Transforming lat and long to Mercator x and y

Question

I've been trying to plot a set of lat and long coordinates to a Mercator map using the following set of equations:

x = long - long0
y = ln(tan(pi/4 + lat/2))

These equations are from a page on Wolfram.

I'm using a Mercator map from Wikipedia, it's from 82 N to 82 S. Based on this I've got the current set of equations to fully map the lat/long to the image:

height = image height in pixels
width = image width in pixels

x = long * PI/180
x = x * width/(2 * PI) + width/2

latRange = 2 * 82 * PI/180
y = ln(tan(PI/4 + lat/2))
y = -(y*height/latRange - height/2)

However when I make the image I get points on my map that are higher than expected (I try to plot the tropic of cancer and I hit the north coast of Algeria).

So, can someone please tell me where I'm going wrong?

Answer 1

The link you are using is a map transform and not a coordinate pair transform. The correct transform is on the main Stack Overflow site at:

https://stackoverflow.com/questions/14329691/convert-latitude-longitude-point-to-a-pixels-x-y-on-mercator-projection

latitude = φ and longitude = λ are:

E = FE + R (λ – λₒ)
N = FN + R ln[tan(π/4 + φ/2)]   

where λ_O is the longitude of natural origin and FE and FN are false easting and false northing.

The formulae are best simplified to (as FE and FH are ignored in most use cases):

The stack overflow link provides pseudocode for use in all languages as well.