提出新型网格表示法，让计算机能准确建模埃舍尔式不可能物体。
Meschers: Geometry Processing of Impossible Objects
- 基于离散外微分几何，构建可处理的不可能物体网格
- 支持平滑、光照等下游图形操作，避免切割或扭曲带来的问题
- 适用于逆向渲染，适合艺术创作与视觉研究
不可能物体是人类可感知但无法在现实中存在的几何构造，长期以来吸引着视觉艺术、认知科学与计算机图形学的关注，但尚未有令人满意的计算机表示方法。以往方法将不可能物体嵌入三维空间，通过切割或沿深度轴弯曲实现，但切割会改变局部几何，影响后续平滑等操作；弯曲则使光照重建变得困难，且可能破坏距离计算等几何运算。为此，本文提出 Meschers，一种可精确表示类似埃舍尔木刻中不可能结构的网格模型。该方法建立在离散外微分几何理论基础上，支持平滑、光照、距离计算等标准几何处理操作。我们还展示了其在逆向渲染中的应用，并与切割和弯曲表示法进行了对比，验证了其有效性与实用性。
原文摘要 · Abstract (English)
Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.
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