Distance from point to line on Earth

Question

I need something as simple as

\"Subject 1.02: How do I find the distance from a point to a line?\"

But that works with Lon/Lat.

Answer 1

You have a line through earth-surface points A and B and a point C which you want to compute distance from.

You can compute the area of triangle ABC, divide it by distance between A and B and then multiply by 2.

function computeDistanceToLine(p, line) {
    var length = computeDistanceBetween(line.startPoint, line.endPoint);
    var triangleArea = computeTriangleArea(p, line.startPoint, line.endPoint);
    return 2 * triangleArea / length;
}

The algorithm for computing distance between two points is well-known. There are tons of implementations. One of them (as noticed in previous answers) can be found there http://www.movable-type.co.uk/scripts/latlong.html

For computing triangle area you can use some algorithm dependent on line lengths. For example

function computeTriangleArea(p0, p1, p2) {
    var r = 6378137;

    var d0 = computeDistanceBetween(p0, p1);
    var d1 = computeDistanceBetween(p1, p2);
    var d2 = computeDistanceBetween(p2, p0);

    var halfPerimeter = (d0 + d1 + d2) * 0.5;

    var t = Math.tan(halfPerimeter) *
        Math.tan((halfPerimeter - d0) * 0.5) *
        Math.tan((halfPerimeter - d1) * 0.5) *
        Math.tan((halfPerimeter - d2) * 0.5);

    return 4 * Math.atan(Math.sqrt(Math.abs(t))) * r * r;
}