FME Form: 2024.1

# LiDAR and Coordinate Systems

LiDAR is changing how we model our world in 3D, bringing with it new data transformation challenges and huge data volumes. It also highlights some old and new challenges with coordinate systems: getting your data into a form where it can be overlaid with other data and where useful properties are maintained (for example, water flowing downhill).

Transforming your data (LiDAR, raster, vector, …) into the right coordinate system allows you to combine it with other data and take advantage of important properties like heights.

## How Coordinate Systems are used with LiDAR

LiDAR data may be captured in a local coordinate system (for smaller projects), in geographic coordinates (latitude, longitude, ellipsoid height), or geocentric coordinates (also called Earth Centered Earth Fixed). Geocentric coordinates are Cartesian coordinates whose x, y, and z ordinates capture the distance from the earth’s center of mass along the interesting axes (based on the International Reference Pole and Meridian; roughly, the north pole and Greenwich). This system is very appealing for LiDAR as the x, y, and z ordinates all use the same units (meters) and can be used seamlessly anywhere in the world.

## Transformation Challenges

The first requirement is to transform your data into a coordinate system suitable for combining with other data. For example, geographic or geocentric data may need to be converted into a projected coordinate system such as a US state plane. Similarly, data in a local coordinate system may need to be georeferenced and converted into a geographic or projected system.

The second requirement is that you may need to convert the heights into a useful form. Typically, geographic and projected coordinate systems use ellipsoid heights. Ellipsoid heights measure the perpendicular distance to an ellipsoid (flattened sphere) which approximates the earth’s shape, and are easy to measure using GPS anywhere in the world. They aren’t sea-level heights, however, so they are counterintuitive near the coast and don’t capture the direction water flows (down) over large areas. As described in Heights in Coordinate Systems, you can use geoid-based techniques to convert between ellipsoid and orthometric heights to restore these properties.

## Coordinate System Metadata and LiDAR Data

The most common LiDAR format, LAS, stores coordinate systems using GeoTIFF keys. However, there are still a few problems to work out with geocentric and vertical coordinate systems. Ongoing standardization will benefit interoperability. The ASTM E57 3D file format, which will likely store 3D and LiDAR data more generally than the LAS format, is under development.