主页期刊介绍编委会编辑部服务介绍道德声明在线审稿编委办公English
2020-2021年专刊出版计划 微信服务介绍 最新一期:2020年第10期
     
在线出版
各期目录
纸质出版
分辑系列
论文检索
论文排行
综述文章
专刊文章
美文分享
各期封面
E-mail Alerts
RSS
旧版入口
中国科学院软件研究所
  
投稿指南 问题解答 下载区 收费标准 在线投稿
程锦,谭建荣.基于三维多项式映射的广义Julia集表示与绘制.软件学报,2006,17(7):1561-1570
基于三维多项式映射的广义Julia集表示与绘制
Representation and Rendering of General Julia Sets Based on Tri-Dimensional Polynomial Maps
投稿时间:2004-07-16  修订日期:2005-07-11
DOI:
中文关键词:  三维多项式映射  等变映射  旋转不变对称性  广义Julia集  四面体群  八面体群  光线跟踪体绘制算法  逃逸距离
英文关键词:tri-dimensional polynomial map  equivariant map  rotational symmetry  general Julia sets  tetrahedron group  octahedron group  ray-tracing volume rendering algorithm  escaping distance
基金项目:Supported bythe National Natural Science Foundation of China under Grant Nos.60375020,50305033(国家自然科学基金);the National Grand Fundamental Research 973 Program of China under Grant Nos.2004CB719402,2002CB312106(国家重点基础研究发展规划(973));the Specialized Research Fou
作者单位
程锦 浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027 
谭建荣 浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027 
摘要点击次数: 3473
全文下载次数: 2956
中文摘要:
      研究了基于三维多项式映射的三维广义Julia集表示方法.从理论上分析并证明了三维多项式映射满足等变的条件,精确地给出了关于正四面体群和正八面体群具有旋转不变对称性的两类三维等变映射的具体公式,在此基础上讨论并证明了三维多项式映射的广义Julia集所具有的性质.提出了基于逃选距离色彩调配的光线跟踪体绘制算法,对给定三维空间中属于Julia集的离散点根据其逃逸距离赋予颜色和不透明度,并采用光线跟踪法进行体绘制.实验结果表明,利用三维多项式映射来构造三维Julia集,不仅可以根据映射的性质预知Julia集的总体结构特征,并且能够通过调控映射的参数来获得多种具有不同旋转对称结构的Julia集,因而有效地克服了现有三维分形集生成方法所构造的分形集包含信息量少、形状结构单一和分形形状无法预测等缺陷.进一步地,三维多项式映射可以应用于其他三维分形的构造,从而为三维分形的生成提供一个新的有效途径.
英文摘要:
      A new approach for the representation of 3D general Julia sets is put forward on the basis of tri-dimensional polynomial maps. The condition for a 3D polynomial map to be equivariant is theoretically analyzed and proved. The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial maps are discussed and proved. A ray-tracing volume rendering algorithm, which defines the color and opacity of every discrete point within a Julia set according to its escaping distance, is proposed in order to acquire high quality 3D fractal images. Experimental results demonstrate that the approach of generating 3D Julia sets from 3D polynomial maps not only enables us to predict the characteristics of Julia sets according to the properties of the maps, but also makes it possible for us to obtain various kinds of Julia sets with different rotational symmetries by altering the parameters of the maps. Consequently, drawbacks such as monotone structure of the resulting fractals and inability to predict fractal shape in the existing methods for generating 3D fractal sets can be effectually avoided. Furthermore, the method of generating 3D Julia sets by 3D polynomial maps can be applied to the construction of other 3D fractals, and hence would result in a different perspective for the generation of 3D fractals.
HTML  下载PDF全文  查看/发表评论  下载PDF阅读器
 

京公网安备 11040202500064号

主办单位:中国科学院软件研究所 中国计算机学会 京ICP备05046678号-4
编辑部电话:+86-10-62562563 E-mail: jos@iscas.ac.cn
Copyright 中国科学院软件研究所《软件学报》版权所有 All Rights Reserved
本刊全文数据库版权所有,未经许可,不得转载,本刊保留追究法律责任的权利