文档介绍：1 /11 Koch 分形曲线与面积计算分形图形的基本特征正交矩阵与正交变换 Koch 分形曲线 Koch 分形雪花面积计算???? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 2 /11 分形(Fractal) 图形最基本特征是自相似性,即某一对象的局部与整体在形态、功能、信息、时间、空间等方面具有相似性。在自相似的图形中,局部只是整体的缩影,而整体则是局部的放大。适当的放大或缩小几何尺寸, 整个结构并不改变。分形概念始现于数学家曼德勃罗 1967 年发表于美国《科学》杂志一篇论文“英国海岸线有多长”。 Mandelbrot 1924- 2010 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 算法描述: 将一条直线段三等分, 删除中间三分之一部分, 用一等边三角形的腰代替, 形成四条线段的折线. 每一线段重复以上操作,迭代产生曲线 K n Koch 分形曲线 Koch 分形曲线 Koch 岛 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ????????3/ cos 3/ sin 3/ sin 3/ cos????:对向量做旋转变换. P 1P 2P 1P 2Q 1Q 2Q 3 (1) Q 1← P 1 + (P 2-P 1 )/3; Q 3← P 1 + 2(P 2-P 1 )/3; (2) Q 2← Q 1 + (Q 3-Q 1)×A T; (3) P 5← P 2 ; P 2← Q 1 ; P 3← Q 2 ; P 4← Q 3. 基本算法 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 5 /11 ???????????? cos sin sin cos A ?????? 2 1x x??????????????????? cos sin sin cos 2 1xx ????????????????????1 00 1 212 1xxx x??????0 1????????? sin cos ??????1 0 ?)0,1(?)1,0(?????????? cos sin ?????????????? 2 1 cos sin sin cosx x???? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 6 /11 f