An approach to the determination of DP triangular surfaces with its quadratic complexity

A proposed model for triangular DP surfaces provided in has been found that there is an inappropriate property in its recurrence formulae. That is, it is lack of convexity, i.e., summation of all blending functions for each degree is not equal to one. Although, Later in 2009, A new model of triangular DP surfaces has been proposed, however, this model is still not satisfied linearly independent property. Consequently, the model cannot be able to find degree elevation, degree reduction as well as conversions from one model to another. This paper presents a new approach to the construction of triangular DP surfaces that possesses the recurrence formulae, and its recursive evaluation algorithm. Some examples of degree elevation formulae are given for some degrees. The convexity property and the quadratic evaluation complexity are also derived. It is obvious that this model of triangular DP surfaces is more efficient than both previous DP surface models.