近年以高精度儀器掃描而得的高密度點式物體得到越來越多的關注，這些取自真實世界的點式物體在電腦圖學、科學繪圖、地誌、數位典藏與逆向工程等領域被廣泛的研究著。本篇論文提出點式物體上的一致性參數化與相容式取樣法，我們所面臨的基本問題是如何在沒有連接關係的條件下將輸入的點式物體嵌入到共同的參數域上面。給定一個只有少數頂點的基礎網面，我們在輸入的點式物體上透過方向場的概念以簡單有效的方式找出一組合適的路徑將此點式物體分割成數塊區域。取得一致分割的區塊以後，我們藉由二維平面三角形的參數化方式找出點對點的對應關係，以重新取樣的方式達到高效能的對應過程。實驗結果顯示我們的方法是穩定的，即使物體間的幾何形狀相差甚鉅我們仍然可以處理的很好；我們亦將此方法應用到點式物體的變形技術上製作出數個美觀的變形動畫。

In recent years, dense point models scanned from high-precision digital scanner devices have received a growing amount of attention. The point models captured from real-world objects have been extensively studied in many research areas such as computer graphics, scientific visualization, topography, digital archive, and reverse engineering. In this thesis, we propose a novel consistent parameterization and compatible re-sampling approach for 3D point models. The fundamental problem of consistent parameterization is how to consistently embed the input point models into a common parametric domain without any connectivity information. Given a base mesh with only a few vertices, we consistently decompose the input point models into several patches by finding a set of proper paths. We propose a novel approach to trace these paths based on direction fields. Once the consistent patches are obtained, we embed them onto a 2D triangle to obtain the correspondence. In the next process, an efficient approach is proposed to consistently re-sample the corresponding parameterizations. The experimental results show that the proposed approach is robust. Even the points clouds have large different in shape, the proposed approach can handle it well. In addition, we apply the proposed approach to the point morphing and several examples of aesthetically pleasing morphs are demonstrated.

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