In 1817 a painter drew the Făgăraș mountains 2–3 times sharper than they are

#How sharp are the mountains in the drawing?

Sharpness is easy to measure: how much the crest line rises or falls with each step to the left or right. In the drawing that line is steeper than in reality, on average by 2.8 times. The painter did not write down where he stood or how much of the horizon he meant to fit on the sheet, so 15 possible places and several widths of view were tried. For a landscape drawn from one place, between a sixth and a quarter of the horizon circle, the result stays between 2.2 and 3.1 times.

Height matters too. Under the same conditions, the tallest peak in the drawing would stand 3.7–5.2 times lower in reality. The result comes from 150 trials; the gentlest gives 2.0 times, the steepest 4.5, and in every one the drawing comes out sharper than the terrain.

The result, by how much of the horizon fits in the drawing

The dot is the middle value over all the places he could have painted from; the line shows where most cases fall (10–90%). 1× would mean a drawing true to reality.

#Why the drawing looks different

The panorama is a composition. The town is enlarged against the mountains, the sky takes half the sheet, and the crests are white and jagged as in an alpine landscape. The museum catalogue files it under the “Transylvanian school”.

The art historian Doina Pungă studied the series of 74 gouaches and watercolours this sheet belongs to (1815–1819) and found real Transylvanian motifs set in fantasy landscapes. The Făgăraș panorama is number 62 on the list, and “62” is also visible in the corner of the sheet. That does not show that the picture is stitched from several views. It only means there is no reason to expect every detail to follow the geometry of a photograph.

Nothing here says the painter erred or meant to deceive. The page only shows how far the sheet drifted from what the eye would have seen from the hill: how much is painting and how much is terrain.

#Method

The sheet: the museum photo shows the paper lying on a table, with EXIF rotation and wood around it. It was straightened with a homography from the four corners of the black ruled border (950×720 px, ratio 0.76) and enlarged two times.

The crest: the line of the white crests was traced by hand, in 50 points, on pixel grids. Slopes were taken between points 20 and 40 px apart on the sheet (2 and 4% of its width).

The terrain: Copernicus GLO-30 (30 m), window 24.3–25.45° E and 45.4–46.0° N. For every standpoint the skyline of terrain above 1,800 m (the high range, not the hills in front) was computed on rays every 0.05°, out to 75 km, with Earth curvature and standard refraction (0.13). The same angular distance was taken on the terrain from the assumed view width: an equal-angle projection, so the same scale horizontally and vertically.

A negative result: matching individual crests to the terrain failed. Several standpoints tens of kilometres apart gave the same correlation, and the landmarks in town (the fortress, the churches) could not be tied with confidence to the painted towers. So the test runs over every standpoint and every plausible view width.

Limits: the town and the mountains in the painting are not at the same scale, so “slope” means appearance, not intent. The Copernicus model is a surface model (forests and buildings included); the crest picked is the tallest in view. The render is a reference, not a photograph. The result is conditional on the equal-angle model and on an outline traced by one person; no independent re-tracings were made. A standpoint is kept if, for at least 60% of the rays towards high terrain, the crest shows at the same angular height as the unobstructed terrain (±0.02°).