Alicia Alonso, director of the Cuban National Ballet, in Havana in 2012. (Reuters/Enrique De La Osa)

As much as a dancer needs a strong body, it’s her mind that needs to be strongest of all. This is the poignant truth at the heart of “Horizons” (“Horizontes”), a revealing documentary by Swiss filmmaker Eileen Hofer about three generations of Cuban ballet dancers, each of whom has an iron will.

Alicia Alonso is the star of the film, the legendary ballerina who became one of American Ballet Theatre’s greatest early stars, in the 1940s, then returned to Havana to lead the Ballet Nacional de Cuba, which she continues to dominate today, at 93. She is virtually blind; she started losing her eyesight early in her career. In a television interview from the 1950s, Alonso is asked how she got through one period of surgeries, with both eyes bandaged, her future uncertain.

“I danced inside of me,” Alonso says. “I danced with my eyes closed, and I kept working for something. Something that was born inside of me that could not die.”

Indeed, her inner light never dimmed. She continued to dance despite her failing vision. She still teaches today, though, as the film makes clear, it’s neither easy for her nor the teachers who assist her, nor the dancers. Alonso appears quite infirm. Still, she carries on, impatient to arrive at her class, intent on continuing her work. It is all she wants to do.

She shares that drive with the film’s two other subjects: Viengsay Valdes, a Ballet Nacional principal dancer struggling to hold on to her position (she dazzled audiences as a guest artist in “Don Quixote,” with the Washington Ballet in 2009), and a willowy teenage ballet student named Amanda de Jesus Perez Duarte, who has arresting eyes and the wistful look of a romantic who knows this affair may not end well but is plunging ahead all the same.

“Horizons” unfolds at a leisurely pace, just like a day in the Caribbean. It captures the crumbling ballet company headquarters and plunky pianos perfectly, the ocean air and termites rendering them forever out of tune. A strong sense of longing pervades this lovely film. The reality is that these three women — the legend, the star, the student — all have a tenuous hold on their art form. Each is facing the possible end of a dream. But if there is some denial at work — particularly on Alonso’s part — their perseverance comes across as a poetic act in itself.

“A young girl who wants to be a dancer has to dedicate her whole life to it,” says Alonso.

She’s talking about herself, of course. We learn that she always kept her ballet shoes in her purse, wherever she went, even when she was incapacitated from yet another eye surgery. She keeps them with her still.

“Knowing her shoes were always close by comforted her,” says a friend, “as if her skill was always there, within reach.”

“Horizons” screens at 7 p.m. Tuesday at the AFI Silver, 8633 Colesville Rd., Silver Spring, as part of the Latin American Film Festival. Filmmaker Eileen Hofer, Ballet Nacional de Cuba dancers and Septime Webre, artistic director of the Washington Ballet, will hold a Q&A afterward. Visit http://www.afi.com/silver.