Mathematics helps make the magic of movies by creating images and actors that don't otherwise exist. Yet while computer-generated images have improved greatly in the past decade, films will still always need actors and their voices.
So suggests Dr Andrew Fitzgibbon, a senior researcher at the Cambridge-based Microsoft European research centre. "It will take us a while to portray actors," he said yesterday.
Dr Fitzgibbon was speaking before his Science Week Ireland lecture last night at NUI Maynooth entitled, Celluloid Sums: the Mathematical Magic behind Harry and Frodo.
"It is about the maths that lies behind certain types of special effects," he explained. This high-powered mathematics is essential to create artificial characters and parts of an otherwise real scene.
It would be used, for example, to place a non-existent castle at the top of a real mountain. The computer software must be able to create a realistic-looking structure that blends naturally with its surroundings, he said.
The challenge becomes significantly more difficult if either the camera - and hence the person's viewpoint - or an artificial object within the frame moves relative to real objects in the frame.
Being able to control this is dependent on imitating the way human vision processes three-dimensional images.
A wide range of mathematics is used to create computer-generated images in films such as Jurassic Park, The Lord of the Ringsand Harry Potter. "There is lots of trigonometry involved and also matrix and vector maths," he said. "The thing I use pretty much every day is calculus."
Quaternions, a four-dimensional form of algebra devised by 19th-century Irish mathematician William Rowan Hamilton, is also used to control complex motion, said Dr Fitzgibbon. He is originally from Dublin and received his undergraduate degree at University College Cork.
These techniques are unlikely to replace actors any time soon, he added. Although the Gollum character in The Lord of the Rings was computer-generated, it still required a human actor to enable Gollum's apparent movements.
"The movement is dependent on a real actor moving through these actions as a way to identify joint position," Dr Fitzgibbon said. The computer graphics then create the character and map the real actor's motion. "The voice is always going to be played by voice actors," he added. "We are quite a way from the first fully computer-generated film."
He highlighted milestones including Alfred Hitchcock's The Birds- where film of birds in flight was overlaid on film of the actors.