Map to/from Window Coordinate Transformation

To draw the map data onto a window or picture box, you need to create a transformation between map coordinate system and picture box coordinate system. Normally this transformation is a similarity transformation between two coordinate systems (map and window coordinate systems). Generally this transformation includes 2 translation and 2 scale parameters (Figure-1), and rotation sometimes. Here we assume there is no rotation between two coordinate systems.

But it is a little bit different when one of the coordinate systems is window or picture box since its coordinate origin is upper left corner of the component. But similarity is still valid. Transformation equations of map and window coordinate system are defined as below.

The definitions of the parameters:

• Xp is X coordinate of point P in metric units
• Yp is Y coordinate of point P in metric units
• Cp is Column coordinate of point P in pixels
• Rp is Row coordinate of point P in pixels
• X0 is X coordinate of Upper Left corner of the Window in metric units
• Y0 is Y coordinate of Upper Left corner of the Window in metric units
• Sx is scale on X axis in metric/pixel units (metric width of 1 window pixel)
• Sy is scale on Y axis in metric/pixel units (metric height of 1 window pixel)

C# code (*) of MapToWindow Transformation and WindowToMap Transformation are below.

        double X0;
        double Y0;
        double Sx;
        double Sy;

        public bool ComputeParams(PointCoor UpperLeft, PointCoor LowerRight, int WinWidth, int WinHeight)
        {

            if (LowerRight.X <= UpperLeft.X)
                return false;

            if (LowerRight.Y >= UpperLeft.Y)
                return false;

            if (WindowHeight <= 0)
                return false;

            if (WindowWidth <= 0)
                return false;

            X0 = UpperLeft.X;
            Y0 = UpperLeft.Y;
            SX = WinWidth / (LowerRight.X - UpperLeft.X); //pix/m = 1/Sx
            SY = WinHeight / (UpperLeft.Y - LowerRight.Y); //pix/m = 1/Sy
            return true;
        }

        public PointCoor MapToWindow(PointCoor MapPnt)
        {
            double x = (MapPnt.X - X0) * SX; //pix=(m+m) * pix/m
            double y = (Y0 - MapPnt.Y) * SY;
            return new PointCoor(x, y);
        }

        public PointCoor WindowToMap(PointCoor WinPnt)
        {
            double x = (WinPnt.X / SX) + X0; //m=(pix/(pix/m)) + m
            double y = Y0 - (WinPnt.Y / SY);
            return new PointCoor(x, y);
        }

(*) THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.