---
_id: '4000'
abstract:
- lang: eng
  text: We present fast implementations of a hybrid algorithm for reporting box and
    cube intersections. Our algorithm initially takes a divide-and-conquer approach
    and switches to simpler algorithms for low numbers of boxes. We use our implementations
    as engines to solve problems about geometric primitives. We look at two such problems
    in the category of quality analysis of surface triangulations.
acknowledgement: Center for Simulation of Advanced Rockets funded by the U.S. Department
  of Energy under Subcontract B341494, NSF under grant CCR-96-19542 and ARO under
  grant DAAG55-98-1-0177.
article_processing_charge: No
article_type: original
author:
- first_name: Afra
  full_name: Zomorodian, Afra
  last_name: Zomorodian
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  ama: Zomorodian A, Edelsbrunner H. Fast software for box intersections. <i>International
    Journal of Computational Geometry and Applications</i>. 2002;12(1-2):143-172.
    doi:<a href="https://doi.org/10.1142/S0218195902000785">10.1142/S0218195902000785</a>
  apa: Zomorodian, A., &#38; Edelsbrunner, H. (2002). Fast software for box intersections.
    <i>International Journal of Computational Geometry and Applications</i>. World
    Scientific Publishing. <a href="https://doi.org/10.1142/S0218195902000785">https://doi.org/10.1142/S0218195902000785</a>
  chicago: Zomorodian, Afra, and Herbert Edelsbrunner. “Fast Software for Box Intersections.”
    <i>International Journal of Computational Geometry and Applications</i>. World
    Scientific Publishing, 2002. <a href="https://doi.org/10.1142/S0218195902000785">https://doi.org/10.1142/S0218195902000785</a>.
  ieee: A. Zomorodian and H. Edelsbrunner, “Fast software for box intersections,”
    <i>International Journal of Computational Geometry and Applications</i>, vol.
    12, no. 1–2. World Scientific Publishing, pp. 143–172, 2002.
  ista: Zomorodian A, Edelsbrunner H. 2002. Fast software for box intersections. International
    Journal of Computational Geometry and Applications. 12(1–2), 143–172.
  mla: Zomorodian, Afra, and Herbert Edelsbrunner. “Fast Software for Box Intersections.”
    <i>International Journal of Computational Geometry and Applications</i>, vol.
    12, no. 1–2, World Scientific Publishing, 2002, pp. 143–72, doi:<a href="https://doi.org/10.1142/S0218195902000785">10.1142/S0218195902000785</a>.
  short: A. Zomorodian, H. Edelsbrunner, International Journal of Computational Geometry
    and Applications 12 (2002) 143–172.
date_created: 2018-12-11T12:06:22Z
date_published: 2002-01-01T00:00:00Z
date_updated: 2023-06-13T11:20:09Z
day: '01'
doi: 10.1142/S0218195902000785
extern: '1'
intvolume: '        12'
issue: 1-2
language:
- iso: eng
month: '01'
oa_version: None
page: 143 - 172
publication: International Journal of Computational Geometry and Applications
publication_identifier:
  issn:
  - 0218-1959
publication_status: published
publisher: World Scientific Publishing
publist_id: '2128'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fast software for box intersections
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 12
year: '2002'
...
---
_id: '4009'
abstract:
- lang: eng
  text: We study the maintenance of a simplicial grid or complex under changing density
    requirements. The proposed method works in any fixed dimension and generates grids
    by projecting cross-sections of a monotone simplicial complex that lives in one
    dimension higher than the grid. The density of the grid is adapted by locally
    moving the cross-section up or down along the extra dimension.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Roman
  full_name: Waupotitsch, Roman
  last_name: Waupotitsch
citation:
  ama: Edelsbrunner H, Waupotitsch R. Adaptive simplicial grids from cross-sections
    of monotone complexes. <i>International Journal of Computational Geometry and
    Applications</i>. 2000;10(3):267-284. doi:<a href="https://doi.org/10.1142/S0218195900000164">10.1142/S0218195900000164</a>
  apa: Edelsbrunner, H., &#38; Waupotitsch, R. (2000). Adaptive simplicial grids from
    cross-sections of monotone complexes. <i>International Journal of Computational
    Geometry and Applications</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0218195900000164">https://doi.org/10.1142/S0218195900000164</a>
  chicago: Edelsbrunner, Herbert, and Roman Waupotitsch. “Adaptive Simplicial Grids
    from Cross-Sections of Monotone Complexes.” <i>International Journal of Computational
    Geometry and Applications</i>. World Scientific Publishing, 2000. <a href="https://doi.org/10.1142/S0218195900000164">https://doi.org/10.1142/S0218195900000164</a>.
  ieee: H. Edelsbrunner and R. Waupotitsch, “Adaptive simplicial grids from cross-sections
    of monotone complexes,” <i>International Journal of Computational Geometry and
    Applications</i>, vol. 10, no. 3. World Scientific Publishing, pp. 267–284, 2000.
  ista: Edelsbrunner H, Waupotitsch R. 2000. Adaptive simplicial grids from cross-sections
    of monotone complexes. International Journal of Computational Geometry and Applications.
    10(3), 267–284.
  mla: Edelsbrunner, Herbert, and Roman Waupotitsch. “Adaptive Simplicial Grids from
    Cross-Sections of Monotone Complexes.” <i>International Journal of Computational
    Geometry and Applications</i>, vol. 10, no. 3, World Scientific Publishing, 2000,
    pp. 267–84, doi:<a href="https://doi.org/10.1142/S0218195900000164">10.1142/S0218195900000164</a>.
  short: H. Edelsbrunner, R. Waupotitsch, International Journal of Computational Geometry
    and Applications 10 (2000) 267–284.
date_created: 2018-12-11T12:06:25Z
date_published: 2000-06-01T00:00:00Z
date_updated: 2023-04-20T13:45:46Z
day: '01'
doi: 10.1142/S0218195900000164
extern: '1'
intvolume: '        10'
issue: '3'
language:
- iso: eng
month: '06'
oa_version: None
page: 267 - 284
publication: International Journal of Computational Geometry and Applications
publication_identifier:
  issn:
  - 0218-1959
publication_status: published
publisher: World Scientific Publishing
publist_id: '2117'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Adaptive simplicial grids from cross-sections of monotone complexes
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 10
year: '2000'
...