基于弧长参数化的曲面W-M分形插值  

W-M fractals interpolation with freeform surface based on arc-length parameterization

作　　者：刘远东[1] 王清辉[2] 刘林[1] 熊巍[1] 

机构地区：[1]华南理工大学设计学院,广东广州510006 [2]华南理工大学机械与汽车工程学院,广东广州510640

出　　处：《图学学报》2012年第6期59-64,共6页Journal of Graphics

基　　金：广东省自然科学基金资助项目(9151030101000007);国家自然科学基金资助项目(50975092)

摘　　要：论文提出了一种以Weierstrass-Mandelbrot分形(简称W-M分形)与参数曲面相合成来实现分形曲面的数字化建模的方法。指出了在参数曲面上合成W-M分形以及实施弧长参数化计算的必要性;论述了弧长参数化的具体算法,并用此方法实现了W-M分形与参数曲面的合成;在此基础上,提出了两向异性分形曲面的一种建模方法,实现了参数曲面上进行两向异性W-M分形的插值模拟。A method of modeling W-M fractal freeform surfaces by superposing W-M fractals on parametric surfaces is proposed in this work.First,the significance of superposing W-M fractals with parametric curves and surfaces is pointed out;then the importance of utilizing arc-length parameterization for the superposing is described,and followed by our specific algorithm with which the fractal simulation with freeform surfaces is achieved;at the last section,an anisotropic approach for presenting freeform fractal surfaces is developed and with demonstrated graphics simulation.

关 键 词：分形 弧长参数化 参数曲面 两向异性 

分 类 号：TB24[一般工业技术—工程设计测绘]