XPost: alt.windows7.general, alt.comp.os.windows-10   
   From: G6JPG@255soft.uk   
      
   On 2026/1/14 8:24:17, R.Wieser wrote:   
   > Hello all,   
   >    
   > I have a world map using the Mercator projection, and would like to plot    
   > some stuff on it using Latitude and Longitude.   
   >    
   > The problem is that I can't seem to get the formule I found to spit out the   
   > correct value for Y.   
   >    
   > -- The map :   
   >    
   > https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Merc   
   tor_projection_Square.JPG/250px-Mercator_projection_Square.JPG   
   >    
   > -- The formula :   
   >    
   > Y = ln( tan(latitude) + sec(latitude) )   
   >    
   > where "ln(...)" is log(...) / log(10)   
   >    
   > ... at least, that is what I could google about it.   
      
   Rather than Googling the formula, my first thought was to go back to   
   first principles: as the name implies, a map projection can be thought   
   of as being created by shining a light through the earth (globe) onto a   
   sheet of paper - either flat and fixed to the globe at one point, or -   
   more commonly - a cylinder wrapped round the globe, touching at one   
   circle (often the equator), and then unrolled. Once this is realised,   
   basic geometry should make calculation of the co-ordinates fairly simple.   
      
   Unfortunately, to do this, one needs to know where the nominal light   
   source is. And - despite it being a _long_ article - I can't find a   
   statement of this in the Wikipedia article about the Mercator projection   
   - other that that - I _think_ - it _isn't_ the centre of the earth   
   (so-called "radial"), though is often thought to be (certainly Google's   
   AI thinks it is).   
      
   If anyone _can_ find out where the light source point is for the   
   Mercator projection, I'd love to know! (And it would answer Rudy's   
   question.)   
      
   (One other position for the light source I remember from last time I   
   looked into this - which was probably over 40 years ago! - is on the   
   opposite surface of the globe to the projection point (i. e. sort of   
   tracking round opposite the map "printing"); I don't think it's that,   
   though, as that would show the poles, though still distorted.   
      
   If it _is_ light-source-at-centre, then the Y co-ordinate would just be   
   the tangent of the latitude (scaled appropriately for the map size).   
   Even if it isn't, this _may_ be close enough - try a few places.   
      
   --    
   J. P. Gilliver. UMRA: 1960/<1985 MB++G()ALIS-Ch++(p)Ar++T+H+Sh0!:`)DNAf   
       
   It has been my experience that folks who have no vices have very few   
   virtues   
   -- Abraham Lincoln, quoted by Mark Lloyd in alt.windows7.general 2018-12-27   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)