Title :
New Monomial Forms Approach for DP and NB1 Curves with Their Proofs
Author :
Savetseranee, Dilokvith ; Dejdumrong, Natasha
Author_Institution :
Dept. of Comput. Eng., King Mongkut´s Univ. of Technol. Thonburi, Bangkok, Thailand
Abstract :
There are several methods used to construct curves in CAGD, e.g., the de Casteljaus algorithm, DP algorithm, and NB1 algorithm. However, they are represented in the forms that are not suitable for performing geometric modeling. A proposed approach for evaluating DP curve, NB1 Curve by using monomial form was introduced by Aphirukmatakun and Dejdumrong in 2009. The authors did not provide any proofs for their propositions. Thus, this paper shows the proofs for the conversions from DP polynomial into its monomial form as well as NB1 polynomial.
Keywords :
CAD; computational geometry; curve fitting; engineering graphics; polynomial approximation; CAGD; DP algorithm; DP curve evaluation; DP curves; DP polynomial; NB1 algorithm; NB1 curves; computer aided geometric design; de Casteljaus algorithm; geometric modeling; monomial form approach; Algorithm design and analysis; Approximation algorithms; Mathematical model; Matrix converters; Polynomials; Shape; Transforms; Curve Conversion; Monomial Matrix; Monomial form;
Conference_Titel :
Computer Graphics, Imaging and Visualization (CGIV), 2013 10th International Conference
Conference_Location :
Macau
DOI :
10.1109/CGIV.2013.17
