The wedge product mentioned in that pseudocode is between two 2D vectors. Calling them U and V, this wedge product gives the following numerical quantity (which is technically a pseudoscalar or antiscalar, but it doesn't matter):
U ∧ V = U.x * V.y - U.y * V.x
I have a Grassmann algebra talk that provides an introduction to the wedge product:
What's been bothering myself more about Lengyel's approach is that he weighs tangents by the equivalent of inverse triangle area (area=cross(p2-p1,p3-p1)/2). Wouldn't it make more sense (and avoid a FP division) to scale by (the equivalent of) triangle area?
Are you talking about the value of r, which is 1.0F / (s1 * t2 - s2 * t1)? This divides out the "area" of the triangle in texture space so that the scale of the texture map doesn't matter, but does not have anything to do with the geometric position of the vertices. The tangents are still weighted based on the geometric area of the triangles because the variables x1, y1, z1, x2, y2, and z2 are not normalized in any way.
I read a bit about that, but it doesn't really seem to have a lot of support (there's a few unofficial exporters I suppose). I also read a lot of criticism on the way it stores stuff. (For example animations are part of a mesh)
The exporters on the opengex.org website are official. As for the criticism, please realize that not everyone who posts an opinion on the internet has the same qualifications. Some people are educated and experienced, and they probably know what they're talking about. Other people have never actually been a professional software developer, and yet they like to bash everything as if they were some kind of expert. There is a lot of praise for OpenGEX out there in addition to the few negative opinions you might have read. It's up to you to decide whether somebody's opinion actually holds water based on their qualifications. And if you can't find out what their qualifications are, then they probably don't have any.