Abstract
The various levels of detail (LODs) of a 3D city model are often stored independently, without links between the representations of the same object, causing inconsistencies, as well as update and maintenance problems. One solution to this problem is to model the LOD as an extra geometric dimension perpendicular to the three spatial ones, resulting in a true 4D model in which a single 4D object (a polychoron) represents a 3D polyhedral object (e.g., a building) at all of its LODs and a multiple-LOD 3D city model is modeled as a 4D cell complex. While such an approach has been discussed before at a conceptual level, our objective in this paper is to describe how it can be realized by appropriately linking existing 3D models of the same object at different LODs. We first present our general methodology to construct such a 4D model, which consists of three steps: (1) finding corresponding 0D–3D cells; (2) creating 1D–4D cells connecting them; and (3) constructing the 4D model. Because of the complex relationships between the objects in different LODs, the creation of the connecting cells can become difficult. We therefore describe four different alternatives to do this, and we discuss the advantages and disadvantages of each in terms of their feasibility in practice and the properties that the resulting 4D model has. We show how the different linking schemes result in objects with different characteristics in several use cases. We also show how our linking method works in practice by implementing the linking of matching cells to construct a 4D model.
Highlights
Three-dimensional city models are characterized by their level of detail (LOD), a concept that describes their complexity and fineness, which is related to their usability [1]
These can be used as a base to create 4D models in following manner: (1) when the 3D objects remain relatively unchanged along the LOD dimension, the 4D model can be extruded from 3D to 4D, creating simple prismatic objects, which are possibly further processed; or (2) when arbitrarily shaped 4D models are needed, the individual faces and volumes on the boundary of the 4D model are incrementally constructed and linked
This new cell complex consists of ‘base’ and ‘top’ faces constructed from the original cell complex, with rmin and rmax respectively added as n-th coordinates in their zero-attributes. These ‘base’ and ‘top’ are joined by a set of additional prismatic faces linking corresponding (n − 2)-cells of the base and top cells. This method is poorly suited for our case, since the two LODs have to have the same topology, which is rare in practice
Summary
Three-dimensional city models are characterized by their level of detail (LOD), a concept that describes their complexity and fineness, which is related to their usability [1]. The different representations of the same set of objects are usually stored separately and are either unconnected or connected only at the object level (e.g., through the use of IDs) This means that complex relationships between objects, such as collapses, aggregations and others that are not one-to-one, are difficult to store, which causes, among others, update and maintenance problems, as well as inconsistencies [7]. An approach to solve the multiple independent representations problem is to model the LOD as an extra geometric dimension, which is independent and perpendicular to the three spatial ones This makes it possible to store all correspondences between objects across discrete.
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