Shifted, scaled and rotated coordinate system

Question

I have a image coordinate system and a tile coordinate system.

I would like to know the Point (u_img / v_img) in the tile coordinate system.

The coordinate system is scaled with sigma. u_img = sigma * u_tile; The shift is given in in the tile coordinate system. The rotation angle between the two coordinate systems is the heading.

what I want is something like (u_tile v_tile) = f( u_img, v_img, sigma, heading, u_trans, v_trans)

I started with:

void   image2tile( uint u_img, uint v_img,
                   int u_trans_tile, int v_trans_tile,
                   float imgPixelSize, float tilePixelSize,
                   float heading,
                   int& u_tile, int& v_tile )
{
      float ratio = imgPixelSize / tilePixelSize;
      int u_trans = u_img * ratio + u_trans_tile;
      int v_trans = v_img * ratio + v_trans_tile;

      v_tile = floor( v_trans * cos( heading ) + u_trans * sin ( heading ) );
      u_tile = floor( -v_trans * sin( heading ) + u_trans * cos ( heading ) );
}

There are results that seem reasonable, but if I put in u_img = 0 and v_img = 0 I should end up with u_trans_tile and v_trans_tile what actually is NOT the case.

I think the solution could look like this:

1.) transforming the translation in tile coordinates to the image coordinates 2.) after that it was just a normal transformation using the scale factor multiplied with the rotation matrix multiplied with the point vector and added by the new translation vector.

u_trans_tile -> u_trans_img v_trans_tile -> u_trans_img

  v_tile = floor( ratio*( v_img * cos( heading ) + u_img * sin ( heading ) + u_trans_img);
  u_tile = floor( ratio*(-v_img * sin( heading ) + u_img * cos ( heading ) + v_trans_img);

But actually I couldn't get it work.. ANY SOLUTIONS?

Is the result not the expected or is there another error? What type are imgPixelSize and tilePixelSize? If they are integers then your problem is integer division which doesn't yield the expected result. — denahiro
The result is not the expected, I think my transformation is not correct. — yokolini
I changed added the function header so you can see that imgPix and tilePix are both float — yokolini
Have you checked that cos(m_currGpsPos_s.heading) returns the value that you expect? Otherwise your transform looks correct, although the code is somewhat confusing as you switched the order of v_tile and u_tile. — denahiro
I edited my question, maybe this will help you. I really don't think that I have the right transformation. — yokolini

Andrey Andrey · Accepted Answer · 2012-08-16T08:48:27

Might it be due to rounding errors caused by casting intermediate results to int?

This is accurate

  float u_trans = u_img * ratio + u_trans_tile;
  float v_trans = v_img * ratio + v_trans_tile;

Shifted, scaled and rotated coordinate system

1 Answers