'I've never felt like a Disney guy," says Glen Keane. "I see myself as an artist first." Never mind that he's created some of the greatest Disney characters - the Beast who charmed Beauty, Ariel in The Little Mermaid, Tarzan, Pocahantas and Aladdin - or that John Lasseter, the genius behind Pixar and now creative boss of Disney, regards him as "one of the greatest animators ever".

With his latest film, Tangled, he has managed to merge all that's beautiful about hand-drawn animation with the three-dimensional depth of computer imagery. It's a retelling of Rapunzel, the fairy tale in which the long-haired princess imprisoned in her tower is more than an equal for the swashbuckling hero who presumes to liberate her. Yet despite the film's dazzling box-office success, Keane still feels unfulfilled.

"There is a need in me to do something personal," he says. "I know that there are people who work at studios for a long time and they lose themselves sometimes. They become like a formula or a caricature of themselves. I really don't want that."

When he was a 21-year-old wannabe from Paradise, Arizona, he submitted his portfolio to the California Institute of the Arts (CalArts) to become a sculptor. "It was sent to the school of animation by accident and I was accepted. And so I've always felt that maybe someday I'll get to follow my original path."

As a rookie animator at Disney 36 years ago, he found a mentor in Freddie Morris. "Mickey Mouse was originally drawn with that very hard kind of circle, and suddenly he became bouncy, squashy, stretchy – that was Freddie Morris. He designed the Seven Dwarfs and created the Disney look. Everything suddenly had a beautiful rhythm."

Morris got this rhythm and beauty of lines from Jean-Honoré Fragonard, the French Rococo painter famous for lush portraits of lovers in gardens.

He was also a fast worker. "If he'd been born today he'd have been an incredible animator," says Keane. "I grew up on images of his work. We lived way out in the desert, but my dad was a cartoonist and had all these books on Modigliani, Degas, Lautrec and Rouault, a whole spectrum of styles. It was like a magic mirror to me through which I could see the dinosaurs or medieval knights. I wouldn't do a drawing just to do a drawing but to step into these other worlds, and I lived in them."

When Keane was seeking a way to tell the story of Rapunzel - an ongoing project first mooted by Walt Disney - he found it in Fragonard's lushly rendered 'The Swing'. Set deep in a verdant grove, the painting depicts a woman being pushed on a swing by her husband who is unaware of a young man hiding in the bushes and peeping furtively up her skirt as she goes high.

"Fragonard like Rembrandt would always light his paintings theatrically.

"You would have imaginary lights hidden someplace to pick up the glint of the girl's cheek at just the right place. 'The Swing' is the equivalent of an animated movie, the kind of narrative painting the king could look at for entertainment. It prompted me to develop a way in which we could actually step dimensionally into that kind of world taking what I loved about hand-drawn animation and marrying it to the three-dimensional possibilities of computer-generated imagery."

All the time in the filming of Tangled ? the Rapunzel title was dropped to shift the emphasis from the story of a damsel in distress to a rip-roaring Errol Flynn-style romance - Keane fought to prevent the computer taking over. "It always tries to do everything symmetrically. Symmetry is cold and austere and lifeless. I invited Ollie Johnson, a Disney veteran who was my mentor, to the studio to see what I was doing. He was 92 and couldn't walk any more. He was getting pretty feeble. He could talk clearly about animation, but that was about all. It was like his life was reduced to the principles of drawing. I showed him a little computer-generated shot of Rapunzel holding a squirrel. Look Ollie, I said, we never had freckles like that on a character before. Look at the satin on her dress, and the light reflecting on it. Look at the sheen on her hair. 'Well, Glen,' he said, with a drawl like Jimmy Stewart, 'What I am wondering is, what is she thinking about?' And, I thought, how right he is. Who cares about the cake if the cake isn't tasty with some substance to it?"

Keane was replaced on Tangled in 2008 by Nathan Greno and Byron Howard, who directed the Disney hit Bolt about a kidnapped dog television star.

"I had a heart attack and I stepped down from directing. I didn't draw for six months and just took walks, thankful for the gift of life. My first day back at work was to design the baby Rapunzel. My daughter had just had a baby called Matisse, and that's the baby you see in the movie. Bring on Matisse, I said. What a wonderful way to start drawing again."

The look of Tangled is entirely Keane's. He drew over every shot in the movie every day, trying to push the animators that bit further. "If you don't watch out, the computer will make you walk off the set with something you don't want."

An exhibition of Keane's sketches has just opened in Paris, his first ever show. "The sketches are the source for everything I have animated, all the little observations of life I've being making all my life. The irony is that you've never seen my drawings on the screen. Everything is always cleaned up or interpreted by somebody else. But there's this longing there to express myself that still drives me."

Tangled opens on Friday