离散曲面间的可逆调和映射
Reversible Harmonic Maps between Discrete Surfaces
摘要：
三角形网格之间的信息传递在计算机图形学和几何处理中具有重要意义。为了促进该过程，通常需要在两个网格之间的平滑且准确的映射。虽然这种映射有时可以在近似等距网格之间计算，但具有不同几何形状的网格的更一般情况仍然具有挑战性。我们提出了一种新的方法，三角形网格之间的直接映射计算没有映射到一个中间域，优化的和谐性和可逆性的前向和后向映射。我们的方法是通用的，它可以接收作为输入的信息，例如点地标，密集的地图或功能图，并在多样性的几何形状，它可以应用。我们证明，我们的地图表现出较低的共形失真比国家的最先进的，同时成功地正确映射输入形状的关键功能。
英文摘要：
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g. point landmarks, a dense map or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state-of-the-art, while succeeding in correctly mapping key features of the input shapes.
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