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Biharmonic Distance
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DOI：10.1145/1805964.1805971.png)
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摘要
En 中文
Measuring distances between pairs of points on a 3D surface is a fundamental problem in computer graphics and geometric processing. For most applications, the important properties of a distance are that it is a metric, smooth, locally isotropic, globally shape-aware, isometry-invariant, insensitive to noise and small topology changes, parameter-free, and practical to compute on a discrete mesh. However, the basic methods currently popular in computer graphics (e.g., geodesic and diffusion distances) do not have these basic properties. In this article, we propose a new distance measure based on the biharmonic differential operator that has all the desired properties. This new surface distance is related to the diffusion and commute-time distances, but applies different ( inverse squared) weighting to the eigenvalues of the Laplace-Beltrami operator, which provides a nice trade-off between nearly geodesic distances for small distances and global shape-awareness for large distances. The article provides theoretical and empirical analysis for a large number of meshes.
Keyword:
Algorithms
Experimentation
Theory
Shape analysis
mesh processing
mesh distance
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