Elementary set operations with d-dimensional polyhedra

Bieri, Hanspeter; Nef, Walter

doi:10.1007/3-540-50335-8_28

Cited by 34 publications

(32 citation statements)

References 16 publications

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“…In the Würzburg Structure [BN88] all faces are stored in the form of their local pyramids, in the Extended Würzburg Structure the incidences between faces are also stored, and in the Reduced Würzburg Structure [Bie96] only the local pyramids of the minimal elements in the incidence relation are stored. For bounded polyhedra all minimal elements are vertices.…”

Section: Definition 25 (Incidence Relation)mentioning

confidence: 99%

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Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation

Granados

Hachenberger

Hert

et al. 2003

Algorithms - ESA 2003

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Section: Definition 25 (Incidence Relation)mentioning

confidence: 99%

“…In their seminal work, Nef and later Bieri and Nef [Nef78,BN88] m algorithm for intersecting a general Nef polyhedron with a convex one; here n and m are the sizes of the input polyhedra and s is the size of the output. The idea of the sphere map is introduced in their paper (under the name local graph).…”

Section: Comparison To Extant Workmentioning

confidence: 99%

Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation

Granados

Hachenberger

Hert

et al. 2003

Algorithms - ESA 2003

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“…An attempt was made to parse and process every object in an IFC file independently using a modified version of IfcOpenShell, where its Open CASCADE (https://www.opencascade.com) -based kernel has been substituted for a new one based on CGAL. The aim of this approach was to use spatial analysis algorithms from the GIS domain and the robust Boolean set operations on Nef polyhedra available in CGAL in order to solve various use cases [29][30][31]. This approach was chosen since previous experience showed that the Boolean set operations in Open CASCADE are not as robust as those available in CGAL.…”

Section: Initial Methodologymentioning

confidence: 99%

Processing BIM and GIS Models in Practice: Experiences and Recommendations from a GeoBIM Project in The Netherlands

Ohori

Diakité

Krijnen

et al. 2018

IJGI

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Abstract:It is widely acknowledged that the integration of BIM and GIS data is a crucial step forward for future 3D city modelling, but most of the research conducted so far has covered only the high-level and semantic aspects of GIS-BIM integration. This paper presents the results of the GeoBIM project, which tackled three integration problems focussing instead on aspects involving geometry processing: (i) the automated processing of complex architectural IFC models; (ii) the integration of existing GIS subsoil data in BIM; and (iii) the georeferencing of BIM models for their use in GIS software. All the problems have been studied using real world models and existing datasets made and used by practitioners in The Netherlands. For each problem, this paper exposes in detail the issues faced, proposed solutions, and recommendations for a more successful integration.

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“…Constructive models based on constructive solid geometry, alternate decompositions [29] or intersections of half-spaces have a strong theoretical background, but attaching attributes to individual elements is difficult, and realising an object involves complex geometric computations. Nef polyhedra [30] are very powerful, but require the construction of an n-dimensional hyperspherical projective kernel, which is also a very complex task in practice [31].…”

Section: Higher-dimensional Data Modelsmentioning

confidence: 99%

Modelling Higher Dimensional Data for GIS Using Generalised Maps

Ohori

Ledoux

Stoter

2013

Lecture Notes in Computer Science

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Real-world phenomena have traditionally been modelled in 2D/3D GIS. However, powerful insights can be gained by integrating additional non-spatial dimensions, such as time and scale. While this integration to form higher-dimensional objects is theoretically sound, its implementation is problematic since the data models used in GIS are not appropriate. In this paper, we present our research on one possible data model/structure to represent higher-dimensional GIS datasets: generalised maps. It is formally defined, but is not directly applicable for the specific needs of GIS data, e.g. support for geometry, overlapping and disconnected regions, holes, complex handling of attributes, etc. We review the properties of generalised maps, discuss needs to be modified for higher-dimensional GIS, and describe the modifications and extensions that we have made to generalised maps. We conclude with where this research fits within our long term goal of a higher dimensional GIS, and present an outlook on future research.

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Elementary set operations with d-dimensional polyhedra

Cited by 34 publications

References 16 publications

Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation

Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation

Processing BIM and GIS Models in Practice: Experiences and Recommendations from a GeoBIM Project in The Netherlands

Modelling Higher Dimensional Data for GIS Using Generalised Maps

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