Analysis of the curve and surface structure in natural objects and its application for gemometric modeling

(1)曲线结构分析方法的发展作为分析曲线特性的一种方法，我们提出了曲率的对数分布图。利用这张图，将审美曲线系统地分为收敛型、发散型、等速型、发散-收敛型和收敛-发散型五种类型。此外，我们还开发了一种基于遗传算法和样条的曲线数据自动分割方法。该方法适用于具有奇异性的曲线数据。利用该方法，我们分析了自然和人工物体的许多特征，并证实了该方法的有效性。(2)自然物体、工艺物体、工厂物体的曲线结构分析我们收集和分析了许多自然物体和工艺物体的曲线，并阐明了曲线的特征。此外，我们还将其与工厂对象的特性进行了比较。结果表明，n .的曲线多数为发散型或等速型，更多的自然物和工艺品为发散型或等速型。同时也阐明了自然物体中很少有曲线是工厂物体中常用的收敛型曲线。(3)应用技术和外围技术的发展我们开发了一套用于逆向工程的曲线自动整流系统。该系统主要由以下几个步骤组成：曲面数据的测量和关键线数据的提取，曲线拟合，将数据划分为曲率单调曲线，分析曲线的特征，将曲线替换为视觉语言，重建关键线。我们还分析了逆向工程中生成曲线和曲面所需的多面体的面结构，并将面结构系统化为视觉语言。此外，我们还研究了汽车前罩形状元素与人类面部形状元素的相似性。因此，我们澄清了它们之间有许多相似的形状特征。少

(1) Development of the methods of analysis for curve structureAs a method for analyzing characteristics of curves, we proposed logarithmic distribution diagram of curvature. Using the diagram, aesthetic curves are systematized into five types: convergent type, divergent type, constant-speed type, divergent-convergent type and convergent-divergent type. Moreover, we developed a method of automatic segmentation for curve data using genetic algorithm and spline. This method is applicable for curve data with singularity. Using the methods, we analyzed many characteristics of natural and artificial objects and confirmed the usefulness of our methods.(2) Analysis of the curve structure of natural objects, craftwork objects, and factory objectsWe collected and analyzed many curves of natural objects and craftwork objects, and clarified the characteristics of the curves. Moreover, we compared the characteristics with those of factory objects. As a result, it was clarified that most curves of n … More atural objects and craftwork objects are divergent type or constant-speed type. And it was also clarified that few curves in natural objects are convergent type which is frequently used in factory objects.(3) Development of applicable and peripheral technologiesWe developed an automatic fairing system of curves for reverse engineering. This system is composed with following steps: measurement of surface data and extraction of key line data, curve fitting, dividing the data into curvature monotonic curves, analyzing the characteristics of the curves, replacing the curves into visual languages, and reconstruction of the key lines.We also analyzed the face structures of polyhedra that are needed for creating curves and surfaces in reverse engineering, and we systematized the face structures into visual languages. Moreover, we investigated the resemblance between shape elements of the front mask of cars and shape elements of the face of human beings. As a result, we clarified that there are many similar shape characteristics between them. Less