NEW YORK (AP) ― If you’ve ever seen British choreographer Matthew Bourne’s version of “Swan Lake,’’ you already know that his birds aren’t the usual delicate, fluttery ballet swans.

They’re muscular, menacing and very, very male ― and now they’re something else: 3-D, for one night only at a movie theater near you.

When Bourne’s distinctive, testosterone-heavy flock swoops in Tuesday to some 220 theaters across the U.S., it will be only the second time a full ballet is presented in 3-D, after “Giselle’’ last year.

For Bourne, whose 1996 “Swan Lake’’ was a hit on Broadway and in London’s West End and has toured the world on and off ever since, the prospect of a third dimension was at first daunting, but ultimately very exciting.

“The astonishing thing about the 3-D is that it gives a sense of space,’’ the choreographer said in an interview from London. “Suddenly you can feel the space between people. It’s quite special ― so much better than I thought.’’

What it’s not, he emphasizes, is a special-effects gimmick: Things won’t pop out and attack you in your seat. “It’s not like in the popcorn movies,’’ he says. “This is more subtle ― a feeling of immediacy, like you’re really there.’’

Because of the 3-D element, Tuesday’s screenings won’t be live. Bourne and his company, New Adventures, prerecorded the performance last year in London with the same cast as last year’s four-week New York revival, led by the broodingly charismatic Richard Winsor as the lead Swan/Stranger.

Besides the West End run, the Broadway run, the three Tony awards and the frequent international tours, Bourne’s show also earned a place in pop culture when it was referenced in the final scene of the 2000 film “Billy Elliot.’’ As Billy’s father arrives to see his grown-up son perform, it turns out Billy has become a Bourne swan.

“That was a great ending, and it’s done us a lot of good,’’ says Bourne. He explains that it wasn’t a total surprise, since he’d been sent the original script of the film for comments ― a script that had grown-up Billy dancing the traditional prince role. He mentioned it might be better if Billy grew up to do something a little more, well, rebellious.

For NCM Fathom, which is presenting the screenings along with More2Screen, Bourne’s “Swan Lake’’ was a particularly apt choice to introduce more people to 3-D ballet ― a concept it obviously hopes will take off. Future screenings are planned for other countries.

“This particular version has some very special qualities about it,’’ says Dan Diamond, senior vice president of NCM Fathom Events. He adds that of all the art forms, ballet fans have responded the most enthusiastically to the concept of 3-D, according to the company’s research and its pilot screenings last summer of “Giselle,’’ another classic.

“First of all, ballet on a big screen is beautiful,’’ Diamond says. “What 3-D does is accentuate the nuances ― the depth of field, the height of jumps. It just brings the audience closer. Our goal isn’t to use 3-D as a gimmick, but to enhance the experience.’’

Bourne says he initially feared it could feel gimmicky, but was delighted with how it all came out. And, he adds, imagine the possibilities.

“The potential for the performance of dance is thrilling,’’ he says.