Distortion-aware measurements - PIX4Dmatic

This article provides a detailed explanation of the slight differences in measurements of distances, areas, and volumes between the project coordinate reference system and the real world, caused by projection distortion and elevation variations.

Enabling or Disabling Distortion-Aware Measurements

To turn distortion-aware measurements on or off in PIX4Dmatic, follow these steps:

1. Navigate to the Settings section.
2. Toggle the Distortion-aware measurements option to enable or disable the feature as needed.
   

Definition

Every measurement in PIX4Dmatic and PIX4Dsurvey—whether length, area, or volume—is calculated within a projected coordinate reference system. This system combines a geographic coordinate reference system (e.g., WGS84) 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 adjusts for the differences caused by projection distortion. When enabled, all measurements are displayed with their real-world values. Additionally, when the user defines a measurement (such as setting the length of a scale constraint), the entered value is interpreted as a real-world measurement, accounting for distortion.

Examples

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

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.

Furthermore, 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.

For example, the two images below provide a visual representation of linear distortion in the US and Europe (Source: National Geodetic Survey).