河床斷面之碎形重建

本研究以仿射轉換並配合碎形理論來建立空間序列之叠代函數系統，由此一系統所得之碎形內揷函數來對一河床斷面予以碎形重建。該法所著重者，係强調資料本身之不規則性及複雜性的整體保存。濁水溪的一河床斷面被用於此一技術的探討，文中針對量測解析度對幾何要素之影響予以敏感度分析，繼而給予單一河床剖面之碎形重建的實際計算，同時深入分析重建斷面對幾何要素所產生的影響。研究結果顯示：使用碎形內揷技術來重建空間序列是可行的，且能在不同尺度間相互變換，又碎形內揷函數或可提供在低解析度下之幾何要素予以校正的機會。因此，該技術可做爲此一相關領域於尺度變換及重建其內在結構的嶄新分析工具。

關鍵字

仿射轉換；碎形理論；叠代函數系統；碎形內揷；碎形重建

並列摘要

Combining the affine transformation with the fractal theory, an iterated function system (IFS) is established for a spatial series. By fractal interpolation function (FIF), the river-bed profile can be reconstructed. This methodology is focused on the preservation of irregularity and complexity. A river-bed profile in Cho-Shui river is selected for the study. Firstly, the sensitivity analysis is used to explore the effect of geometric elements under different measured resolutions. Secondly, a practical fractal reconstruction of single river-bed profile is implemented and its geometric elements are also analyzed. The results show that it is possible to reconstruct a spatial series by fractal interpolation technique and the different scalings can be also transformed. Besides, the FIF gives an opportunity to correct the geometric elements under the low resolution. As a result, the FIF technique can be served as a new analyzer in the domain of scaling transformation and reconstruction of internal structure.

並列關鍵字

Affine transformation ； Fractal theory ； Iterated function system ； Fractal interpolation ； Fractal reconstruction

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