Reconstruction Using Witness Complexes

@article{Guibas2007ReconstructionUW,
  title={Reconstruction Using Witness Complexes},
  author={Leonidas J. Guibas and Steve Oudot},
  journal={Discrete & computational geometry},
  year={2007},
  volume={40 3},
  pages={325-356}
}
We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to Chew's surface meshing algorithm, with one notable difference: the restricted Delaunay triangulation is replaced by the witness complex, which makes our algorithm applicable in any metric space. To prove its correctness on curves and surfaces, we highlight… CONTINUE READING
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