Winter sun and the horizon of every town

Four boxes at the top: direct sun on 21 December, what a flat horizon would give, when the sun appears and disappears behind the ridges, and the days it never arrives.

• The green silhouette is the horizon from the town hall, north-east through south to north-west; the scale on the left is in degrees.
• Five curves trace the sun on 21 June, March, February, January and December, highest to lowest: solid where it shines, dashed where it is behind the mountain.
• The buttons switch dates on and off and give each one's sunshine; hover or touch for the time, the sun's height and whether the village is in shade.
• Below, the year: gold for direct sun day by day, dashed for a flat horizon. The gap is what the mountains take.

A calculation, not a measurement, done the same way for all 215 towns.

• Terrain. Copernicus GLO-30, a height every 30 m, reaching into the Austrian and Slovenian mountains; buildings, tree rows and copses removed, relief kept.
• Horizon. From the town hall, eye 2 m above ground, along 720 rays of 60 km, allowing for the Earth's curvature and refraction.
• Sun. NOAA's algorithm, recomputed every 30 seconds for a whole year; a moment counts as sunny once the upper rim of the sun's disc rises above the ridge line.

A test where the answer is known: Viganella, in Piedmont's Verbano-Cusio-Ossola province, goes without sun for 83 days a year according to its mayor, speaking to The Sunday Times in 2006; our reckoning gives 82.

• One point. Move 250 m and the 21 December figure changes; under the chart the tool shows by how much: around Tarvisio from 2 h 55 min to 5 h 7 min.
• Clear skies. Cloud, fog and diffuse light are left out: this is the sun that could arrive.
• Woods and ridges. Forest on the slopes stays in the terrain and lifts ridges slightly; narrow pinnacles are smoothed, and where the sun grazes a ridge, the first and last day of shade may move by a few days.

The darkest villages and hamlets are in the guide winter sun. For one particular house there is the house identity card, which redoes the calculation from its address.