以碎形理論為基礎的程序化紋理合成之研究

Abstract

紋理合成（texturing）是電腦繪圖學（computergraphics）中的最重要 的研究領域之一。如果沒有應用紋理合成技術，電腦所繪的物體就無法逼 真（realistic）。程序化的紋理合成（procedural texture syn- thesis）方式是一種較精緻的方法。然而，卻很難找出紋理規則。在本論 文中，我們根據複數動力系統（complex dynamic system）裡，複數點在 Julia與Fatou set中的疊代（iteration）行為的圖形特性，特徵了兩個 特徵圖形-眼狀（eye-like spot）與河流狀（river-like至於紋理的對應 （texturemapping），我們設計一個兩階段（two-pass mapping）的對應 技術用以結合蝴蝶翅膀的紋理與蝴蝶翅膀的輪廓。並且設計一個直接對應 技術（direct texture mapping）用以結合所建構的羽毛與合成的紋理。 最後，我們呈現所有的實驗結果用以證明所有提出的方法的有效性與功能 性。 Texturing is one of the most important research fields in computer graphics. Computer generated images can not reach realism without employing texturing techniques. The procedural approach for texture synthesis is an elegant approach, but still an art form. In this thesis, we have an insight into the traits of iteration behaviors of the complex dynamical system to characterize two fundamental patterns: the eye-like spot resulting from the basin of attraction in the Fatou set and the river-stripe resulting from chaotic structure between basins of attraction. On texture mapping, we design a two-pass mapping technique to transform the whole texture pattern of a butterfly wing into the regarding contour. A elegant direct texture mapping technique also propsed to associate texels with points on surface of object. Additionally, a powerful modeling approach is developed to construct almost all kinds of branching objects flexibly and easily. Finally, we present some experimental results to show the effectiveness, efficiency and flexibility of our approaches.