基于随机中点位移法的三维地形模拟

3D Terrain Simulation Based on the Method of Random Mid-point Displacement

分形布朗运动FBM是分形几何的重要内容 ,利用它可以构建出极具分形特性的三维几何模型 ,这种几何模型可以用来生成多种不同的自然对象 ,如山脉、云彩等的真实感图形。随机中点偏移法是生成分形布朗运动的重要方法。该文简单介绍了随机中点位移法模拟地形的几种方法 ,特别是其中的菱形 -方形法 (Diamond -Square法 ) ,详细介绍了其原理 ,位移量以及实现的算法 。

The Fractal Brown Motion(FBM) is an important content of the fractal geometry. Using the FBM method, many three-dimension geometrical models with fractal characteristics, such as mountains , clouds and so on can be developed. The random mid-point displacement method is an important method in the FBM. This paper introduces three methods of random mid-point displacement for simulating the terrain, especially the method of Diamond-Square. The theory , displacement and the arithmetic are discussed in detail. A picture of Diamond-Square method is improved at last.