New Monomial Forms Approach for DP and NB1 Curves with Their Proofs

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.