i'm trying to find the point in south africa furthest from the sea or a landward boundary.
my method thus far:
i obtained a first guess at the centre of the inscribed circle and the three segments of boundary this circle might touch using a compass and 1:2 500 000 map.
i then clipped these three segments of boundary from a data set of boundary coordinates supplied by national geo-spatial information (WGS84; decimal degrees; 9 decimal places; roughly one point for every 40 metres of boundary).
i converted the boundary coordinates to radians and used cartesian equations (distance between two points and centre of a circle through three points) to iteratively improve the centre of my circle and the three boundary points it touches. (obviously, i'm ignoring curvature; i'm effectively finding the centre of the base of the spherical cap defined by the inscribed circle -- i.e. a point approximately 16km underground.)
is it reasonable to plug lat-long coordinates expressed in radians into cartesian equations to find the centre of the base of the spherical cap defined by the inscribed circle (given that the surface distance represented by one radian varies with latitude, and that the base of the spherical cap in question is roughly 800km in diameter and spans latitude 30S)? what order of error might be involved here?
is it reasonable to assume that the three boundary points tangential to the base of the spherical cap will likewise be the three boundary points closest to the actual point in the country furthest from a boundary?
i have the feeling i'm not even asking the right questions here. i guess there must be a better way to find the point in a country furthest from a boundary ...