Construction of triangular DP surface and its application

In this paper, a new type of bivariate basis on a triangle is presented, which is constructed by extending the univariate NTP basis proposed by Delgado and Peña. Some algebraic properties and its recursive formulae are given. Then a new type of surfaces that is called triangular DP surface is defined, and its recursive evaluation algorithm is obtained. Also, in the case of low degree, its subdivision algorithm and degree elevation algorithm are derived. It is shown that this type of surfaces is obviously more advantageous than triangular Bézier surface, and hence extremely useful for geometric design, especially for the situation in which the surface needs to be evaluated quickly.