Abstract
The paper presents a very straightforward and effective algorithm to convert a space partitioning, made up of polyhedral objects, into a 3D block of voxels, which is fully occupied, i.e. in which every voxel has a value. In addition to walls, floors, etc. there are 'air' voxels, which in turn may be distinguished as indoor and outdoor air. The method is a 3D extension of a 2D polygon-to-raster conversion algorithm. The input of the algorithm is a set of non-overlapping, closed polyhedra, which can be nested or touching. The air volume is not necessarily represented explicitly as a polyhedron (it can be treated as 'background', leading to the 'default' voxel value). The approach consists of two stages, the first being object (boundary) based, the second scan-line based. In addition to planar faces, other primitives, such as ellipsoids, can be accommodated in the first stage without affecting the second.
Highlights
Three-dimensional grids, where data are represented as values at regularly-spaced grid points, are drawing attention increasingly, in addition to the more common 3D vector representations
It seems natural to have objects like buildings and vegetation, as well as the terrain, represented by voxels too, when they play a role in applications that use field representations. Another application area where grid representations are currently studied is navigation, where routes are computed along which persons, robots, or drones are moving through collections of 'free space' or 'air' voxels
As many 3D GIS models are in existence and are represented by vector data sets, there is a need for 3D vector-toraster conversion algorithms that translate vector models into grid representations
Summary
Three-dimensional grids, where data are represented as values at regularly-spaced grid points (voxels), are drawing attention increasingly, in addition to the more common 3D vector representations. For certain categories of spatial analysis, such as those involving 3D scalar or vector fields (air pollution, noise, wind) that vary continuously over space, gridded data representations offer clear advantages. Such representations has been largely used for modelling of geological structures. The algorithms are developed for a specific connectivity (i.e. 26-connected only), which influences the performance in case of large data sets This issue has been lately revisited by the same research group (Cohen-or & Kaufman 1997). The different algorithms show various degrees of strictness (vs. tolerance) w.r.t. their input formats, for instance
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