Modeling rational spline for visualization of shaped data

Modeling rational spline for visualization of shaped data Abstract -The presented paper focuses on two objectives, the development of a new curve interpolation scheme and its application towards the visualization of shaped data. A C 1 piecewise rational cubic function, with two parameter family, is developed and presented. The affect of parameters on the shape of the model curve is examined mathematically and illustrated graphically. Simple sufficient data dependent constraints are obtained on one family of the parameters to visualize positive, monotone and convex data. However, the other family of parameters can assume any positive values. The problem of visualization of constrained data is also addressed when the data is lying above a straight line and curve is required to lie on the same side of the line. Moreover, the approximation order of the proposed rational cubic function is also investigated and is found to be O ( h 3 i ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Numerical Mathematics de Gruyter

Modeling rational spline for visualization of shaped data

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Publisher
de Gruyter
Copyright
Copyright © 2013 by the
ISSN
1570-2820
eISSN
1569-3953
DOI
10.1515/jnum-2013-0003
Publisher site
See Article on Publisher Site

Abstract

Abstract -The presented paper focuses on two objectives, the development of a new curve interpolation scheme and its application towards the visualization of shaped data. A C 1 piecewise rational cubic function, with two parameter family, is developed and presented. The affect of parameters on the shape of the model curve is examined mathematically and illustrated graphically. Simple sufficient data dependent constraints are obtained on one family of the parameters to visualize positive, monotone and convex data. However, the other family of parameters can assume any positive values. The problem of visualization of constrained data is also addressed when the data is lying above a straight line and curve is required to lie on the same side of the line. Moreover, the approximation order of the proposed rational cubic function is also investigated and is found to be O ( h 3 i ).

Journal

Journal of Numerical Mathematicsde Gruyter

Published: Mar 1, 2013

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