Convert LAT/LON to Screen and back to screen works

I have a 1024 x 1024 form with nothing on it.  I have the code below in it that takes some LAT and LON coordinates and converts them to screen coordinates and draws them on the screen with the LAT/LON and the screen coordinates in text.  This all works very nicely.  The problem I am having is trying to figure out how to go in the opposite direction.  In other words, if I click on the form I want to be able to show the LAT/LON in the form caption.  Can anyone figure out how to do this and provides me with a working example?  

While we are at it I welcome any comments that might help me improve on the code I already have here.  I know I shouldn't but for the sake of getting this to work I have all of the coordinates hard coded in this example.

*** I got the math to do this from Wolfram Research Resource Library based on reasearch by J.P Snyder USGS Pro Paper 1395
Map Projections -- A Working Manual.  I only wish I was smart enough to have come up with them myself =)

Thanks for any and all assistance.

Rich

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, Math, StdCtrls;

type
  TForm1 = class(TForm)
    procedure FormCreate(Sender: TObject);
    procedure FormPaint(Sender: TObject);
    procedure FormClick(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
   function ValidateLon(VAR Lon:Extended): Boolean;
   procedure ValidateLat(VAR Lat:Extended);
   procedure PolyconicLLtoCartesian(Lat, Lon: Extended;
                                                   VAR CartX, CartY: integer);
  end;

var
  Form1: TForm1;
  origin_X, origin_Y :integer;
  MCECanvas:TCanvas;
  MCELatitude :Extended = 30.407;   //Default Latitude for Center
  MCELongitude :Extended = -88.921;  //Default Longitude for Center

   //the shifts required to make the key location in the middle of the screen
   //also used to track user offsets
  LatShift : Extended = 0.0;
  LonShift : Extended = 0.0;
  ScaleExpansion : Integer = 2;      //shown in submenu area EXP=
  ScaleMultiplier : Double = 100.0;     //used to expand map to correct size

implementation

{$R *.dfm}

(******************************************************************************)
(* This function makes sure the Longitude is within the range of              *)
(* 180.0 to -18.0 and returns true if the Longitude sent was OK to start with *)
(* If it has to adjust the Longitude, it will return false.                   *)
(******************************************************************************)
function TForm1.ValidateLon(VAR Lon:Extended): Boolean;
begin
   Result := True;           //default is a valid Lon

   while (Lon > 180.0) do    //make sure Lon is a valid number
     begin
       Lon := Lon - 360.0;
       Result := False;       //return of false means it was invalid
     end;

   while (Lon < -180.0) do
     begin
       Lon := Lon + 360.0;
       Result := False;
     end;
end;
(******************************************************************************)
procedure TForm1.ValidateLat(VAR Lat:Extended);
begin
   while (Lat > 90.0) do
     Lat := Abs(Lat - 180.0);

   while (Lat < -90.0) do
     Lat := -(Lat + 180.0);
end;

(******************************************************************************)
(*   Receives latitude and logitude and uses them as polyconic coordinate     *)
(*   values and returns X,Y scaled to Cartesian coodinate system with the     *)
(*   lesson location longitude centered.                                      *)
(******************************************************************************)
procedure TForm1.PolyconicLLtoCartesian (Lat, Lon: Extended;VAR CartX, CartY: integer);
const
  PrevLonIsValid : Boolean = True;
var
  r : Extended;
  CotanLat, LonSinLat : Extended;
  NextLonIsValid : Boolean;
begin          
  r := 58.0;               //arbitrary scaler to make it look right
                           //must match CartesianToPolyconicLL procedure
                           //ScaleMultiplier * r = 215 to work right

  //spin the world to make current location's longitude
  // in the center of the screen.  DO NOT shift latitude like this since it
  // is to scale only at the center longitude in this type projection.
  Lon := Lon - LonShift;

  //if Lon is a valid number ValidateLon returns true
  NextLonIsValid := ValidateLon(Lon);
  //check to see if the previous and next numbers cross 180 degrees from the
  //central meridian
  //save info for next time

