變形的演算法大致上可以分為兩個步驟，第一為找出原始模型和目標模型之間的對應關係或是建立一個同時包含有原始模型和目標模型之特性的資料結構，第二個步驟為相對應點之間的座標值內插。通常，對應點之間的座標值內插都是採用線性內插的方式，本研究的重點放在兩輸入模型之間的對應關係。
本研究提出一種創新的元件對應方式，來讓系統達到自動地找出變形過程間的相對應關係，所要處理的資料型態為封閉且拓撲結構為two-manifold之三維網格物體。本研究所提出的演算法大致上可分為三個部份，分別是元件擷取、元件分析與元件對應。首先，先將系統的輸入模型根據幾何和拓撲特性來萃取出模型中有意義的部份。接著，我們將取出的元件加以分析，可得到各元件的相關特性資訊，利用這些資訊來將兩個輸入模型做對齊的動作，以免除掉模型之間所設定之方位不同的影響，並且更進一步的將兩輸入模型間之各元件的特性來做比較，具有相似特性的就設定為相對應的部分。根據所提出之演算法，可以利用被切割好後的元件所具有的特性來找出特性相似的元件，並且指定其為相對應的部份，以達到較佳的自動對應效果。

The process of morphing can be divided into two steps; to find out the correspondence between source and target models or create a structure sharing both the characteristics of the input models and to transform the vertices smoothly from source to target object by interpolations. In the thesis, a novel method for mapping the components between two closed manifold genus-0 polyhedral models was proposed for mesh mapping. The proposed algorithm can be divided into three steps which are component extraction, component analyzing, and component matching. The first step is to divide both of the input models into components based on geometric and topological characteristics and create their corresponding component tree. In the second step, find the principal component for both of the models and make the two principal components in alignment. For the last step, the components of the two component trees are mapped according to their properties. Case studies were shown that the proposed algorithm is performed well, especially for these objects with protruding features.

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