# Find the side of a polygon pointed by an azimuth

I have a dataset of points (longitude, latitude) and I used QGIS get a Voronoi diagram of these points. Each point has an azimuth and a wedge width that I also managed to visualize in QGIS. As you can see, each point is in a polygon made by Voronoi. I wanted to know if there is a way to find which side of the polygon intersects the two lines formed by the wedge width. For example, in the following picture it would be the two sides in blue. A bit involved way, but anyway...

(1) Convert Voronoi polygons to lines (Polygons to lines tool)

(2) Convert Voronoi lines to segments (Explode lines tool)

(3) Extract by expression tool on the `Exploded` layer from above (2)

``````intersects(
make_line(
project(
geometry(get_feature('points', 'fid', "fid")),
1000, radians(wedge_azimuth - 0.5 * wedge_width)) ,
geometry(get_feature('points', 'fid', "fid")),
project(
geometry(get_feature('points', 'fid', "fid")),
1000, radians(wedge_azimuth + 0.5 * wedge_width))) ,
\$geometry)
``````

where:

• `'points'` shall be replaced by your points layer name.
• `fid` is the id field. Usually Voronoi tools inherit id field from the point data, so checking `'fid'` against `"fid"` will find the point- Voronoi pairs.
• `wedge_azimuth` is your wedge azimuth field name
• `wedge_width` is your width field name
• `1000` is the length of the line extending out from the points. It is probably too much for you as your data is on geographical - latlong coordinates. Very small number, say `0.001` would be more appropriate.