Simplicial complex augmentation framework for bijective maps
Simplicial complex augmentation framework for bijective maps
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DOI：
10.1145/3130800.3130895
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发表时间：
2017-11
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通讯作者：
Zhongshi Jiang;S. Schaefer;Daniele Panozzo
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文献类型：
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作者：
Zhongshi Jiang;S. Schaefer;Daniele Panozzo
双射贴图通常用于许多计算机图形和科学计算应用中，包括纹理、位移和凹凸贴图。然而，由于问题的全局性质，它们的计算在数值上具有挑战性，这使得标准平滑优化技术过于昂贵。我们建议使用一个支架结构，以减少这个具有挑战性的和全球性的问题，以一个局部的注入性条件。这种构造使我们能够受益于局部内射映射优化的最新进展，以有效地计算大规模双射映射（2D和3D），从而避免显式检测和避免碰撞的需要。我们的算法保证鲁棒地计算全局双射映射，无论是在2D和3D。为了证明其实用性，我们使用它来计算全局双射单个补丁参数化，将多个图表打包到单个UV域中，从现有模型中删除自交，并在防止自交的同时使3D对象变形。我们的方法实现简单、高效（比竞争方法快两个数量级）并且鲁棒，正如我们在具有超过一百个网格的参数化数据集的压力测试中所证明的那样。
Bijective maps are commonly used in many computer graphics and scientific computing applications, including texture, displacement, and bump mapping. However, their computation is numerically challenging due to the global nature of the problem, which makes standard smooth optimization techniques prohibitively expensive. We propose to use a scaffold structure to reduce this challenging and global problem to a local injectivity condition. This construction allows us to benefit from the recent advancements in locally injective maps optimization to efficiently compute large scale bijective maps (both in 2D and 3D), sidestepping the need to explicitly detect and avoid collisions. Our algorithm is guaranteed to robustly compute a globally bijective map, both in 2D and 3D. To demonstrate the practical applicability, we use it to compute globally bijective single patch parametrizations, to pack multiple charts into a single UV domain, to remove self-intersections from existing models, and to deform 3D objects while preventing self-intersections. Our approach is simple to implement, efficient (two orders of magnitude faster than competing methods), and robust, as we demonstrate in a stress test on a parametrization dataset with over a hundred meshes.