Hi,

I am currently engaged in the study of building VEX tools.
Of course in doing that one really does not get far without broadening the knowledge of the mathematical aspect of computer graphics.

The two books I have chosen for my studies are “Modeling & Texturing - A Procedural Approach, 3rd Ed.” by Ebert et al. and “Mathematics for Computer Graphics, 2nd Ed.” by John Vince.

So far I think I am getting along reasonably well learning all the things that I have up to now been working with through means of GUI handles and parameter panes.
What I have noticed though, is that there is a broader range of basic terms and definitions which are assumed to be known that can be used differently from author to author even within the same book. This makes it difficult for me to tie it to existing VEX terminology. For example:

1. Are S and T coordinates the same as U and V coordinates in the sense of describing surface directions in parameter space - or are there slightly differing definitions as in that when stating ST coords we talk about parametric geometry and when stating UV coords we talk about texture projections?

2. In VEX on the Globals node, is “Pw” or the Point W Coordinate only applicable for solid textures (I believe Image3D is the Houdini term - please correct me if I am wrong) or can it be used elsewhere?

3. What does the Greek letter omega (small omega - looks like a ‘w’) usually stand for in computer graphics and/or image processing?
From guessing by context in image processing the small omega stands for something related to frequency and in CG it stands for something akin to a perturbed vector or similarly distorted entities.

Thank you very much for reading my post! Please do correct me - I'd love to learn. It's a very fascinating topic and Houdini just gives you so much power in this regard.


Andre

andreb
1. Are S and T coordinates the same as U and V coordinates in the sense of describing surface directions in parameter space - or are there slightly differing definitions as in that when stating ST coords we talk about parametric geometry and when stating UV coords we talk about texture projections?

In VEX, yes, that's right: ST->parametric (by design), and UV->texture (by convention). The distinction being that the vector-valued, bound parameter/attribute “uv” is not declared, maintained, or enforced in any way by Mantra/VEX, whereas the two varying global float parameters “s” and “t” are. The UV* SOPs will give these texture attributes the names “uv”, “uv2”, “uv3”, etc so it may feel like a built-in feature but it's not; those names are just a convention; from the POV of a shader they're completely arbitrary and they could be given any other name – the only guaranteed attributes/parameters are the two globals ‘s’ and ‘t’ (which denote parametric, not texture coords).
In RSL however, things are a little different (and somewhat reversed when compared to VEX).

andreb
2. In VEX on the Globals node, is “Pw” or the Point W Coordinate only applicable for solid textures (I believe Image3D is the Houdini term - please correct me if I am wrong) or can it be used elsewhere?

In the SOP context (N/A in shading contexts), I believe this is the spline weight of the point P, and is only meaningful for parametric curves or surfaces like NURBs or Beziers.

andreb
3. What does the Greek letter omega (small omega - looks like a ‘w’) usually stand for in computer graphics and/or image processing?
From guessing by context in image processing the small omega stands for something related to frequency and in CG it stands for something akin to a perturbed vector or similarly distorted entities.

It could stand for just about anything I'm afraid. In simulation contexts it's often used to denote angular frequency, and in shading it's often used to denote an incidence/exitance direction when describing a BRDF, for example. But don't assume any particular meaning – even the venerable PI gets often used to symbolize things that have nothing to do with the ratio of a circle's circumference to its diameter.

Hope that helps.

Yes that totally helps!
Thank you very much for taking the time to write it all up

Your explanation about these definitions and how they are used within Mantra is most helpful.

Andre