考慮原始概率向量定義三維IFSP 的規(guī)范形式,并給出了相應(yīng)規(guī)范變換計算的定理證明。運用到三維分形變形的實例表明了該算法研究的必要性,使得變形過程保持了仿射不變性,進一步充實了三維變形理論,為其發(fā)展及應(yīng)用提供了堅實的基礎(chǔ)。
關(guān)鍵詞: 分形變形;迭代函數(shù)系統(tǒng);三維規(guī)范變換
2 (The Key Laboratory of Contemporary Design and Integrated Manufacturing Technology,
Ministry of Education, Northwestern Polytechnic University, Xi’an 710072) Abstract At first the three-dimensional IFSP canonical form with original probability vector is defined, and then the theorem about the calculation of the corresponded canonical transformation is given. Experiments on morphing of three-dimensional fractal attractors with interpolation show
the necessity of this algorithm’ research and it makes the morphing process keep affine stability. This algorithm will enrich the theory of the three-dimensional morphing ulteriorly and provide the foundation of its developments and applications.
Keywords fractals’ morphing; IFS; the 3D canonical transformation