Parameterization Method on B‐Spline Curve

H Haron,A Rehman,S P Lim,D I S Adi,T Saba

doi:10.1155/2012/640472

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.

Highlights

The usage of computer graphics allows real life to be modeled in a computer model
The generation of the B-spline curve interpolation is started by parameterizing the data points followed by generating knot vector and finished by solving the system of linear equations
The experiment on proposed method is conducted on various datasets which include collinear data points, two adjacent data points, and a long distance of consecutive data points

Summary

Introduction

A computer model makes the work much easier and more effective. There are many applications in engineering, scientific visualization, medical imaging, image processing, design, and entertainment industry that use the aid of computer graphics. The sophisticated computer graphics techniques, which involve the geometric modeling of curves and surfaces, differential geometry, and so forth, are needed for realistic 3D modeling such as virtual reality and computer-aided design CAD. One of example of emerging application in CAD is the reverse engineering process in manufacturing industry. The parameterization of 2D or 3D data points is one of the fundamental steps in many CAGD applications such as texture mapping, remeshing, typography, and curve and surface fitting. Some previous research works have been done on parameterization method starting from the easiest method such as uniform 6, intermediate method, for instance, exponential 7, universal 8, and hybrid 9, until complex calculation such as rational chord length parameterization 10

Methods

Discussion

Conclusion