A rational cubic spline technique for preserving the positivity of data
This work intends to address the problem of the visualization of curves (2-dimensional data representation) and surfaces (3-dimensional data representation) with the aim and provision that their display looks smooth and modifiable. In order to achieve these goals, we proposed a C1 spline interpolat...
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| Format: | Thesis |
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| Language: | English |
| Subjects: | |
| Online Access: | http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77083/1/Page%201-24.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77083/2/Full%20text.pdf http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/77083/4/Anas%20Khalaf.pdf |
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| Summary: | This work intends to address the problem of the visualization of curves (2-dimensional data representation) and surfaces (3-dimensional data representation) with the aim and provision that their display looks smooth and modifiable. In order to achieve
these goals, we proposed a C1 spline interpolation. For the treatment of the 2D data visualization problem, the proposed function has been made to contain three positive shape parameters in each subinterval of its construction. Simple data-dependent
constraints are derived for single shape parameter to ensure preserving the positivity through given positive data while the remaining two parameters are left free for designer’s choice for the curves’ refinement and/or manipulation. This interpolation has been extended into rational bi-cubic spline interpolation to treat the problem of 3D data visualization. The extended interpolation has been made to involve six positive shape parameters in each rectangular patch of the surface construction. In this case, constraints are derived for two shape parameters for conserving the surface positivity while the remaining four parameters are left free according to designer’s will for the surface smoothing and/or manipulating. Half of these shape parameters are set in the x-direction and the other half are set in the y-direction in such a way that each one of the free parameters can be changed separately to obtain different data representation models accordingly. The scheme under discussion is locally effective on the data intervals and does not allow to be inserted with any new knots to preserve the positivity. Numerical
examples are provided to demonstrate that the proposed scheme is successfully producing
interactive, smooth and modifiable curves and surfaces. |
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