. The surfaces are produced using the method of Clough-Tocher split. Sufficient non-negativity conditions on the Bézier ordinates are derived to ensure the non-negativity of a cubic Bézier triangular patch. New set of lower bounds is proposed to the Bézier ordinates. The initial values of the Bézier ordinates are determined by the given data and the estimated gradients at the data sites. The Bézier ordinates are adjusted if necessary by modifying the gradients at the data sites so that the Bézier ordinates fulfill the non-negativity conditions. The scheme for constructing the non-negativity preserving surface is local. It constructs 1C interpolating surface to scattered data subject to constraint plane. Some graphical examples are presented. 2019-05 Thesis http://eprints.usm.my/48367/ http://eprints.usm.my/48367/1/Thesis%28YEONG%20YEE%20YON%29%20cut.pdf application/pdf en public masters Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1-939 Mathematics
spellingShingle	QA1-939 Mathematics Yeong, Yee Yon C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
description	Nowadays, scientific visualization is an important branch in computer graphics to graphically visualize the scientific data from three dimensional phenomena. The construction of a surface usually involves generating a set of surface patches that smoothly connected together and the surface should inherit certain shape property of the data like non-negativity. The construction of non-negativity preserving 1C interpolation surface to scattered data is considered. The given data is triangulated using Delaunay triangulation. The interpolating surface to scattered data is piecewise with Bézier triangular patches. The surfaces are produced using the method of Clough-Tocher split. Sufficient non-negativity conditions on the Bézier ordinates are derived to ensure the non-negativity of a cubic Bézier triangular patch. New set of lower bounds is proposed to the Bézier ordinates. The initial values of the Bézier ordinates are determined by the given data and the estimated gradients at the data sites. The Bézier ordinates are adjusted if necessary by modifying the gradients at the data sites so that the Bézier ordinates fulfill the non-negativity conditions. The scheme for constructing the non-negativity preserving surface is local. It constructs 1C interpolating surface to scattered data subject to constraint plane. Some graphical examples are presented.
format	Thesis
qualification_level	Master's degree
author	Yeong, Yee Yon
author_facet	Yeong, Yee Yon
author_sort	Yeong, Yee Yon
title	C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
title_short	C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
title_full	C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
title_fullStr	C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
title_full_unstemmed	C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation
title_sort	c1 non-negativity preserving interpolation using clough-tocher triangulation
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2019
url	http://eprints.usm.my/48367/1/Thesis%28YEONG%20YEE%20YON%29%20cut.pdf
_version_	1747821924769071104

C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation

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