## More Challenging Limits

Source: More Challenging Limits

## MATHS GOES TO THE MOVIES

### Maths goes to the movies

Got your popcorn? Picked a good seat? Are you sitting comfortably? Then let the credits roll…

## MATHEMATICS PROUDLY PRESENTS…

We have all marvelled at the incredibly life-like computer generated images in the movies. What most of us don’t realise is that the dinosaurs of Jurassic Park and the wonders of Lord of the Rings — particularly the star turn of Gollum — would not have been possible without mathematics.
But how are these amazing images made? Computer graphics and computer vision are huge subjects. In this article we will take a simplified look at some of the mathematics it takes to get to a final product. First we’ll create the world seen in the movie, and then we will bring it to life.

## SETTING THE SCENE

First objects are modelled as wire skeletons made up from simple polygons such as triangles.
The first step…

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# Finding your way home without knowing where you are

The life of a foraging ant is tedious and boring. It involves nothing more than repeated trips between food sources and the nest. These trips are arduous and long. A single foraging trip of an ant, one of many in a day, might be hundreds of metres. We can put this in human terms by comparing this foraging distance to the body-length of an ant. A 200m journey for an ant represents a distance of over 26,000 body lengths. For a human of average height that would equate to a trip of 30 miles. An ant forager will repeat this journey until she drops dead from exhaustion.

The foraging trips aren’t just long, they also follow complex zig-zag paths. So how do ants manage to find their way back home? And how do they manage to do so along a straight…

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## INTRODUCTION

There is a legendary story of the sage who posed the question: ‘A normal elephant has four legs; if an elephant’s trunk is called a leg, how many legs does it have?’ He asked a mathematician, who continued to stare at a pile of paper on which he was scribbling as he muttered: ‘four and one make five’. Next to him a philosopher mused enigmatically and puffed for a few moments on his pipe before observing: ‘The fact that it is called a leg, doesn’t change the fact that it is not a leg, so the answer isfour ‘. ‘Excuse me,’ said a passing zoologist, ‘if a trunk is classified as a leg, clearly this will also apply to the tail, so it has six legs, and it’s an insect’. A logician joined the conversation: ‘A normal elephant has four legs…

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