Re: tangent maps

[André Adam <a_adam(at)49games.de>]

Hi Bernard,

the tangent property in XSI is the so called tangent map, or tangent 
space. Encoded in there you can find a given texture space's u-direction 
(the reason why you have to reference a texture projection when creating 
a tangent property) in 3d space (you could call this the "texture 
mapped" u-direction) on a per sample basis, so we're talking of vectors 
here. In absence of a more convenient property Softimage decided to 
encode the tangents into vertex colors. That means you have a little bit 
of math to do to revert them back to vector data: (VC-0.5)*2. This 
formula stretches the RGB vertex color values, which have a 0-1 range, 
back to a vector's -1 to +1 range.

The reason you need a tangent space when dealing with normal maps is 
that a "normal map in tangent space" (there is also an object space flavour)
stores relative information as to where a given normal should be bent, 
which after all is what bump mapping is all about (bump mapping and 
normal mappinng are practically the same thing). The lila-blueish color 
in a tangent space normal map means that the geometry's input normal 
should not be altered, where cyan, magenta, etc colours indicated a 
shift in normal orientation.
This shift, which is a relative bit of information as it does not point 
to global world coordinates, needs a reference on the object itself from 
which the relative shift should be calculated - the tangent space. The 
tangent space offers a predefined vector for each sample point and is 
directly generated from the texture projection the normal map is mapped 
with onto the object.

I've written a small utility that creates little pointers from the 
tangent space right on the object's surface to better show the vectors 
encoded there. I've attached two screenshots which might clearify that a 
bit. The first one shows a straight spherical mapping, the second one is 
twisted. As soon as a texture space shows distortions (or even worse: 
seams), just like the second one, tangent spaces become tricky; the 
samples for a single vertex point in different directions, which finally 
would create artifacts during normal mapping. To cope with this issue 
the tangent operator in XSI has a smoothing value, which basically 
middles the different sample's tangent vectors using an angle-based 
approach.

Since the normal map stores its data relative to the tangent space, 
generation, as done with the ultimapper for example, therefore always 
needs to reference it during generation to provide correct results. 
Ultimapper basically marries referenced object curvature from a high 
resolution source object with the normals of the low resolution source 
object and the tangent space of the low resolution object.

The Photoshop plugins and tools provided by graphics hardware vendors 
don't have this kind of 3d information available when generating normal 
maps from heightmaps. They assume that the object the generated normal 
map might get mapped onto shows an ideal tangent space, which usually is 
nonsense. The more distorted the texture space on the mapped object is, 
the wronger (is that english?!) the bump mapping results with such a 
textures are. I'd stay away from these tools for production work.

Hope that makes some sense, cheers!

   -André



Bernard Lebel wrote:

-snip-
> - you need to use a "Tangent" property. If someone could tell me why
> I'd be more than happy. I suspect this is due to the fact that tangent
> normal maps are heavily used in realtime rendering, and the Tangent
> property is a color at vertices property (which also makes it an
> absolute nightmare scripting-wise... why not having a new cluster
> property for this one, please oh God?) so there must be something
> related here.
-snip