Calculate field of view / angle of a point to a shapefile

Question

I am trying to automate a calculation of the blocked fraction of a field of view from a point to a shapefile. I.e. find α in

, such that α / 360 gives me the fraction of the field of view covered by the shapefile in reference to the total field of view.

I know ArcGIS features a 'field of view' based on a DEM/raster (right?), but I am looking for a simpler application, between a simple point and polygon shape.

Is anyone aware of software / a function that is able to do this? It is very easy to do by hand, but I need to process roughly 250 cases, so I thought I'd better ask for other suggestions :)

Answer 1

There are three points you need the coordinates for:

• a = x,y of the viewer location
• b = x,y of where the view line meets the "top" of the polygon
• c = x,y of where the view line meets the "bottom" of the polygon

These form a triangle and the solution is just trigonometry:

angle alpha = cos^-1 ( ((b-c)^2+(c-a)^2-(c-b)^2))/(2*((c-b)^2)^(1/2)*((c-a)^2)^(1/2)

*see SSS triangle solutions http://mathworld.wolfram.com/SSSTheorem.html