Voxelisation Algorithms and Data Structures: A Review

Abstract

Voxel-based data structures, algorithms, frameworks, and interfaces have been used in computer graphics and many other applications for decades. There is a general necessity to seek adequate digital representations, such as voxels, that would secure unified data structures, multi-resolution options, robust validation procedures and flexible algorithms for different 3D tasks. In this review, we evaluate the most common properties and algorithms for voxelisation of 2D and 3D objects. Thus, many voxelisation algorithms and their characteristics are presented targeting points, lines, triangles, surfaces and solids as geometric primitives. For lines, we identify three groups of algorithms, where the first two achieve different voxelisation connectivity, while the third one presents voxelisation of curves. We can say that surface voxelisation is a more desired voxelisation type compared to solid voxelisation, as it can be achieved faster and requires less memory if voxels are stored in a sparse way. At the same time, we evaluate in the paper the available voxel data structures. We split all data structures into static and dynamic grids considering the frequency to update a data structure. Static grids are dominated by SVO-based data structures focusing on memory footprint reduction and attributes preservation, where SVDAG and SSVDAG are the most advanced methods. The state-of-the-art dynamic voxel data structure is NanoVDB which is superior to the rest in terms of speed as well as support for out-of-core processing and data management, which is the key to handling large dynamically changing scenes. Overall, we can say that this is the first review evaluating the available voxelisation algorithms for different geometric primitives as well as voxel data structures.

Voxelisation and Voxel Management Options in Unity3d

“…In the case of having sparsely represented voxels, the use of plane arrays can result in a high memory footprint. Therefore, more efficient voxel data structures are suggested (Aleksandrov et al, 2021).…”

“…This is unfortunate since the VDB data structure allows to manage effectively voxels in scenarios when voxels often update positions like in simulations. Aleksandrov et al, (2021) presented that many geometrical primitives exist including points, lines, triangles, polygons, surfaces and volumes, where for each one of them different voxelisations can be achieved considering the application of interest. Apart from the geometrical transition to discretised shape, it is important to consider attributes preservation during the process.…”

“…The first step in understanding what kind of voxelisation is possible to achieve is important to assess the available implemented algorithms. One of the main issues as suggested by Aleksandrov et al, (2021) is the availability of these approaches in common software and platforms for usage and testing. Storing additional information for each voxel goes in the direction of non-binary voxelisation, which is useful in preserving some properties needed for voxel rendering, management, and interaction.…”

“…Apart from voxels visualisation, 3D spatial queries and simulations can be performed over voxels. Aleksandrov et al (2021) indicated that for modelling more dynamic phenomena such as smoke propagations and fluid simulations the use of voxel data structures such as SPGrid (Setaluri et al, 2014) and VDB (Museth, 2013) are suggested. Therefore, it is crucial to understand if these data structures are easily available or some other data structures are more commonly utilised.…”

Influence of Voxel Size and Voxel Connectivity on the 3d Modelling of Australian Heathland Parameters

“…The voxel neighbourhood connectivity is another important voxel property of voxelisation. Connectivity is a measure of the way that voxels are linked to their neighbouring voxels (Aleksandrov et al, 2021). In three-dimensional space, neighbouring voxels are connected through either 6, 18 or 26 voxel neighbourhood connectivity (Figure 3).…”