Transforming coordinates of one rectangle to another rectangle

Question

in the above image I have shown two rectangles

• rectangle 1 whose x can vary from -900 to 13700 and Y can vary from -600 to 6458
• rectangle 2 whose coordinate X can vary from 0 to 3000 and y can vary from 0 to 2000

Also: rectangle 2 has its starting point at left top position(0,0) whereas rectangle 1 has starting point( width/2, height/2).

What I need to do: to convert a point of rectangle 1 to point of rectangle 2 using scaling or translation.

So, what should be scaling factor for x and y coordinates in order to transform the coordinate of rectangle 1 to rectangle 2?

Answer 1

If:

Rectangle 1 has (x1, y1) origin and (w1, h1) for width and height, and
Rectangle 2 has (x2, y2) origin and (w2, h2) for width and height, then

Given point (x, y) in terms of Rectangle 1 coords, to convert it to Rectangle 2 coords:

xNew = ((x-x1)/w1)*w2 + x2;
yNew = ((y-y1)/h1)*h2 + y2;

Do the calculation in floating point and convert back to integer after, to avoid possible overflow.

In C#, the above would look something like:

PointF TransformPoint(RectangleF source, RectangleF destination, PointF point)
{
    return new PointF(
        ((point.X - source.X) / source.Width) * destination.Width + destination.X,
        ((point.Y - source.Y) / source.Height) * destination.Height + destination.Y);
}