Putting Holes in Holey Geometry: Topology Change for Arbitrary Surfaces

Publication

ACM Transactions on Graphics (Siggraph 2013)

Abstract

This paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces—that is, we prove a backwards-compatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors.

Resources

• Paper (3.3 MB)

Citation

@article{10.1145/2461912.2462027,
  author = {Bernstein, Gilbert Louis and Wojtan, Chris},
  title = {Putting holes in holey geometry: topology change for arbitrary surfaces},
  year = {2013},
  issue_date = {July 2013},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {32},
  number = {4},
  issn = {0730-0301},
  url = {https://doi.org/10.1145/2461912.2462027},
  doi = {10.1145/2461912.2462027},
  abstract = {This paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces---that is, we prove a backwards-compatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors.},
  journal = {ACM Trans. Graph.},
  month = jul,
  articleno = {34},
  numpages = {12},
  keywords = {topology, sculpting, non-manifold geometry, intersections, deformations, 3d modeling}
}