Re: [Algorithms] Texel area

[Olivier G. <gal...@po...>]

  Hi,

On Mon, Feb 07, 2011 at 10:04:23AM -0000, Diogo de Andrade wrote:
> I'm just unclear on a couple of things:
> 
> > That's a rather usual linear system.  Noting the inverse determinant
> 
> How does this matter? Not questioning it, just trying to understand what
> follows from here...

It matters just because equation systems of the form:
  ax+by = c
  dx+ey = f

have a well known solution.


> > You'll notice that all these are linear systems, which means a texel
> rectangle size is independant of its position.  
> 
> This seems counter-intuitive... I understand your reasoning, and I can't
> find a mistake in your logic, but it seems to me that the size shouldn't be
> constant (from an intuitive standpoint)...

Your intuition is thinking "projected on the screen" while your
question was "in world space".  In world space, camera position
doesn't matter.  Mapping the texture is equivalent to cutting a
triangle in the texture with points on the (u, v) positions, and
streching it like is was made of rubber to fit the world-space
triangle.  The squares that are the texels stretch into
parallelograms, but they all end up the same size.

  OG.