地形模拟的细分细化方法

SUBDIVISION SCHEME OF TOPOGRAPHY SIMULATION

提出一类几何造型的方法——ｐ 细分法，并用生成多项式的代数方法给出其收敛性和光滑性条件．进一步，将其运用于地形模拟，提出细分细化方法．为了有效地控制地形形状，作者选取了满足插值条件的对称插值ｐ细分法．为了减少计算量，提高速度，在细分３层的基础上，进一步对细分加密特征网使用细化方法，直到满足精度要求．细分细化方法始终满足插值性质，因而能很好地控制地形形状．为了模拟不同地貌特征的地形，一方面，根据最终要求，选取合适的“控制光滑性参数β”；另一方面，对特征网格的法向进行不同幅度扰动以真实感显示．所提方法能快速模拟不同地貌特征的地形，为自然景观仿真提供了有效手段．

In this paper, the generalized subdivision for geometric modeling, p subdivision scheme, is presented.The analysis of its convergence and smoothness is then discussed. In addition, the subdivision scheme of topography simulation is also given. In order to control the form of topography, interpolatory subdivision scheme is used. Furthermore, this paper subdivides the every patch of control net into small ones until it satisfies given precision. For all subdivision are interpolatory, the form of topography can be easily controlled. For the sake of rending variant topography, the authors choose different control parameter β and make normal perturb at certain extent when patch is really displayed. The algorithm presented offers an efficient means for simulation of natural scene.