Corpus ID: 235265957

Integer Coordinates for Intrinsic Geometry Processing

@article{Gillespie2021IntegerCF,
  title={Integer Coordinates for Intrinsic Geometry Processing},
  author={M. I. Gillespie and Nicholas Sharp and Keenan Crane},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.00220}
}
In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geometry processing of surface meshes, taking a low-quality mesh and retriangulating it with high-quality intrinsic triangles. However, existing representations either support only edge flips, or do not offer a robust procedure to recover the common subdivision, that is, how the intrinsic triangulation sits along the… Expand

References

SHOWING 1-10 OF 36 REFERENCES
Navigating intrinsic triangulations
TLDR
A data structure that makes it easy to run a large class of algorithms from computational geometry and scientific computing on extremely poor-quality surface meshes by considering intrinsic triangulations which connect vertices by straight paths along the exact geometry of the input mesh. Expand
An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing
TLDR
An incremental algorithm is given to construct an intrinsic Laplace-Beltrami operator together with an overlay structure which captures the relationship between the extrinsic and intrinsic triangulations. Expand
Mesh arrangements for solid geometry
TLDR
This work proposes a systematic recipe for conducting a family of exact constructive solid geometry operations, which generalizes unary mesh-repair operations, classic binary boolean differencing, and n-ary operations such as finding all regions inside at least k out of n inputs. Expand
You can find geodesic paths in triangle meshes by just flipping edges
TLDR
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. Expand
A Laplacian for Nonmanifold Triangle Meshes
We describe a discrete Laplacian suitable for any triangle mesh, including those that are nonmanifold or nonorientable (with or without boundary). Our Laplacian is a robust drop‐in replacement for… Expand
Tetrahedral meshing in the wild
TLDR
This work proposes a novel tetrahedral meshing technique that is unconditionally robust, requires no user interaction, and can directly convert a triangle soup into an analysis-ready volumetric mesh, offering a robustness and reliability comparable to, e.g., image processing algorithms. Expand
Tracing compressed curves in triangulated surfaces
TLDR
The abstract tracing strategy is applied to two different classes of normal curves: abstract curves represented by normal coordinates, which record the number of intersections with each edge of the surface triangulation, and simple geodesics, represented by a starting point and direction in the local coordinate system of some triangle. Expand
Discrete conformal equivalence of polyhedral surfaces
This paper describes a numerical method for surface parameterization, yielding maps that are locally injective and discretely conformal in an exact sense. Unlike previous methods for discrete… Expand
The Vector Heat Method
TLDR
The numerical behavior of the method is studied, showing empirically that it converges under refinement, and the construction of intrinsic Delaunay triangulations are augmented so that they can be used in the context of tangent vector field processing. Expand
Guaranteed-quality mesh generation for curved surfaces
  • L. Chew
  • Computer Science, Mathematics
  • SCG '93
  • 1993
TLDR
This paper presents a technique for creating high-quality triangular meshes for regions on curved surfaces, an extension of previous methods developed for regions in the plane. Expand
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