Background: Point clouds with increased point densities create new opportunities for analyzing landscape structure in 3D space. Taking advantage of these dense point clouds we have extended a 2D forest fragmentation index developed for regional scale analyses into a 3D index for analyzing vegetation structure at a much finer scale. Methods: Based on the presence or absence of points in a 3D raster (voxel model) the 3D fragmentation index is used to evaluate the configuration of a cell’s 3D neighborhood resulting in fragmentation classes such as interior, edge, or patch. In order to incorporate 3D fragmentation into subsequent conventional 2D analyses, we developed a transformation of this 3D fragmentation index into a series of 2D rasters based on index classes. Results: We applied this method to a point cloud obtained by airborne lidar capturing a suburban area with mixed forest cover. All processing and visualization was done in GRASS GIS, an open source, geospatial processing and remote sensing tool. The newly developed code is also publicly available and open source. The entire processing chain is available and executable through Docker for maximum reproducibility. Conclusions: We demonstrated that this proposed index can be used to describe different types of vegetation structure making it a promising tool for remote sensing and landscape ecology. Finally, we suggest that processing point clouds using 3D raster methods including 3D raster algebra is as straightforward as using well-established 2D raster and image processing methods.