改进四点细分法及其应用

Improved Four Points Subdivision Scheme and its Applications

对经典的四点细分格式进行推广,提出了可通过对形状参数的适当选择来实现对极限曲线形状调整和控制的四参数四点细分曲线造型方法,并把该方法扩展到曲面上,对其连续性和收敛性进行了分析。把四参数四点细分法运用于山地模拟,由于其中四个参数选取的灵活性,可对生成的地形形状进行适当的调整,生成比较丰富的地貌形状。细分方法具有多尺度特点,所以可对地貌进行细节描述。试验证明能够较好地生成模拟山地地形,为山地地形模拟仿真提供了一种有效的方法。

This paper extends the classical 4 point interpolating subdivision scheme, and brings forward a new 4-point subdivision scheme with four parameters for curve design, which can be controlled by choosing these four parameters appropriately. At the same time, we expand it to surface design. The sufficient conditions of the uniform convergence property and continuity properties of the subdivision scheme are proved. It can generate expectable terrain shapes using 4 point subdivision scheme with four parameters in terrain simulation. Through selecting four parameters flexibly, we can adjust generating terrain shape suitably and produce ample physiognomy shape. We can describe physiognomy de tail because subdivision scheme has multi-scale character. The method can generate terrain simulation preferably and of fer an effective scheme for terrain simulation.