[OSM-dev] [OSM-newbies] Mercator problems

[Andy Robinson]

On 02/12/2007, Bettersoftware <barry at bettersoftware.co.uk> wrote:
>
> I'm implementing a "slippy" map using VB.Net in a Windows application and
> everything works quite well at zooms 10 to 17.  On the "Slippy" map I
> indicate the lat/lon of the cursor position and the lat/lon of the map
> centre. However, at zooms < 10 the accuracy of the Latitude degrades
> considerably. The Longitude accuracy also degrades but to a lesser extent.
>
> After two weeks of debugging I'm stumped as my maths knowledge is not up to
> the task in hand.
>
> The error I think is on in these two pieces of code :- ( You Javascript
> people should be able to follow this easily)
>
>
> Private Function getMercatorLatitude(ByVal lat As Double, ByVal Zoom As
> Integer) As Single
>
>
>
> If (lat > 89.5) Then
>
> lat = 89.5
>
> End If
>
> If (lat < -89.5) Then
>
> lat = -89.5
>
> End If
>
> Dim phi As Double = Math.PI * lat / 180
>
> Dim res As Double = 0.5 * Math.Log((1 + Math.Sin(phi)) / (1 -
> Math.Sin(phi)))
>
> Dim maxTileY As integer = Math.Pow(2, Zoom)
>
> Dim Tile As Single = ((1 - res / Math.PI) / 2) * maxTileY
>
> Return Tile
> End Function
>
>
>
> Private Function getOSMTileDetails(ByVal x As Integer, ByVal y As Integer,
> ByVal zoom As Integer) As Object
>
> '
>
> ' Returns a Rectangle2D with x = lon, y = lat, width=lonSpan, height=latSpan
>
> ' for an x,y,zoom as used by OSM/Google.
>
> '
>
> Dim lon As Double = -180 ' x
>
> Dim lonWidth As Double = 360 ' width 360
>
> Dim lat As Double = -1
>
> Dim latHeight As Double = 2
>
> Dim tilesAtThisZoom As Integer = Math.Pow(2, zoom)
>
> lonWidth = 360.0 / tilesAtThisZoom
>
> lon = -180 + (x * lonWidth)
>
> latHeight = 2.0 / tilesAtThisZoom
>
> lat = ((tilesAtThisZoom / 2 - y - 1) * latHeight)
>
> '
>
> ' Convert lat and latHeight to degrees in a transverse mercator projection
>
> ' note that in fact the coordinates go from about -85 to +85 not -90 to 90!
>
> '
>
> latHeight += lat
>
> latHeight = 2 * Math.Atan(Math.Exp(Math.PI * latHeight)) - (Math.PI / 2)
>
> latHeight *= (180 / Math.PI)
>
> '
>
> lat = (2 * Math.Atan(Math.Exp(Math.PI * lat))) - (Math.PI / 2)
>
> lat *= (180 / Math.PI)
>
> '
>
> latHeight -= lat
>
> If lonWidth < 0 Then
>
> lon = lon + lonWidth
>
> lonWidth = -lonWidth
>
> End If
>
> If latHeight < 0 Then
>
> lat = lat + latHeight
>
> latHeight = -latHeight
>
> End If
>
> Dim tileDetails As TileDetails
>
> tileDetails.X = lon
>
> tileDetails.Y = lat
>
> tileDetails.Height = latHeight
>
> tileDetails.Width = lonWidth
>
> Return tileDetails
>
> End Function
> I apologise if this is not the correct place for a query such as this.
>
> Any assistance with this will be much appreciated
>
> Best regards
>
> Barry
> _______________________________________________
> newbies mailing list
> newbies at openstreetmap.org
> http://lists.openstreetmap.org/cgi-bin/mailman/listinfo/newbies
>
>

Barry, forwarded to dev where you may find someone to help you.

Cheers

Andy
-- 
Andy Robinson