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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 640472, 22 pages
http://dx.doi.org/10.1155/2012/640472
Research Article

Parameterization Method on B-Spline Curve

1Faculty of Computer Sciences and Information Systems, Universiti Teknologi Malaysia, 81310 Skudai, Johor Bahru, Malaysia
2College of Computer and Information Science, Al-Imam Muhammad Bin Saud Islamic University, Riyadh 11432, Saudi Arabia

Received 18 July 2011; Revised 30 September 2011; Accepted 7 October 2011

Academic Editor: Carlo Cattani

Copyright © 2012 H. Haron et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the representation of 2D and 3D primitive entities and parameterization method using B-spline interpolation. However, there is no parameterization method which can handle all types of data points such as collinear data points and large distance of two consecutive data points. Therefore, this paper presents a new parameterization method that is able to solve those drawbacks by visualizing the 2D primitive entity of scanned data point of a real object and construct 3D computer model. The new method has improved a hybrid method by introducing exponential parameterization method in the beginning of the reconstruction process, followed by computing B-spline basis function to find maximum value of the function. The improvement includes solving a linear system of the B-spline basis function using numerical method. Improper selection of the parameterization method may lead to the singularity matrix of the system linear equations. The experimental result on different datasets show that the proposed method performs better in constructing the collinear and two consecutive data points compared to few parameterization methods.