Non-manifold level sets
Non-manifold level sets
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DOI：
10.1145/2816795.2818100
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
Nathan Mitchell;Mridul Aanjaneya;Rajsekhar Setaluri;Eftychios Sifakis
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文献类型：
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作者：
Nathan Mitchell;Mridul Aanjaneya;Rajsekhar Setaluri;Eftychios Sifakis
水平集作为一种高度通用的隐式曲面表示方法，在建模和动态仿真等图形应用中得到了广泛的应用。然而，水平集通常被认为是有限的，相比显式网格，在他们的能力，以表示域薄的拓扑特征（如窄缝和间隙），甚至更糟的是，材料重叠。具有这种特征的几何形状可能来自于允许偶尔自相交的建模工具、通过设计创建窄或零宽度切口的裂缝建模算法，或者作为可变形物体的碰撞处理流水线中的瞬态。如果栅格大小无法解析薄要素，则将此类模型转换为级别集可能会更改其拓扑。我们认为，这种表面上的限制是不是一个固有的缺陷的隐式表面的概念，但用于存储水平集值的标准笛卡尔格的附带后果。我们建议将有符号距离值存储在规则的六面体网格上，该网格可以具有多个并列的立方元素和非流形分叉以适应非平凡的拓扑结构。我们展示了如何从方便的替代几何表示系统地生成这样的非流形水平集。最后，我们展示了如何这种表示可以促进快速和强大的自碰撞体积弹性变形体的模拟处理。
Level sets have been established as highly versatile implicit surface representations, with widespread use in graphics applications including modeling and dynamic simulation. Nevertheless, level sets are often presumed to be limited, compared to explicit meshes, in their ability to represent domains with thin topological features (e.g. narrow slits and gaps) or, even worse, material overlap. Geometries with such features may arise from modeling tools that tolerate occasional self-intersections, fracture modeling algorithms that create narrow or zero-width cuts by design, or as transient states in collision processing pipelines for deformable objects. Converting such models to level sets can alter their topology if thin features are not resolved by the grid size. We argue that this ostensible limitation is not an inherent defect of the implicit surface concept, but a collateral consequence of the standard Cartesian lattice used to store the level set values. We propose storing signed distance values on a regular hexahedral mesh which can have multiple collocated cubic elements and non-manifold bifurcation to accommodate non-trivial topology. We show how such non-manifold level sets can be systematically generated from convenient alternative geometric representations. Finally we demonstrate how this representation can facilitate fast and robust treatment of self-collision in simulations of volumetric elastic deformable bodies.