使用三維掃瞄器可以取得現實中物件的幾何資訊，且三維掃瞄器的輸出為點資料集合。爲點資料集合重構出其表面是三維電腦圖學中一項重要的研究領域。本篇論文提出了一個簡單的方法去重構出點模型的表面。我們使用以拉普拉斯為基礎的樣板網格，利用疊代的方式，建構出點資料集合的表面，且可以應用重新取樣的方式提高重構表面的品質。

大部分幾何處理的應用，都需要兩個或是多個模型的一對一對應關係。這些對應關係建立出來後，必需要能夠表現出原模型的特徵及形狀。且模型間的各部位必須要能夠有好的對應，例如腳對到腳，眼睛對到眼睛。大部分的應用也需要這些模型能夠以一致性模型的方式表現。利用對應關係，可以在模型間做形變，形狀混合之類的應用。本篇論文提出了一個架構，不僅可以重構點集合資料的表面，亦可以將其延伸至建立一致性的模型。為各模型間建立出一致性模型後，即可以做幾何處理的應用。

Today geometry of objects in real world can be obtained easily by scanning devices, and the output is always point data sets. The reconstruction of surface mesh from these point data sets is a vital and fundamental research in computer graphics. In this thesis, we propose a novel fitting method to reconstruct surface from given point models. To our algorithm, the input includes: 1) a selected laplacian-based template and 2) point data sets. The mesh surface of point models can be reconstructed by this novel fitting process, and high-quality surface can be acquired by further resampling.

In digital geometry processing, many applications such as morphing, deformation and texture transfer etc. require a bijective mapping between two or among more models. This mapping needs to express features and shape of original models, e.g. mapping legs to legs, eyes to eyes, and so on. Most of the applications require the models to be represented by compatible meshes. In this thesis, we also provide a novel framework for this cross-surface bijective mapping. Our framework is very flexible enough to handle meshes as well as point data sets. In contrast to previous works, this novel approach generates better reconstruction quality for cross-parameterized mesh surface.

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