圆明亮琢型几何结构的研究  

Research of Geometric Structure of Round Brilliant Cut

作　　者：黄翰强 卢振坤[2] 陈炳忠[2] 

机构地区：[1]梧州光学仪器厂,广西梧州543002 [2]梧州学院,广西梧州543002

出　　处：《宝石和宝石学杂志》2014年第1期56-61,共6页Journal of Gems & Gemmology

基　　金：广西科技术开发项目(桂科攻11107007-4);梧州市科技术开发项目(201101049)

摘　　要：采用数学方法和可视化计算机软件Pro/E与MATLAB处理圆明亮琢型切工参数与该琢型其它几何元素之间的定量关系。首先,用数学语言描述托尔可夫斯基琢型亭部演化的规律。随后,用分析表达式和图形表达以下几个问题的新见解:(1)星刻面倾角不能随意取值,它是某些切工参数的函数;(2)腰棱厚度和腰棱总面积能够用数学公式定量描述;(3)冠部俯视图的变化服从一定的数学约束条件,认为台宽比评定中的"弧度法"不可行。分析结果表明将现代光学分析和MATLAB等计算机技术结合,可用于宝石最优化设计。Geometrical elements （point, line, plane, etc. ） of round brilliant cut exist a func- tional relation, which can be expressed through analytic expressions. In this paper, quantita- tive relation of round brilliant cut, including cut parameters and the other geometric ele- ments, is processed by mathematical method, visual computer software Pro/E and MAT- LAB. Evolution of pavilion of round brilliant cut is visualized and analyzed quantitatively by Pro/E and MATLAB. The technical standards of the former Soviet Union put forward by Tolkowsky and Bruce Harding, are unified in our mathematical framework. Positive and in- verse function relationship of β-μ is revealed. Thus, gemstone optics and geometry are linked. Strictly speaking, round brilliant cut is an aesthetic effect of optical prism. Effect of the light and the material are embedded through the angle of components. Mathematical formula of star facet inclination （γ） which is a function of table size（M）, crown angle（β） and crown girdle facets（β） are derived. Star facet inclination（γ） can not take any value freely. Therefore, it corrected Tolkowsky＇s biased viewpoint. The thickness and total area of waist can be quantitatively described by mathematical formula. In the paper, brain is minimum thickness of waist ridge which meets the structuralmechanical demand, and ensures that the finished product is not easy to be broken. Three geometrical forms of crown vertical view are shown by using mathematical formu- las and visualizations, and radian method which is one of the detection methods to determine the table size is denied.

关 键 词：圆明亮琢型 几何结构 

分 类 号：TS93[轻工技术与工程]