论文标题
四边形布局沉浸：表面四边形布局的数学上等效表示
The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout
论文作者
论文摘要
表面上的四边形布局在纹理映射中很有价值，对于四边形网格和拟合花纹而言至关重要。先前的工作已经表征了这样的布局，例如表面上的特殊度量，或具有有限轨迹的Meromorormormormormormormorormormormormorormorric差异差异。在这项工作中，表面四边形布局的特征是特殊的沉浸在表面切割到欧几里得平面中的特殊浸入。我们将其称为四边形布局沉浸。这种特征虽然以平滑的拓扑为生，但自然而然地将分段线性表示。因此，它在数学上描述并概括了整数网格图，这些图形在计算机图形设置中很常见。最后，通过在感兴趣的表面上提取四边形布局来证明表示形式的效用。
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic quartic differential with finite trajectories. In this work, a surface quadrilateral layout is alternatively characterized as a special immersion of a cut representation of the surface into the Euclidean plane. We call this a quad layout immersion. This characterization, while posed in smooth topology, naturally generalizes to piecewise-linear representations. As such, it mathematically describes and generalizes integer grid maps, which are common in computer graphics settings. Finally, the utility of the representation is demonstrated by computationally extracting quadrilateral layouts on surfaces of interest.
