It turned out to be the hardest model to get correct, and I'm not even sure that my final version is actually correct. Y'see, the Wolfgang Engel book I was originally using was hopeless - you'd get less typo's per page if you allowed a monkey to re-type that chapter [flaming]
In what I can only describe as a sick joke, I go to Wolfgang Engel's website, follow the link to the errata page to which is states:
There are numerous typos in the equations in chapter 15. Please download the following PDF file with the correct equations in it (Chapter15.pdf).
(Chapter 15 being the one covering Ashikhmin-Shirley). Clicking on the provided link give me... a 404 not found.
An error with the errata page - how funny [rolleyes]
As a side note; the pacing, layout and coverage in Engel's book is great. I just wish he'd consider a 2nd edition where it had actually been given to a proof reader. It's not just Chapter 15 - the whole damn book is full of stupid mistakes that really should not have made it into a final print run.
So I went to the original research paper (linked at the start) and went through implementing it from there. Seems to be quite different to Engel's implementation in a few places. But still, there are a couple of terms in the equations that seem to magically appear from nowhere. That combined with a few general typo's in the main text doesn't inspire me with confidence that even the original source was any good.
It's such a shame when great resources are ruined by such pointless mistakes [sad]