Open AccessProceedings Article
Accurate Computation of Geodesic Distance Fields for Polygonal Curves on Triangle Meshes
David Bommes,Leif Kobbelt +1 more
- pp 151-160
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TLDR
This work generalizes the algorithm originally proposed by Surazhsky et al. and inserts new vertices at critical locations on the mesh such that the final piecewise linear interpolant is guaranteed to be a faithful approximation to the true geodesic distance field.Abstract:
We present an algorithm for the efficient and accurate computation of geodesic distance fields on triangle meshes. We generalize the algorithm originally proposed by Surazhsky et al. [1]. While the original algorithm is able to compute geodesic distances to isolated points on the mesh only, our generalization can handle arbitrary, possibly open, polygons on the mesh to define the zero set of the distance field. Our extensions integrate naturally into the base algorithm and consequently maintain all its nice properties. For most geometry processing algorithms, the exact geodesic distance information is sampled at the mesh vertices and the resulting piecewise linear interpolant is used as an approximation to the true distance field. The quality of this approximation strongly depends on the structure of the mesh and the location of the medial axis of the distance field. Hence our second contribution is a simple adaptive refinement scheme, which inserts new vertices at critical locations on the mesh such that the final piecewise linear interpolant is guaranteed to be a faithful approximation to the true geodesic distance field.read more
Citations
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Geodesics in heat: A new approach to computing distance based on heat flow
TL;DR: The heat method for computing the geodesic distance to a specified subset (e.g., point or curve) of a given domain is introduced and numerical evidence that the method converges to the exact distance in the limit of refinement is provided.
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Geodesics in Heat
TL;DR: In this paper, the heat method for computing the shortest geodesic distance to an arbitrary subset of a given domain is presented. But the heat algorithm is not suitable for the problem of estimating the geodesics of a set of points.
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The heat method for distance computation
TL;DR: Numerical evidence indicates that the heat method converges to the exact distance in the limit of refinement; the method can be applied in any dimension, and on any domain that admits a gradient and inner product---including regular grids, triangle meshes, and point clouds.
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Montage4D: interactive seamless fusion of multiview video textures
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You can find geodesic paths in triangle meshes by just flipping edges
Nicholas Sharp,Keenan Crane +1 more
TL;DR: This paper introduces a new approach to computing geodesics on polyhedral surfaces to iteratively perform edge flips, in the same spirit as the classic Delaunay flip algorithm, and demonstrates that the method is both robust and efficient, even for low-quality triangulations.
References
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The discrete geodesic problem
TL;DR: An algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface and generalizes to the case of multiple source points to build the Voronoi diagram on the surface.
Proceedings ArticleDOI
Feature sensitive surface extraction from volume data
TL;DR: In this paper, a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm is presented.
Feature Sensitive Surface Extraction from Volume Data
TL;DR: A new technique for surface extraction is presented that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm.
Journal ArticleDOI
Fast exact and approximate geodesics on meshes
TL;DR: To compute the shortest path between two given points, a lower-bound property of the approximate geodesic algorithm is used to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
Proceedings ArticleDOI
Adaptive meshes and shells: irregular triangulation, discontinuities, and hierarchical subdivision
TL;DR: The adaptive mesh model is extended in several ways and techniques for adaptive hierarchical subdivision of adaptive meshes and shells based on triangular and rectangular elements are developed.