An intrinsic algorithm for computing geodesic distance fields on triangle meshes with holes

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• 作者：Dao T.P. Quynh^a ; ^{daot0006@e.ntu.edu.sg} ; Ying He^a ; ^{yhe@ntu.edu.sg} ; Shi-Qing Xin^a ; ^{sqxin@ntu.edu.sg} ; Zhonggui Chen^b ; ^{chenzhonggui@xmu.edu.cn}
• 关键词：Discrete geodesics ; Triangle mesh ; Global optimization ; Geodesic distance field ; Intrinsic algorithm
• 刊名：Graphical Models
• 出版年：2012
• 期刊代码：130_15240703
• 类别：cp
• 出版时间：July, 2012
• 卷：74
• 期：4
• 页码：209-220
• 文件大小：2271 K

摘要

As a fundamental concept, geodesics play an important role in many geometric modeling applications. However, geodesics are highly sensitive to topological changes; a small topological shortcut may result in a significantly large change of geodesic distance and path. Most of the existing discrete geodesic algorithms can only be applied to noise-free meshes. In this paper, we present a new algorithm to compute the meaningful approximate geodesics on polygonal meshes with holes. Without the explicit hole filling, our algorithm is completely intrinsic and independent of the embedding space; thus, it has the potential for isometrically deforming objects as well as meshes in high dimensional space. Furthermore, our method can guarantee the exact solution if the surface is developable. We demonstrate the efficacy of our algorithm in both real-world and synthetic models.