A Shape Preserving Verification Technique for Parametric Curves

Abstract

Typically, the shape preserving property for a parametric curve can be verified by checking for the total positivity of the collocation matrix or finding the existence of corner cutting algorithm as presented in [8]. However, there are several cases that although the curve is satisfied the shape preserving property, the shape of the curve does not preserve the shape of the control points, e.g., Delgado-Pena curves (DP curves). Hence, an alternative algorithm for the shape preserving verification was proposed based on five factors for verifying shape preserving property: the position of the control points, the order of the control points, the type of the curve, the weights of the rational curves, and the number of duplicate control points. Ultimately, four varieties of parametric curves, e.g., Bezier, Said-Ball, Wang- Ball and DP Curves, were verified and compared for their shape preserving property.