Question

I’m trying to calculate the Y position on a map with mercator projection given the latitude in degrees. Here’s what I need:

//mapHeight might be 600 (pixels), for example
//latitudeInDegrees ranges from -90 to 90
public double CalculateY(double mapHeight, double latitudeInDegrees)
{
    //what on earth do I do here to calculate the Y offset on the map?
    return ???;
}

I’ve tried all sorts of things I’ve found online (including wikipedia and stackoverflow), but none of it has worked for me. I’m probably doing something stupid but I can’t figure out what. Can anyone save my sanity?

Answer 1

public double CalculateY(double mapHeight, double latitudeInDegrees)
{
    return Math.Log(Math.Tan(latitudeInDegrees / 360d * Math.PI + Math.PI / 4));
}

Don’t remember scale y with mapHeight (you should know max and min value of latitudeInDegrees for taht)

Quote from Wikipedia:

At latitudes higher than 70° north or
south, the Mercator projection is
practically unusable.

You should write code like this:

private double CalculateYRelative(double latitudeInDegrees)
{
    return Math.Log(Math.Tan(latitudeInDegrees / 360d * Math.PI + Math.PI / 4));
}
...
minY = CalculateYRelative(MinLatitudeInDegrees);
maxY = CalculateYRelative(MaxLatitudeInDegrees);
...
public double CalculateY(double mapHeight, double latitudeInDegrees)
{
    return mapHeight*
           (CalculateYRelative(latitudeInDegrees) - minY) / (maxY - minY);
}

For more information:

Wikipedia

Same question

Same question 2