Indeed, Andersen's story begins with a magic mirror created by the devil that ultimately breaks, the shards of glass piercing people's hearts and filling them with contempt. Hardly what constitutes friendly family fun, you might say. So it's perhaps doubly impressive that Lee and her co-director Chris Buck have managed to turn Andersen's dark-lined fairy tale into , a colourful 3-D computer animation with uplifting Broadway-style musical numbers.

Video: Trailer for Frozen

The original Andersen story centred on Kai and Gerda - and the latter's journey to save her friend after he becomes "cursed with negativity", as Lee puts it, from one of the shards of glass. takes a different tack. Set in the Scandinavian kingdom of Arendelle, the film focuses on two sisters, Princess Elsa (voiced by Idina Menzel) and her younger sibling Anna (Kristen Bell). Elsa, it transpires, has the power to create snow and ice at will - a dangerous skill that almost killed Anna when they were young and later drives Elsa to a self-imposed exile.

"We said, 'What if we gave Kai's journey to Elsa?' And doing that, she became more sympathetic and we could make it more complex," says Lee. In other words, is not simply a classic tale of good versus evil but one about fear and love.

"We started to say, 'How can we redefine true love? Can true love - at least for us at Disney - be different from the kiss from the male lead?' So that was a goal of ours, to play with that," says Buck. "It was those kinds of things that led us to a slightly different version of ."

does shake up the tried-and-tested Disney formula with a story where the princesses aren't always charming. This came partly through the casting of Kristen Bell as Anna. The star grew up on Disney movies, says Lee.

"But as much as she loved them, she was looking for a character that was more like a lot of us - that maybe is a little clumsy, sloppy, talks too fast, stains her dress easily. Not perfect, but still inspirational. And we were 100 per cent on board with that."

Buck, an animator whose credits at Disney include , and , first pitched the idea of five years ago. Early versions, however, did not go well, with Elsa even being designed at one point as blue with black spiky hair.

"You have to try everything," he shrugs. "I can't tell you how many versions I've seen of movies that everyone thinks are brilliant, that were a mess. was a mess for a while, and it took a while for it to find its way. That happened on ."

For the first Disney animation to be shot in the CinemaScope technique since 1959's , Buck and his research team did everything they could to give the film an authentic flavour; they visited an ice hotel in Quebec, and incorporated some Norwegian folk art into the visuals.

Then, two years ago, Jennifer Lee arrived. A co-screenwriter on - Disney's 2012 animation set in the world of video games - Lee graduated to as the sole screenwriter, before joining Buck as co-director.

It meant that Lee became the first female director at Disney in the history of the company. "I was surprised, but it feels like a sign of things to come," she says. "More and more women are in animation, and I think we're a little ahead of live action in terms of that balance."

Equally important was the arrival of husband-and-wife lyricists Bob Lopez (a three-time Tony Award winner) and Kristen Anderson-Lopez to create the songs. With Lopez's credits including such adult-oriented hits such as and , it's no wonder Buck gleefully refers to his sensibility as "twisted".

Buck points to the song built around Olaf - the talking snowman Anna befriends on her way to bring her sister home from her exile. So what does Olaf sing a song about? How he desperately wants to see summer - unaware of what heat will do to his body.

If this is typical of the off-kilter humour that Lopez and his wife injected into , it's never done with cynicism.

"They're also very sincere and they love the classics themselves," says Lee. "And they have a big Broadway sound."

None more so than with , the catchy number sung by Elsa (and beautifully rendered by Menzel) as she reveals her snowy powers in full. In the US, took in US$93.6 million in its first five days of release, setting a new record for a Thanksgiving opening. It certainly suggests that Disney's animation division is back on track after a fallow period.

"We're really hitting our stride," says Buck, "and there's more great stuff to come."

Next year it's the Marvel-inspired , a film which will look to further reinvent the Disney image.

Animation at the "Mouse House", it seems, has just got exciting again.

opens on December 19