# Manual – Displacement Vectors and Circles

Vectors of displacement graphically illustrate the accuracy of each pair of points. A vector connects the position of a point with its transformed counterpart. Each vector line starts at a point in the analyzed map and ends at the position where the point would be if the analyzed map were as accurate as the modern reference map. This endpoint results from an affine transformation between the two sets of points. MapAnalyst uses the transformation that you select in Analyze - Transformation to compute the endpoint. Exceedingly long vectors are easily identifiable and indicate outliers that are due to gross positional errors in the map. Hence, the longer the vector, the less accurate the point is.

## Show Displacement Vectors

Select the Show button to display vectors and circles of displacement.

## Vectors and Circles

Choose between Vectors, Circles or Vectors & Circles to select whether vectors and/or circles are displayed. The area of a circle of displacement is proportional to the length of a corresponding displacement vector. Vectors are usually preferable, because their length is proportional to the displacement and their orientation indicates the local direction of distortion of the map. Circles may be preferred to increase the legibility of the resulting graphic or when the direction of distortion varies almost randomly.

## Scale Factor

The length of the vectors and the area of the circles can be multiplied by a Scale Factor. The default scale value is 1. Set this factor to a value greater than 1 to visually emphasize distortions. However, if the scale factor is greater than 1, the displacement vectors do not point at the location where the point would be if the analyzed map were as accurate as the reference map.

## Outliers

Select the Mark Outliers (L > 3 Sigma) button to highlight vectors and circles with an value bigger than three times the standard deviation. A special color can be assigned to outliers using the last button in this rows.

## Symbolization

Adapt the color, width and type of the lines for optimum legibility.