The use of 3D features within GIS has been increasing due to the need to represent, query, manipulate, and analyze man-made objects in relationship to other 3D features related to the surface of the earth. This will yield an increased use of 3D boundary representations of the features. The spatial relationship between two or more features is often evaluated using a geometrical overlay of these features, which reveals whether these features overlap and—if they do—to which extent. We present the design of a 3D overlay algorithm which overlays 3D triangulated boundary representations through a constrained tetrahedral mesh. The intersections between the constrained facets of the 3D features are calculated on the fly and within a restricted neighborhood. We can identify and reconstruct the overlaid parts of the 3D boundary representation within the tetrahedral mesh. The implementation is based on the Computational Geometry Algorithms Library, which proved to have the functionality needed but also has its limitations.
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Verbree et al. (2005) studied this question.