三角域曲面的TPIFS模型分形逼近

Fractal Approximation of Triangular Surfaces Based on TPIFS Model

提出了一种三角域上逼近具有分形特征的自然复杂曲面和普通光滑曲面的统一数学模型 该模型是迭代函数系统与传统自由曲面造型的一种结合 ,文中给出的定理证明了它可以逼近任意三角域上的连续函数 模型的主要用途是曲面造型。

In this paper, a unified model for approximating smooth or rough surfaces defined in the triangular field is introduced. This model is called triangular projected iterated function system (TPIFS). The model combines the classical iterated function system (IFS) model and the free form approximation theory, and it is also proved that the model can approximate any continuous functions defined in the triangular field. The main applications of the model are surface modeling, shape description and image compression.