3.3 TINs and Other Spatial Data Models
Beyond vector and raster — triangulated irregular networks, point clouds, voxels, and hexagonal grids.
Key takeaways
- Vector and raster aren't the only two data models — TINs, point clouds, voxels, and hex grids are common.
- Each model is optimised for a specific class of phenomenon and analysis.
- Choosing the right model saves time and produces more defensible analyses.
Introduction
Vector and raster dominate the textbooks, but real-world GIS uses a handful of other models for specific jobs. This lesson introduces the most common non-vector-non-raster models — TINs, point clouds, voxels, hex grids, and discrete global grid systems — so you know when to reach for each.
TIN — Triangulated Irregular Network
A TIN represents a continuous surface (elevation, temperature, interpolated demand) as a mesh of non-overlapping triangles whose vertices are sampled observations. Each triangle is planar; the surface between samples is linearly interpolated.
Advantages over a raster DEM:
- Adaptive resolution — dense triangles where terrain varies, sparse where it's flat. Efficient storage.
- Honours breaklines — discontinuities (cliff edges, stream channels) can be embedded as mandatory edges.
- Preserves sample points exactly — no aliasing onto a grid.
Disadvantages:
- More complex data structure.
- Most analytical tools expect rasters; TINs often get converted for analysis.
TINs are usually built by Delaunay triangulation from a point cloud, often augmented with breaklines. Used heavily in engineering (site grading, volume calculations) and in games/simulations (terrain meshes).
Point clouds
A point cloud is a 3D set of points (x, y, z) with optional attributes (intensity, return number, RGB, classification). Sources:
- LiDAR — aircraft or terrestrial laser scanners; millions to billions of points per project.
- Photogrammetry — dense-matched points from overlapping aerial or drone photos.
- Depth cameras — indoor mobile scanners.
Storage formats: LAS / LAZ (the compressed version), Entwine EPT, COPC (Cloud Optimised Point Cloud). See Module 19 for LiDAR fundamentals.
Typical operations on point clouds:
- Classify ground vs non-ground returns.
- Rasterise to a DEM (ground) or DSM (top-of-surface).
- Extract building roof planes.
- Compute canopy height models (CHM = DSM − DEM).
Voxels (3D rasters)
A voxel is a cubic cell in 3D — the 3D analogue of a pixel. Used when phenomena genuinely live in 3 dimensions:
- Atmospheric chemistry (pollutant concentrations by altitude).
- Sub-surface geology (drill-core interpolations).
- Medical imaging (MRI, CT scans).
- Flow simulations (computational fluid dynamics).
Storage: NetCDF, Zarr, HDF5. Voxels cost cubically — doubling resolution multiplies storage by 8 — so resolution decisions are significant.
Hexagonal and triangular tessellations
A tessellation covers the plane with non-overlapping shapes. Squares (regular raster) and triangles (TIN) are the most common, but hexagons have notable advantages:
- Every hexagon has six equidistant neighbours (squares have four equidistant + four diagonal).
- Hexagons minimise the "edge effect" — their perimeter-to-area ratio is closer to a circle.
- They look nicer for dot-density and aggregation maps.
H3 (Uber, 2018) is a hierarchical hex grid indexing the globe. S2 (Google) uses curved quadrilaterals. Both support level-based coarsening and neighbour lookups in constant time — extremely useful for logistics and large-scale aggregations.
1import h3
2# Cell containing a point at ~1 km resolution (level 8)
3cell = h3.latlng_to_cell(37.7749, -122.4194, 8)
4# Neighbouring cells (immediate ring)
5neighbours = h3.grid_disk(cell, 1)Discrete global grid systems (DGGS)
A DGGS is a global tessellation designed for consistent spatial analytics across the planet. Beyond H3 and S2, other systems include rHEALPix and OGC's DGGS standard. DGGS are ideal for:
- Joining datasets across countries without chasing every local CRS.
- Aggregating sparse point events (mobility, crime, deliveries) into consistent cells.
- Building global heatmaps with fair areal weighting.
Graph / network model
A road network, a utility grid, or a public-transit system is fundamentally a graph — nodes and edges with attributes. Storing this as plain lines misses the connectivity; storing it as a proper graph unlocks:
- Shortest-path and travel-time queries (Dijkstra, A*, contraction hierarchies).
- Isochrone / service-area analysis.
- Flow modelling (traffic assignment, hydraulics).
Module 13 treats network analysis in depth.
Object-oriented / feature model
Beyond raw geometry, features can be modelled as objects with behaviour: a parcel has owners, can be subdivided, has zoning rules. Esri's geodatabase and OGC's General Feature Model formalise this. For most analysts this is "just" an attribute-rich vector — but it shows up in enterprise GIS and BIM (building information modelling) integrations.
Choosing a model
| Phenomenon | Best model |
|---|---|
| Building footprints | Vector polygons |
| Roads and junctions | Network graph |
| Land cover | Raster (categorical) |
| Elevation (full resolution) | Raster DEM or TIN |
| LiDAR / drone reconstructions | Point cloud |
| Global ride-share demand | Hex grid (H3) |
| Atmospheric pollution by altitude | Voxel |
| City buildings in 3D | 3D vector (CityGML) or mesh |
| Weather variables over time | NetCDF (stacked raster, temporal axis) |
Sometimes you need multiple models of the same phenomenon: a DEM as raster for visualisation, TIN for engineering calculations, contours as vector for cartography.
Self-check exercises
1. Why would you choose a TIN over a raster DEM for a site-grading project?
TINs preserve breaklines (sharp terrain discontinuities like retaining walls, cliff edges, stream channels) exactly. They also store only as much detail as the terrain warrants, so they're efficient in flat areas and dense in variable ones. Rasters force a uniform resolution and smooth over sharp edges.
2. What advantages do hexagons offer over square raster cells for aggregation?
Each hexagon has six equidistant neighbours (squares only have four cardinal + four diagonal at different distances), they have a lower edge-to-area ratio (closer to circular), and they avoid the directional bias of a square grid. This makes them good for dot-density, heatmap, and neighbour-based analyses.
3. You're analysing ride-share demand across three countries. Which data model would make the analysis most consistent?
A DGGS like H3. It gives every country identical cell sizes at a chosen level, aggregates trivially, and supports fast neighbour lookups. Mixing each country's local CRS and administrative units would create comparability headaches.
Summary
- Vector + raster cover most jobs, but TINs, point clouds, voxels, and hex grids solve important specific problems.
- Graph models unlock network analysis beyond what line features alone provide.
- DGGS (H3, S2) are the modern choice for global, consistent aggregations.
- Picking the right model upstream saves enormous pain downstream.
Further reading
- Uber Engineering — H3: Uber's Hexagonal Hierarchical Spatial Index.
- Sahr, K. — DGGRID and discrete global grid systems.
- PDAL documentation — standard tooling for LiDAR workflows.
- OGC — Discrete Global Grid Systems standard.
