# GeoLocation of iModels

An iModel is a digital representation of an infrastructure asset or project, as a part of an Infrastructure Digital Twin. As such, the expectation is that every iModel can be positioned at one permanent location on the earth. The conversion from Cartesian points in SpatialModels to a location on the earth in Cartographic coordinates is referred to as the GeoLocation of an iModel.

That conversion can be in 3 different forms for any given iModel, depending on the source data:

1. Unknown
2. Linear
3. Projected

If no location information is available, we say that such an iModel is not GeoLocated, and GeoLocation conversion attempts will fail.

One simple way to understand the difference between a Linear GeoLocation iModel and a Projected GeoLocation iModel is to examine "what does the z axis mean"?

• For iModels of structures such as a Plant, Building, Substation, or even a Campus, the z axis typically means height above the ground floor or some other base point. Then, Z=0 is an infinite plane with no consideration for the curvature of the earth (i.e. lines in the z direction are not necessarily directed towards the center of the earth.) Obviously such iModels can only encompass a small area, so that the curvature of the earth doesn't really matter - generally a few kilometers. The conversion from Cartesian {x,y,z} to Cartographic {lat,long,height} coordinates is accomplished through a linear transform about a single point. Source applications such as Bentley's Open Building Designer, OpenPlant, and Revit create iModels with Linear GeoLocation.

• For iModels that are created from mapping data, the z axis usually means some form of height above the earth's surface (e.g. sea level, terrain, ellipsoid, etc.) Therefore the Z=0 plane in the iModel projects the earth's ellipsoid, and lines in the z-direction always point towards the center (elliptical centroid) of the earth. Cartesian {x,y,z} values are converted to Cartographic {lat,long,height} coordinates via a non-linear map projection, the description of which is stored in the iModel as as Geographic Coordinate System. Source applications such as Bentley Map, OpenRoads, Civil 3D, GIS applications, etc. create iModels with Projected GeoLocation.

## The IModel class

Information about GeoLocation is available in iTwin.js from the IModel class, on instances of it subclasses:

### Spatial Coordinates in iModels

There is only one spatial coordinate system in an iModel for all SpatialModels. This allows iModels to have an index of all SpatialElements for fast Spatial Queries.

Coordinates in iModels are always stored in Meters, regardless of the units used by source applications. There ways to display coordinate/distance/volume/etc. values in other units, but internally they are always Meters.

### The Project Extents

It is often helpful to know the volume of space of interest for an iModel (e.g. for a "zoom to extents" command, or limiting volumes for Geometric queries.) To facilitate this, iModels hold a property called Project Extents that is an Axis Aligned Bounding Box that defines the extrema for {X,Y,Z} coordinates in the iModel. Any elements, or parts of elements, outside of IModel.projectExtents are considered invalid and are not displayed.

As mentioned above, the Project Extents are aligned with the axes of of the project. To convert the Project Extents into a shape in Cartographic coordinates, or to determine the minimum and maximum lat/long, you can use logic like:


/** get a 5 point shape of Cartographic points that encloses the project on the ground plane. */
public async convertExtentsToCartographicShape(iModel: IModelConnection): Promise<Cartographic[]> {
// convert extents to an 8 point array
const pts = Frustum.fromRange(iModel.projectExtents).points;

// the first 4 points are on the front plane
const shape: Cartographic[] = await iModel.cartographicFromSpatial(pts.slice(0, 4));
for (let i = 0; i < 4; ++i)
shape[i].height = 0; // set at ground level

shape[4] = shape[0]; // close shape
return shape;
}

/** get the low and high Cartographic range of this iModel */
public async getProjectMinMaxCartographic(iModel: IModelConnection) {
let low: Cartographic | undefined;
let high: Cartographic | undefined;

const pts = Frustum.fromRange(iModel.projectExtents).points;
for (const pt of pts) {
const geoPt = await iModel.spatialToCartographic(pt);
if (undefined === low || undefined === high) {
low = geoPt;
high = geoPt.clone();
continue;
}
low.latitude = Math.min(low.latitude, geoPt.latitude);
low.longitude = Math.min(low.longitude, geoPt.longitude);
low.height = Math.min(low.height, geoPt.height);
high.latitude = Math.max(high.latitude, geoPt.latitude);
high.longitude = Math.max(high.longitude, geoPt.longitude);
high.height = Math.max(high.height, geoPt.height);
}

return { min: low!, max: high! };
}


### The Global Origin

All spatial coordinate values are stored in an iModel in IEEE 754 floating point numbers. As such, the highest precision is obtained by numbers close to zero. For this reason, it is sometimes desireable to store a bias distance to be added to all coordinates. This value is called the Global Origin for an iModel, and it applies to all spatial coordinates. The Global Origin may be obtained by IModel.globalOrigin.

• Global Origin only apples to Spatial Models.
• The Global Origin is added to spatial coordinates before converting them to Cartographic coordinates.

### The ECEF Location

The Earth Centered Earth Fixed coordinate system is a Cartesian Coordinate system with its origin at the center of mass of the Earth. This forms a convenient reference frame for describing a linear transformation to position an iModel on the earth. This is held in IModel.ecefLocation. There are two parts of the ECEF Location:

• the position of the iModel's Global Origin in ECEF coordinates
• the YawPitchRollAngles that is the rotation from the iModel's Spatial coordinates to ECEF coordinates

• For iModels that are not GeoLocated, IModel.ecefLocation will be undefined.

• For iModels with Linear GeoLocation, there will be a ECEF Location, but no GCS.

• For iModels with Projected GeoLocation, there will be a valid ECEF Location. This can be used as a (sometimes very rough) approximation for converting to Cartographic coordinates without requiring a (sometimes very expensive) round-trip to a server for the full non-linear projection calculation. The approximation gets worse as the distance from the center of the project extents increases.

• There is a convenience method IModel.getEcefTransform to get the ECEF location as a Transform.

### The Geographic Coordinate System

A projected iModel stores information used to convert its spatial coordinates to/from Cartographic points in a property known as its "GCS" (Geographic Coordinate System). The GCS of a projected iModel describes both its Geodetic datum and the Map projection system and parameters. The non-linear conversion can only be done on the backend, often with the use of external data tables.

For historical reasons, some applications such as MicroStation store a GCS, even for a Linear GeoLocation. This means that some iModels that are really Linear iModels instead appear as being Projected. This does not generally cause problems, since a Linear iModel cannot be very large geographically, and hence the projection "warping" throughout the project extents is negligible, if it is ever applied.

## How Geographic Coordinates are used in iTwin.js

For display purposes, Geographic coordinates are only relevant for Spatial views. They are obviously used for showing Cartographic coordinates to users.

They are also used for:

• positioning reality meshes within a spatial view. Reality meshes are displayed with a linear transform that combines the ECEF Location of the iModel with their spatial coordinates.
• positioning maps and other projected GIS information within a spatial view. Note that for projected iModels, if the datum and projection systems are not identical, the map/GIS data is "warped" to match the iModel's GCS.
• positioning spatial views relative to the user's location and orientation via GPS or other location services. For performance reasons, this is done on the front end using ECEF Location, even for projected iModels.

Last Updated: 09 June, 2023