### Abstract

There is substantial value in the use of higher-dimensional (>3D) digital objects in GIS that are built from complex real-world data. This use is however hampered by the difficulty of constructing such objects. In this paper, we present a dimension independent algorithm to build an n-dimensional cellular complex with linear geometries from its isolated (n − 1)-dimensional faces represented as combinatorial maps. It does so by efficiently finding the common (n − 2)-cells (ridges) along which they need to be linked. This process can then be iteratively applied in increasing dimension to construct objects of any dimension. We briefly describe combinatorial maps, present our algorithm using them as a base, and show an example using 2D, 3D and 4D objects which was verified to be correct, both manually and using automated methods.

Original language | English |
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Title of host publication | Applied Algorithms |

Subtitle of host publication | First International Conference, ICAA 2014, Kolkata, India, January 13-15, 2014. Proceedings |

Editors | P. Gupta, C. Zaroliagis |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 37-48 |

Number of pages | 12 |

Volume | 8321 |

ISBN (Electronic) | 978-3-319-04126-1 |

ISBN (Print) | 978-3-319-04125-4 |

DOIs | |

Publication status | Published - 2014 |

Event | 1st International Conference on Applied Algorithms, ICAA 2014 - Kolkata, India Duration: 13 Jan 2014 → 15 Jan 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8321 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Conference

Conference | 1st International Conference on Applied Algorithms, ICAA 2014 |
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Country | India |

City | Kolkata |

Period | 13/01/14 → 15/01/14 |

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## Cite this

*Applied Algorithms: First International Conference, ICAA 2014, Kolkata, India, January 13-15, 2014. Proceedings*(Vol. 8321, pp. 37-48). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8321). Springer. https://doi.org/10.1007/978-3-319-04126-1_4, https://doi.org/10.1007/978-3-319-04126-1_4