In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micr...In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.展开更多
In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system o...In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved, the theorem of fractal dimension of fractal interpolated surface is derived, and the case that practical data are used to interpolate fractal surface is studied.展开更多
原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面...原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面、水泥路面、比利时路面和砂石路面的三维路面不平度;基于分形理论,采用迭代函数法重构这四种路面谱;结合路面不平度的统计特性评价指标和分形维数对四种路面的原始谱和重构谱进行评价。研究结果表明:重构前、后路面谱的平均值、标准差、峰度系数以及分形维数变化范围在±5%以内,除水泥路面的偏态系数变化范围均在±9%以内,重构路面谱与原始谱具有一致性;重构路面谱保持了原始路面的结构特性,并具有路面的细微结构。展开更多
基金Projects(50975092,50805052,U0834002) supported by the National Natural Science Foundation of ChinaProject(9151030101000007) supported by the Natural Science Foundation of Guangdong Province,ChinaProject(2009ZZ0041) supported by the Fundamental Research Funds for the Central Universities in China
文摘In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.
文摘In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved, the theorem of fractal dimension of fractal interpolated surface is derived, and the case that practical data are used to interpolate fractal surface is studied.
文摘原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面、水泥路面、比利时路面和砂石路面的三维路面不平度;基于分形理论,采用迭代函数法重构这四种路面谱;结合路面不平度的统计特性评价指标和分形维数对四种路面的原始谱和重构谱进行评价。研究结果表明:重构前、后路面谱的平均值、标准差、峰度系数以及分形维数变化范围在±5%以内,除水泥路面的偏态系数变化范围均在±9%以内,重构路面谱与原始谱具有一致性;重构路面谱保持了原始路面的结构特性,并具有路面的细微结构。
