Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Nested maps—a formal, provably correct object model for spatial aggregates
GIS '96 Proceedings of the 4th ACM international workshop on Advances in geographic information systems
Provably correct and complete transaction rules for GIS
GIS '97 Proceedings of the 5th ACM international workshop on Advances in geographic information systems
The Unified Modeling Language user guide
The Unified Modeling Language user guide
Extracting buildings from aerial images using hierachical aggregation in 2D and 3D
Computer Vision and Image Understanding
Geoinformatica
Exploiting 2D concepts to achieve consistency in 3D GIS applications
GIS '03 Proceedings of the 11th ACM international symposium on Advances in geographic information systems
GIS: A Computing Perspective, 2nd Edition
GIS: A Computing Perspective, 2nd Edition
Updating 3D city models: how to preserve geometric-topological consistency
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
How to achieve consistency for 3D city models
Geoinformatica
Review: 3D geo-database research: Retrospective and future directions
Computers & Geosciences
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This article deals with topological concepts and models which are necessary to represent three-dimensional urban objects in a geographical information system (GIS). Depending on the shape and the representation of features, several classes with increasing topological complexity are identified and described. This complexity has strong impacts on the models and tools which are required to represent, manage and edit the data. One specific model we call `2.8-D map' is identified, which covers many 3-D applications in GIS. It is a slight extension of a 2-D or 2.5-D model and preserves the algorithmic and conceptual simplicity of the 2-D case as much as possible. The model is described in a formal way. Integrity axioms are given, which detect errors in corresponding data sets safely and guarantee the consistency of 2.8-D maps in a mathematically sound and provable way. These axioms are effectively and efficiently checkable by automatic procedures. The model extends digital terrain models (2.5-D) by allowing for vertical walls and projections like balconies or ledges. The conceptual simplicity is due to the two-dimensional topology of the model. Thus bridges and tunnels are special cases; it is shown how to detect and handle these cases efficiently. Based on this model, thematic objects and their aggregation structures are defined in a consistent way.