三維曲面的破洞修補與平滑化

Hole-filling and Smoothing on 3D surfaces

曹祐豪(Yu-Hao Tsao)

指導教授 ： 林文偉

國立交通大學/理學院/應用數學系暨研究所/碩士(2018年)

摘要

在三維的模型掃描中，我們藉由掃描所得到的模型會有所破損幾乎是不可避免的。為了使得模型的完整，破洞的修補就變的是必須的。在這裡，我們首先根據曲面破洞周圍的點來產生切平面並將其邊界映射上去，接著在平面上生成新的點與網格，最後在藉由Bezier patches反算新的點在三維空間中的座標。再來，我們對補完洞的曲面進行平滑化，使得我們在掃描時因為雜訊所導致的凹凸不平減少。在這之後，對於一個三維中的曲面，我們可以將曲面保角映射到一個單位圓盤上。藉由這樣的映射，我們可以在圓盤上重鋪網格在映射回到曲面，使得曲面的點數減少也使得網格的分部均勻且平滑。

關鍵字

三角網格 ； 破洞修補 ； 曲面平滑 ； 保角映射 ； 網格重鋪

並列摘要

In the three-dimensional model scan, it is almost inevitable that the model we obtained by scanning will be damaged. In order to make the model complete, the repair of the hole becomes necessary. In this thesis, we first generate a tangent plane based on the points around the hole of the surface and map its boundaries, then generate new vertices and grids on the plane, and finally compute the three-dimensional coordinate of new vertices by Bézier patches. After we fill holes, we smooth the surface, which caused us to reduce the unevenness caused by noise during scanning. For a surface in 3D, we can map the surface conformal to a unit disk. With such a mapping, we can re-lay the mesh on the disc to inverse map to the surface, so that the number of vertices on the surface is reduced and the mesh is near uniform and smooth.

並列關鍵字

Triangular mesh ； Hole filling ； Surface Smoothing ； Conformal Mapping ； Re-meshing

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