How to calculate Transformation between different projections

Mmmmm my problem was that i was calculating wrong the BBox of each tile, based in the coordinate. That mistake was giving me a distortionated the map as result.

After fixing it it worked right "out of the box"

/// Some code from my WMS Provider
public function getTileUrls(coord:Coordinate):Array
{
var sourceCoord:Coordinate = sourceCoordinate(coord);
var total:Object = tiles.totalTiles(coord.zoom);
if (coord.row < 0 ||
coord.row >= total.vertical ||
coord.column < 0 ||
coord.column >= total.horizontal) {
return null;
}
return [ config.baseUrl + config.getConfig() + "BBOX=" + getBBox(coord)];
}

protected function getBBox(coord:Coordinate):String
{
var size:Number= tiles.tileSize(coord.zoom);

var left:Number = tiles.limits.minX + coord.column * size;
var right:Number = tiles.limits.minX + (coord.column + 1) * size;

var top:Number = tiles.limits.maxY - coord.row * size;
var bottom:Number = tiles.limits.maxY - (coord.row + 1) * size;
return "" + left + "," + bottom + "," + right + "," + top;
}

// CODE FROM AND AUXILIARY CLASS
public function tileSize(zoom:int):Number
{
_maxDist = Math.max(distX, distY)
return _maxDist / Math.pow(2, zoom);
}

public function totalTiles(zoom:int):Object
{
var size:Number = tileSize(zoom);
return {horizontal: Math.ceil(distX / size), vertical: Math.ceil(distY / size)};
}

Now I will start to implement POSGAR projection, with that math you posted here

I will post any result when it's done.

Thanks for your guidance.

I've a very rudimentary implementation of the formula that appears at the bottom of http://mathworld.wolfram.com/MercatorProjection.html

(Note that the IProjection interface is my own, not the one used in modest map core)

The problem is that's not working properly.... Am I missing something?
Input location is in real degrees, output should be the projected location

public class EPSG22182 implements IProjection
{
public function transform(loc:Location):Location
{
var phi:Number = loc.lat;
var phiZero:Number = -90;

var lambda:Number = loc.lon;
var lambdaZero:Number = -69;

var B:Number = Math.cos(phi) * Math.sin(lambda - lambdaZero);
var x:Number = MyMath.atanh(B);
var y:Number = Math.atan((Math.tan(phi)/Math.cos(lambda - lambdaZero))) - phiZero;

var l:Location = new Location(x, y);
return loc;
}

public function toString():String
{
return "EPSG:22182";
}
}

Ahhhhhhh.... stupid mistake ¬¬

I'm using it to create a valid bounding box string in a generic WMS Provider.
The idea was to convert the location into a valid location for the given projection.

I returned a location to have a uniform data type inside the calculations of the WMS Provider mentioned above