OpenEuphoria

Polygon coordinates transformation

• Posted by Tommy Carlier <tommy.carlier at pandora.be> Mar 18, 2004
• 365 views

I want to add a routine to Win32Dib, that can draw a part of a bitmap on 
another bitmap, but stretched to a polygon. To do this, I need to find an 
algorithm that transforms coordinates from 1 polygon to another one.

I have 2 polygons with each 4 points:
polygon_source = {{u1, v1}, {u2, v2}, {u3, v3}, {u4, v4}}
polygon_destination = {{x1, y1}, {x2, y2}, {x3, y3}, {x4, y4}}

I need to find a formula that transforms a coordinate {x, y} inside 
polygon_destination to a coordinate {u, v} inside polygon_source.

I've looked for tutorials on texture mapping, but didn't find any non-3D 
transformation formula. I've looked for methods to solve linear equations, 
but didn't find the right method.

Can anyone solve the following set of equations?

x1 * a + y1 * b + c = u1
x2 * a + y2 * b + c = u2
x3 * a + y3 * b + c = u3
x4 * a + y4 * b + c = u4

a, b and c are the unknown variables. u?, x? and y? are known values. If 
these equations can be solved, I can transform coordinates with the 2 
simple functions:

u = x * a + y * b + c
v = x * d + y * e + f   -- d, e and f can be found with the same set of 
equations, but with v? instead of u?

This finds the coordinate {u, v} in polygon_source that represent the 
coordinate {x, y} in polygon_destination.

Let's see if there are any math geniuses in the Euphoria-community!

-- 

Tommy Carlier
tommy online: http://users.pandora.be/tommycarlier