  // These evil calculations are brought to you by Wolfram Research Resource
  // Library based on reasearch by J.P Snyder USGS Pro Paper 1395
  // Map Projections -- A Working Manual

  //pre-calculate to make CartX, CartY formula easier
  LonSinLat := Lon * Sin(DegToRad(Lat));

  //don't send a 0 to Cotan function
  if ((Lat > 0.0) OR (Lat < 0.0)) then
    begin
      CotanLat := Cotan(DegToRad(Lat));
      CartX :=  Round(ScaleMultiplier * (r * CotanLat * Sin(DegToRad(LonSinLat))));
    end
  else
    begin
      CotanLat:= 0.000001;
      CartX := Round(ScaleMultiplier * (r * DegToRad(Lon)));
    end;

  CartY :=  Round(ScaleMultiplier * (r * (DegToRad(Lat - LatShift) +
                        (CotanLat * (1.0 - Cos(DegToRad(LonSinLat)))))));

end;
(******************************************************************************)

procedure TForm1.FormCreate(Sender: TObject);
begin
  MCECanvas := TCanvas.Create;
  //get the handle for the Tod frame
  MCECanvas.Handle := GetDC(Handle);

  origin_X := (Width div 2);
  origin_Y := (Height div 2);

  //Logical units are mapped to arbitrary units with equally scaled axes
  SetMapMode(MCECanvas.Handle, MM_ISOTROPIC);

  SetWindowExtEx(MCECanvas.Handle, Width, Height, nil);

  //the negative Frame.Height causes positive y to be up
  SetViewportExtEx(MCECanvas.Handle, Width, -Height, nil);

  //set the origin in middle of frame
  SetViewportOrgEx(MCECanvas.Handle, origin_X, origin_Y, nil);

  MCECanvas.Brush.Style := bsClear;//bsSolid;   //bsClear to see behind text
  MCECanvas.Brush.Color := clBlack;   //color behind TextOut
  MCECanvas.Font.Name := 'System';
  MCECanvas.Font.Color := clBlack;

  MCECanvas.Pen.Color := clBlack;
  MCECanvas.Pen.Style := psSolid;
  MCECanvas.Pen.Width := 2;

  LatShift := MCELatitude;
  LonShift := MCELongitude;
end;

procedure TForm1.FormPaint(Sender: TObject);
var
  Here : TPoint;
  MyLat, MyLon : extended;
  IntLatLon : TPoint;
  mid : TPoint;
begin
  //Clear off the canvas
  MCECanvas.Brush := Brush;
  MCECanvas.FillRect(ClientRect);

  //get the target's lat/lon and convert to Cartesian coords
  PolyconicLLtoCartesian(30.407, -88.921, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '30.407 : -88.921');

  PolyconicLLtoCartesian(34.682, -88.921, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '34.682 : -88.921');

  PolyconicLLtoCartesian(34.58, -94.086, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '34.58 : -94.086');

  PolyconicLLtoCartesian(34.58, -83.757, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '34.58 : -83.757');

  PolyconicLLtoCartesian(26.128, -88.922, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '26.128 : -88.922');

  PolyconicLLtoCartesian(26.043, -93.655, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '26.043 : -93.655');

  PolyconicLLtoCartesian(26.043, -84.188, Here.x, Here.y);
  MCECanvas.Ellipse(Here.X, Here.Y, Here.X + 10, Here.Y + 10);
  mid.x := (Here.x + 5);
  mid.y := (Here.y + 5);
  MCECanvas.Font.Color := clRed;
  MCECanvas.TextOut(Here.x + 10, Here.y + 10, IntToStr(mid.X) + ':' + IntToStr(mid.Y));
  MCECanvas.Font.Color := clBlue;
  MCECanvas.TextOut(Here.x - 40, Here.y - 10, '26.043 : -84.188');

  MCECanvas.Brush.Color := clRed;
  MCECanvas.Ellipse(0, 0, 10, 10);
end;

procedure TForm1.FormClick(Sender: TObject);
begin
  //need to show the Lat and Lon of the loacation where the mouse was clicked
end;

end.