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“First of all, ballet on a big screen is beautiful,” Mr. Diamond said. “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.”

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

“The potential for the performance of dance is thrilling,” he said.