三維多面體的形變技術

Abstract

在三維空間中，一個任意形狀的物體漸漸轉變成另一個不同形狀物體的過程，我們稱之為三維物體形變(3D metamorphosis or 3D morphing)。在目前已經發表的技術中，尚未提供使用者一個有效率的方法來指定物體形變過程中的對應關係。因此，本論文的主要目的是要提供一簡單且有效的使用者掌控介面，先由使用者給定少數物體特徵的相對應點，系統將自動產生其餘的對應關係，進而完成形變的過程。我們提出了突出特徵點的偵測方法及兩種不同的區塊切割方式，依照偵測的結果對物體表面區塊進行特徵切割法或平均切割法，有效的將物體表面區塊切開。對於兩個不同物體實施同樣的切割過程，所產生的區塊集合之間存在著一對一的對應關係，完成物體初步的對應工作。接下來，利用harmonic map和狄勞尼三角化(Delaunay triangulation)程序將相對應的區塊在二維區域內做合併的動作，使得相對的區塊內能有相同的網格架構，達成點對應的目的。最後利用線性內差計算出所有點在形變過程中的位置，將結果顯像出來，便完成了物體的形變過程。

The metamorphosis or the 3D morphing is the process of continuously transforming one object into another. Many morphing techniques for polygonal objects have been proposed. Most techniques suffer from the complicated human effort involved in setting up the vertex correspondence necessary for the morphing. In this thesis, we have tried to alleviate such human intervention. In the proposed morphing system, the user is required to specify only a few vertex correspondences of the two objects. And then based on the given vertex correspondences, object’s boundary meshes are subdivided into four patches each of which are recursively subdivided in-correspondence until certain conditions are reached. As a result, the source and target meshes are subdivided into patches that are in one-to-one correspondence. The patches are subdivided in a way that features of the meshes can be maintained To attain the correspondence of all the vertices, Harmonic map and Delaunay triangulation are used to establish the vertices that are in common topology and in one-to-one correspondence inside each pair of correspondent patches. In morphing from the source to target mesh, a traditional linear interpolation is used. Finally, the smooth morphing result will be process between the two objects.