A New Type of DP-NTP Curve with Shape Parameters and its Application

In order to improve the effects of shape control,we extended the normalized totally positive(NTP) basis,in literature(Delgado J,Pea J M.A shape preserving representation with an evaluation algorithm of linear complexity.Computer Aided Geometric Design,2003,20(1): 1-10) and obtained a new type of DP-NTP basis with multiple shape parameters.Then the DP-NTP curves with shape parameters are defined,some basic geometric properties and the conversion formulae from the new basis to the Bernstein basis are derived.At last,the geometric meaning of each shape parameter is discussed,some examples are given to show the effects of shape control.Moreover,some examples are illustrated to show the effective shape control by shape parameters.