# Distortion-aware measurements - PIX4Dsurvey

## This article explains in detail the slight difference between measurements of distances, areas and volumes made in the project coordinate reference system and in the real world due to the projection distortion and elevation.

### Definition

Every measurement taken in PIX4Dmatic and PIX4Dsurvey be that of a length, area, or volume, is taken in a projected coordinate reference system, which is a geographic coordinate reference system (such as WGS84) combined with a projection.

For all commonly used projections in surveying, this means that there is a slight projection distortion. That is, accurately mapped points that are exactly 1m apart in the real world are not exactly 1m apart in the projected coordinate system. How large this difference is depends on the projection used, the location of the project, and its elevation. Importantly, the projection distortion is not unknowable but can be precisely computed for any point given these elements.

The distortion due to elevation is not directly dependent on the choice of projection, but is due to the curvature of the earth: Given two coordinates in latitude & longitude, increasing the elevation f both coordinates will result in a larger distance between them. In a projected coordinate system, however, the distance between two points will not change if both their elevations are adjusted by the same amount.

### Explanation

The Distortion-aware measurements feature in PIX4Dmatic and PIX4Dsurvey makes the application account for the described difference due to distortion. If it is turned on, all measurements display their real-world value. Also, when a measurement is defined by the user, such as when setting the length of a scale constraint,  the entered value is interpreted as a real-world measurement.

### Examples

If a proper coordinate reference system for surveying in the area of interest is used, the projection distortion factor, that is the ratio between the real-world distance and the distance in the projected system, is typically below 0.05%. For coordinate systems spanning a large area of use, such as EPSG:3034 (ETRS89-extended / LCC Europe) below which spans all of Europe, the effect can however be much larger. For example:

 EPSG:26918 (NAD83  /UTM zone 18N) at 0 ellipsoidal height Location Distance in EPSG:26918 Real-world distance New York 100m 100.032m Washington 100m 99.999m Kingston, Jamaica 100m 99.943m
 EPSG:3034 (ETRS89-extended / LCC Europe) at 0 ellipsoidal height Location Distance in EPSG:3034 Real-world distance Berlin 100m 103.516m Barcelona 100m 102.240m Svalbard, Norway 100m 87.426m

While the distortion factor technically changes throughout the project, these differences are minuscule for common project sizes. We therefore compute the factor once for the center of the project and apply it to all measurements.

Further, the projection distortion only applies to horizontal measurements, vertical measurements are undistorted. For measurements at an oblique angle, the magnitude of the distortion depends on this angle.