Parameterization method on B-spline curve
type: Item
instance of: scholarly article
title: Parameterization method on B-spline curve
zbMATH Open document ID: 1264.65024
DOI: 10.1155/2012/640472
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 6173452
Wikidata QID: Q58912375
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/640472
OpenAlex ID: W2137292379
cites work: The best parameterization for parametric interpolation
cites work: A practical guide to splines.
cites work: Choosing nodes in parametric curve interpolation
cites work: A universal parametrization in B-spline curve and surface interpolation
cites work: Curves with chord length parameterization
cites work: Q4278198
cites work: Hybrid Computation Using Neuro-Genetic and Classical Optimization for B-spline Curve and Surface Fitting
cites work: Weighted extended B-spline approximation of Dirichlet problems
cites work: Surface approximation to scanned data
description: scientific article; zbMATH DE number 6173452