How to interpolate latitude and longitude coordinates

Question

I need to find interpolation points between a set of two coordinates that lie on a line. The pseudo C# code that I was thinking of is this:

private static List<Coordinate> SampleLine(Coordinate start, Coordinate end, int Samples)
    {

        List<Coordinate> LineStringSample = new List<Coordinate>();
        // Calculate equal interval between two points 
        var diff_X = start.X - end.X; //latitudes
        var diff_Y = start.Y - end.Y; //longitudes
        var length = Math.Sqrt(diff_X * diff_X + diff_Y * diff_Y);
        var interval_X = diff_X / length;
        var interval_Y = diff_Y / length;

        Coordinate last = start;
        for (int i = 1; i <= Samples; i++)
        {
            LineStringSample.Add(new Coordinate(start.X + interval_X * i, start.Y + interval_Y * i));
        }
    }

Where for example start = (49.13512,6.4321) end = (49.13515,6.4333) Samples=1000 ,which are basically the latitude and longitude coordinates. I need to know if this is the right way of interpolating two coordinate points of a polyline, or if there is another way of doing this?

Answer 1

This interpolation is not exact, and errors will increase when coordinate difference grows. It might still be suitable for small lines like your example.

Better approach - find interpolation points at big circle arc. Look here in part "Intermediate point".

Formula:
 a = sin((1−f)⋅δ) / sin δ
 b = sin(f⋅δ) / sin δ
 x = a ⋅ cos φ1 ⋅ cos λ1 + b ⋅ cos φ2 ⋅ cos λ2
 y = a ⋅ cos φ1 ⋅ sin λ1 + b ⋅ cos φ2 ⋅ sin λ2
 z = a ⋅ sin φ1 + b ⋅ sin φ2
 φi = atan2(z, √x² + y²)
 λi = atan2(y, x) 
where   

f is fraction along great circle route (f=0 is point 1, f=1 is point 2),
δ is the angular distance d/R between the two points.