Ted Nasmith's artistic influence is clearly seen in Peter Jackson's Lord of the Rings films — however, if you had been a long-time fan of his art, you would be as shocked as I was to learn that he never actually worked on the films!
In an interview at Dreamish.com, Ted explains:
"I was contacted by a producer in early '99. They invited me to be there with the others in New Zealand to help with conceptual art, and made me a nice offer. However, I was going through a personal crisis unrelated to my art, and in the end, being that it would also force me to abandon my freelance obligations and be away indefinitely, I reluctantly declined, settling the question in my mind after very careful deliberation. It was a difficult decision." — Ted Nasmith
Even though Ted did not take the job, it seems clear that his established base of Tolkien artwork was used as a basis for some of the visual design of the film.
Keep in mind that Peter Jackson and New Line Cinema didn't approach Alan Lee, Ted Nasmith and John Howe because they were artists with experience in film-making and the related concept design, etc. — rather, they hired them so that they could take possession of their backlog of previous Lord of the Rings illustrations. They knew that the best way to make it "feel authentic" to Tolkien fans was to use the imagery of the top three established Tolkien artists — works that fans had known for years from the illustrated books, calendars, posters, etc. (This isn't just conjecture; they explain this themselves during the making-of featurettes on the DVDs.)
Below, I will present some examples of Ted Nasmith's artwork, side by side with stills from Peter Jackson's films (with chapter references from the Special Extended Edition DVDs) in just the straight chronological order. This is by no means a complete reference to all similarities; just the ones that particularly leapt out at me.
When looking at these, keep in mind that we're not looking for an exact representation of the painting copied onto film: we're looking for influence. Any film concept artist will tell you that their work is just a starting point — sculptors, set decorators, and all kinds of artists are between their initial concept art and the final product seen on screen.