Understanding Transformation parameters

[jachym]

In Geo.py Transformation.untransform, on the input, it is expected (at least how ModestMaps is used by TileStache), that the input point coordinates are representing row and column of requested tile.

According to http://blog.kartena.se/local-projections-in-a-world-of-spherical-mercator/, cx and cy parameters are supposed to be Origin of the tile set, which is given in map units (meters in my case).

Therefore, the transform/untransform function can not work well, if cx and cy parameters are given in map units, because it's calculating with input rows/columns.

Either the code is wrong, or it's usage in TileStache or my understanding of Transformation (based on the blog mentioned earlier)

class Transformation:
...
    # point uses coordinates representing columns/rows of given tile
    # cx and cy are given in map units (meters) of the tile set origin - or maybe not?
    def untransform(self, point):
        return Point((point.x*self.by - point.y*self.bx - self.cx*self.by + self.cy*self.bx) / (self.ax*self.by - self.ay*self.bx),
                 (point.x*self.ay - point.y*self.ax - self.cx*self.ay + self.cy*self.ax) / (self.bx*self.ay - self.by*self.ax))

[migurski]

The transform() method might be a bit more readable:

def transform(self, point):
    return Point(self.ax*point.x + self.bx*point.y + self.cx,
                 self.ay*point.x + self.by*point.y + self.cy)

point here will have been projected. The parameters are an implementation of a 2D affine transformation matrix; I’ve not made any attempt to relate them to map units or origins though there will be a connection.

Working with the matrices can be confusing, so I’ve included deriveTransformation() as a way to generate them from three pairs of points.