根據對應歧異點集合之全域性表面對應

Abstract

在電腦圖學的領域中，許多應用都需要計算一個平滑且合理的表面對應。例如網 格間的屬性轉移、形狀混合，或是物體形變。其中一種計算對應的方式是將給予 的表面參數化到共同的基底模型，但若將表面切割成數塊區域並分別局部參數 化，區域間的分界線處會不平滑，因此必須對於不平滑處套用某些平滑演算法做 事後處理。本篇論文發表了一個透過基底模型做全域性的表面對應，而不需要使 用任何平滑演算法。主要概念是利用「離散瑞奇流」以及「物體間一致的保留形 體之錐形歧異點集合」來計算「平坦錐形度量」，並將此度量攤平在基底模型上 來做到表面對應。平坦錐形度量能保留原本表面的角度關係，並且可被想成是一 種攤平在基底模型的全域參數化結果。簡言之，我們提出一個新的概念透過基底 模型做全域性的表面對應。

In computer graphics, computing a smooth and reasonable surface correspondence or intersurface mapping is needed for applications such as mesh attributes transferring, shape blending, and object morphing. One of the methods for computing the correspondence is to parameterize the given surfaces to a common base-complex. However, the patch boundaries would not be smooth if surfaces are segmented and locally parameterized and hence some smoothing operations are normally applied as a post-processing. This thesis proposes a global inter-surface mapping based on the base-complex approach without the need of smoothing operation. The main idea is to make good use of discrete Ricci flow and the shape-preserving corresponding cone singularity set between surfaces to compute flat cone metrics, which is regarded as the common domain of the inter-surface mapping. The flat cone metric is conformal to the original surface and could be thought as a global parameterization on the common domain. To sum up, our framework provides a novel idea to map between surfaces via a common base-complex and global parameterization.