%0 Journal Article
%T Representation and Rendering of General Julia Sets Based on Tri-Dimensional Polynomial Maps<br>基于三维多项式映射的广义Julia集表示与绘制
%A CHENG Jin
%A TAN Jian-Rong
%A <br>程锦
%A 谭建荣
%J 软件学报
%D 2006
%I 
%X 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.
%K tri-dimensional polynomial map
%K equivariant map
%K rotational symmetry
%K general Julia sets
%K tetrahedron group
%K octahedron group
%K ray-tracing volume rendering algorithm
%K escaping distance<br>三维多项式映射
%K 等变映射
%K 旋转不变对称性
%K 广义Julia集
%K 四面体群
%K 八面体群
%K 光线跟踪体绘制算法
%K 逃逸距离
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=AAB67BB65756BDA4&yid=37904DC365DD7266&vid=BCA2697F357F2001&iid=DF92D298D3FF1E6E&sid=E0EA1E85C42D382D&eid=0DDE48E4C6ED47B1&journal_id=1000-9825&journal_name=软件学报&referenced_num=4&reference_num=17