Optimized Topological Surgery for Unfolding 3D Meshes
Optimized Topological Surgery for Unfolding 3D Meshes
复制标题
用于展开 3D 网格的优化拓扑手术
DOI：
10.1111/j.1467-8659.2011.02053.x
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发表时间：
2011
影响因子：
2.5
通讯作者：
and H.-C. Yen
中科院分区：
文献类型：
--
作者：
S. Takahashi;H.-Y. Wu;S. H. Saw;C.-C. Lin;and H.-C. Yen
构建一个3D纸工艺品模型从它的展开一直是有趣的孩子和成人，因为我们可以在现实世界中再现虚拟3D模型。然而，促进纸工艺的构建过程仍然是一个具有挑战性的问题，特别是当输入模型的形状复杂时，它的表面曲率变化很大。本文提出了一种新的启发式方法来展开三维三角形网格而不产生任何形状畸变，因此我们可以通过简单的原子操作来构建三维纸工艺模型，即在二维展开的周围粘合边界边缘。我们的方法受到拓扑外科概念的启发，其中展开的封闭表面的边界边缘的外观可以使用符号表示进行编码。为了完全简化纸工艺的构建过程，我们开发了一种基于遗传的算法，用于将3D网格展开为单个连接的补丁，同时优化纸张的使用和该补丁形状的平衡。包括几个示例和用户研究，以证明所提出的方法适用于广泛的3D三角形网格。
Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new heuristic approach to unfolding 3D triangular meshes without any shape distortions, so that we can construct the 3D papercraft models through simple atomic operations for gluing boundary edges around the 2D unfoldings. Our approach is inspired by the concept of topological surgery, where the appearance of boundary edges of the unfolded closed surface can be encoded using a symbolic representation. To fully simplify the papercraft construction process, we developed a genetic‐based algorithm for unfolding the 3D mesh into a single connected patch in general, while optimizing the usage of the paper sheet and balance in the shape of that patch. Several examples together with user studies are included to demonstrate that the proposed approach works well for a broad range of 3D triangular meshes.