Developability of Triangle Meshes
Developability of Triangle Meshes
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DOI：
10.1145/3197517.3201303
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发表时间：
2018-08-01
影响因子：
6.2
通讯作者：
Crane, Keenan
中科院分区：
文献类型：
--
作者：
Stein, Oded;Grinspun, Eitan;Crane, Keenan
可展开表面是那些可以通过平滑地弯曲平板而无需拉伸或剪切而制成的表面。我们引入了三角形网格可展性的定义，它准确地捕捉了平滑可展表面的两个关键属性，即可展平性和直线标线的存在。这个定义为可展曲面建模中的算法提供了一个起点——我们考虑一种变分方法，将给定的网格驱动到由规则接缝曲线分隔的可展片。计算相当于在顶点星的支持下对能量进行梯度下降，而不需要显式地对补丁进行聚类或识别接缝。我们简要探讨了可开发设计和制造的应用。
Developable surfaces are those that can be made by smoothly bending flat pieces without stretching or shearing. We introduce a definition of developability for triangle meshes which exactly captures two key properties of smooth developable surfaces, namely flattenability and presence of straight ruling lines. This definition provides a starting point for algorithms in developable surface modeling-we consider a variational approach that drives a given mesh toward developable pieces separated by regular seam curves. Computation amounts to gradient descent on an energy with support in the vertex star, without the need to explicitly cluster patches or identify seams. We briefly explore applications to developable design and manufacturing.