Re: [pygame] Pixel Location in 3D Space?

["Mike C. Fletcher" <mcfletch@xxxxxxxxxx>]

HandyGM wrote:

> Imagine taking a balloon in the shape of the 3D object, 'painting' the
> texture map on it, then popping the balloon, leaving the paint hanging
> where it was in 3D space when the model existed. For each 'dot of paint'
> (pixel in the texture map), I want to know where it is in 3D space.
>
> Basically, I want to map all the points in a texture map, to their
> corresponding points in 3D space, given a standard 3D object of
> arbitrary-sized polygons. Most of the time, the model is composed of
> triangles and quadrangles, but sometimes there are polygons with more 
> sides.
>
> Does anyone have an idea on how this might be accomplished?

   * textures are mapped linearly across a triangle
         o All polygons can be reduced to triangles during tessellation
         o The corner of each triangle has a texture coordinate, again,
           often generated during tessellation
         o For any point on the surface of the triangle, the pixel
           displayed is a linear blending of the texture coordinates of
           the 3 points of the triangle, you'll find an equation in the
           OpenGL spec for how that math works
   * textures are applied (normally) to large numbers of triangles, and
     can be repeated even within a single triangle (texture coordinates
     with differences > 1), so for each pixel in the texture you have
     up to NUMTRIANGLES 3D points for that pixel
         o So, for each pixel
               + for each tessellated triangle
                     # for imagewidth in texture coordinate triangle width:
                           * for imageheight in texture coordinate
                             triangle height:
                                 o test if
                                   imagewidth+pixel,imageheight+pixel
                                   is within coordinate triangle
                                       + if it is:
                                             # take a linear blend of
                                               the 3D points of the
                                               triangle with the
                                               weights for the texture
                                               coordinates

However, that's a fairly generalised approach, if you've got X standard 
objects and you just want to work with those you can likely simplify 
some assumptions considerably.  I've also not spent much time on how to 
optimise it, there's likely a better way to do the "does this pixel in 
any repetition show up within the triangle" test.

HTH,
Mike

--
________________________________________________
 Mike C. Fletcher
 Designer, VR Plumber, Coder
 http://www.vrplumber.com
 http://blog.vrplumber.com