分形插值曲面理论及其应用<sup>*</sup>

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分形插值曲面理论及其应用^*

基金项目: * 首届国家杰出青年科学基金,国家教委跨世纪人才专项基金

Institute of Fractal Mechanics, Beijing Graduate School, China University of Mining and Technology, Beijing 100083, P.R.China

摘要: 本文叙述了分形曲面的生成原理,给出了分形插值曲面的计算公式,证明了分形插值曲面迭代函数系唯一性定理,导出了分形插值曲面的维数定理,并应用实际数据进行了分形插值曲面的实例研究。
- 分形几何 /
- 高维分形 /
- 分形插值曲面 /
- 分形维数
Abstract: In this paper the principle of construction of a fractal surface is introduced,interpolation functions for a fractal interpolated surface are discussed,the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved,the theorem of fractal dimension of fractalinterpolated surface is derived,and the case that practical data are used to interpolate fractal surface is studied.
- fractal geometry /
- higher dimension fractals /
- fractal interpolated surface /
- fractal dimension

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