Translating co-ordinate from one rectangle to another rectangle

Question

I am trying to translate a co-ordinate from one rectangle to another. In realty, the second rectangle is the first rectangle "scaled-up".

I am using the following method:

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 co-ords, to convert it to
Rectangle 2 co-ords: 
            xNew = ((x-x1)/w1)*w2 + x2; 
            yNew = ((y-y1)/h1)*h2 +y2;

In code, this simply looks like that:

float floatX = ((((point.X - source.X) / source.Width) * destination.Width + destination.X));
float floatY = ((((point.Y - source.Y) / source.Height) * destination.Height + destination.Y));

However, I don't think this is correct.

Example 1:

Rectangle1 x=9, y=9, Width= 310 Height = 190
Rectangle2 x=0, y=0, Width= 800 Height = 800
Given Point 799,799 in Rectangle 2, I get 318.6125, 198.7625 

Example 2:

Rectangle1 x=9, y=9, Width= 2 Height = 2
Rectangle2 x=0, y=0, Width= 800 Height = 800
Given Point 300,300 in Rectangle 2, I get 9.75, 9.75

In Example 1 if I Round Up I get the desired result. In Example 2 if I Round Down I get the desired result.

How do I get one size fits all solution? Do I need to apply a scaling factor to get the correct Rounding logic?

Answer 1

Probably the best is to round to nearest in all cases, but there are problematic cases. In your example 2, you only have the choice to output $9,10,$ or $11$ in each direction. If you round to nearest, inputs of $0-200$ will go to $9$, $200-600$ will go to $10$ and $600-800$ will go to $11$, which means that half the inputs go to the middle. The conflicts at $200,600$ will be determined by how you round an exact $0.5$. This is an extreme case because the destination is so small. If you go the other direction in example 2, you can only output $0, 400$ or $800$. There is no rounding.