Mr. Bourne said that when he choreographed “Swan Lake,” he hadn’t set out to alter ideas about men in dance; but he was conscious of wanting to create something for a group of men that “had beauty to it, that played a part of expressing a different kind of masculinity.”

Speaking from Washington, where he was rehearsing, he said he had been surprised by the strong reactions to the piece. “Before ‘Swan Lake,’ there were often gay elements in my work, or homoerotic relationships, and I never thought about it as a problem,” he said. “But it’s when you take something so iconic and change it; that image of the woman in a white tutu and point shoes is so imprinted, and here you had a man taking that place.”

Aside from its gender reversal, what was important about “Swan Lake” was that “it returned the dramatic male dance performance to center stage,” said Luke Jennings, a former dance critic for The Observer in Britain. Mr. Bourne’s work appeared “at the point when male dancing was more and more riveted on technique and tricks,” he said. “But here, you needed the old-fashioned business of charisma, drama, acting, understanding, pacing and nuance.”

Mr. Bourne’s “Swan Lake” also helped to bring more men into dance by offering a true-to-life range of physical types and personalities to emulate, said the former Guardian dance critic Judith Mackrell. “If you were funny or weedy or magnificent or strange, if you were a guy who weren’t sure how your body or personality fitted into the dance landscape,” she said, “here was something for you.”

Mr. Bourne said that his ballet, along with “Billy Elliot” — which featured a short segment from the Bourne “Swan Lake” — gave opportunities to male dancers and provided different types of role models, which dance on television does in a similar way now.