On valid and invalid three-dimensional geometries

Abstract

Advances in storage management and visualization tools have expanded the frontiers of traditional 2D domains like GIS to 3Dimensions. Recent proposals such as CityGML and associated gateways bridge a long-standing gap between the terrestrial models from the GIS and the CAD/CAM worlds and shift the focus from 2D to 3D. As a result, efficient and scalable techniques for storage, validation and query of 3D models will become a key to terrestrial data management. In this paper, we focus on the problem of validation of 3D geometries. First we present Oracle's data model for storing 3D geometries (following the general OGC/ISO GML3 specifications). Then, we define more specific and refined rules for valid geometries in this model. We show that the solid representation is simpler and easier to validate than the GML model but still retains the representative power. Finally, we present explicit examples of valid and invalid geometries. This work should make it to easy to conceptualize valid and invalid 3D geometries.