Re: [Algorithms] Texel area

[Jason H. <jh...@st...>]

Actually, all this talk about triangles being flat is somewhat 
confusing.  :-)  The only way a triangle really represents a sliver of a 
plane is if the vertex normals are all parallel.  Otherwise, it's really 
an approximation to a curved surface, and you're inducing faceting in 
your samples by assuming they are planar.  Shouldn't the correct mapping 
should be concave or convex, according to the flex in the curvature of 
the triangle?  Just saying...

JH

On 2/7/2011 12:15 PM, David Neubelt wrote:
>
>                 The gradient will be constant across the triangle. If 
> it's constant in dx and it's constant in dy then it's constant 
> everywhere. If you know the gradient in the two directions then you 
> know it everywhere (dx, dy, 0)
>
> *From:*Manuel Massing [mailto:m.m...@wa...]
> *Sent:* Monday, February 07, 2011 2:47 AM
> *To:* Game Development Algorithms
> *Subject:* Re: [Algorithms] Texel area
>
> Hi Diogo,
>
> > 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)...
>
> you are probably thinking about the usual texture mapping setup, where
>
> a projective mapping (from screen space to texture space) is performed.
>
> In this canonical case, the texture footprint is position dependent (you
>
> describe the mapping of projective planes by a homography, which is
>
> linear in homogenous coordinates, but non-linear in texture/screen 
> coordinates due to the perspective division).
>
> Your setup is just a linear transform of a 2D subspace (you want to 
> transform
>
> the UV plane into the world space triangle plane), i.e. you seek a 
> mapping of the UV-basis vectors to their respective world-space 
> counterparts.
>
> cheers,
>
> Manuel
>
>
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