Free-boundary linear parameterization of 3D meshes in the presence of constraints
Free-boundary linear parameterization of 3D meshes in the presence of constraints
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DOI：
10.1109/smi.2005.22
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发表时间：
2005-06
期刊：
影响因子：
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通讯作者：
Zachi Karni;C. Gotsman;S. Gortler
中科院分区：
文献类型：
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作者：
Zachi Karni;C. Gotsman;S. Gortler
具有圆盘拓扑的三维网格的线性参数化通常使用由Tutte和Floater开创的重心坐标方法来执行。这在参数化上强加了一个凸边界，这可能会显著扭曲结果。最近，几种方法显示了如何放松凸边界要求，同时仍然使用重心坐标公式。然而，这种松弛可能导致参数化中的其他伪影。在本文中，我们探索这些方法，并给出了一个一般配方的“自然”边界条件的家庭所谓的“三点”重心坐标。我们讨论了这些方法的缺点，并展示了如何使用迭代方案或精心制作的“虚拟边界”来纠正它们。最后，我们将展示这些方法如何轻松地适应解决约束参数化的问题。
Linear parameterization of 3D meshes with disk topology is usually performed using the method of barycentrie coordinates pioneered by Tutte and Floater. This imposes a convex boundary on the parameterization, which can significantly distort the result. Recently, several methods showed how to relax the convex boundary requirement while still using the barycentric coordinates formulation. However, this relaxation can result in other artifacts in the parameterization. In this paper we explore these methods and give a general recipe for "natural" boundary conditions for the family of so-called "three point" barycentric coordinates. We discuss the shortcomings of these methods and show how they may be rectified using an iterative scheme or a carefully crafted "virtual boundary". Finally, we show how these methods adapt easily to solve the problem of constrained parameterization.