Am 22.06.2016 um 22:06 schrieb Bald Eagle:

>> Contrary to what Jerome posted, the UV coordinates are not interpolated
>> between 3 points, but between all 4 of them.
> 
> Interesting.   The ways docs are written, it strongly suggests that Bezier
> patches are subdivided into triangles, which would lead one to assume that it
> was interpolated in the same manner.

AFAIK, Bezier patches are subdivided into quadrilaterals, which in turn
are divided into two triangles each for no other reason than to ensure
that each of the fundamental elements is guaranteed to be perfectly planar.

> I understand the general concept of the uv-mapping.  It's a projection of sorts.

Technically it is indeed a projection, but that term might be misleading
since it is usually associated with simple linear projections where each
point in 2D texture space has an entire infinite straight line or ray in
3D geometry space mapped to it. In UV mapping, rules for how geometry
space is mapped to texture space are only defined for the surface of the
object in question.

> My real present interest is to use 6 patches for the face of a cube and uv-map
> the cube.  They're not "uvw" vectors, so I'm struggling to understand what
> programmers of modelers do in order to get all of the uv-mapping of 3D objects
> to map "smoothly", or "as expected".

In practice, UV mapping is rarely ever seamless. In all but the most
trivial cases there will be locations where the object's surface is
contiguous but the corresponding texture is "ripped apart". It is the
artist's responsibility to make sure that the texture portions at both
sides of the seam match up -- or that the seam is hidden away where it's
the least obvious.

There are also tools that allow to paint directly on a (virtual) 3D
shape, automatically painting on both sides of any seams.

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