![]() ![]() Vectors are written as $(x,y,z)$, for instance $(1,2,3)$ means move 1 in the x-direction, 2 in the y-direction and 3 in the z-direction. For instance, if I say $x=3$, $y=1$, $z=5$, you find the point by walking 3 metres in the direction of your right hand, then 1 metre in the direction of your left hand, and then getting a ladder and climbing up 5 metres. I can now give you a vector and you'll be able to find For instance, put one arm out pointing to the right, and the other pointing straight forward. You can think of these numbers as how far you have to go in 3 different directions to get to a point. A vector is 3 numbers, usually called $x$, $y$ and $z$. Here is a picture of what this looks like.Ī vector is a mathematical way of representing a point. We call this the intersection of the line and the In fact, sometimes you can't find the intersection, because they don't meet and sometimes the line is inside the plane so they meet at every point on the line, but this doesn't happen in the cases we're interested in. If you have a line and a plane, you can find the point where the line cuts through the plane. There are more complicated shapes, called solids, like a cube or a sphere. A plane is a more complicated shape, it is a flat sheet, like a piece of paper or a wall. A straight line is just the simplest shape joining two points ![]() (It's quite difficult to explain what a point is, it is basically just a position, for instance, the very end of your nose is a point). ![]() Geometry is the study of shapes of various sort. To begin to explain how these games work, you need to know a bit about geometry, vectors and transformations.Ģ.1 Geometry, Vectors and Transformations Polygons). Computer graphics have improved vastly over the past 40 years, and the main reason for this is the improvement in processors which allows more polygons to be rendered.Ī screenshot from Zelda: Breath of the Wild by Nintendo These polygons can be decorated in a number of ways to make them look better, but in this section we focus on the geometry and the process of rendering it (drawing the 3D artists can spend days creating an object with tens of thousands of polygons. The virtual world you encounter in a computer game is basically made up of a space occupied by polygons with decorations on. The answers are at the end of the article, but do have a go at solving them on your own first. There are some exercises which you can do (if you want) throughout this article. Physics - making the world behave in a way which is believable. Pathfinding - the basis for finding routes around the game world. Geometry - the shapes that make up the world you move around, and all the characters within it. There are three aspects of games which we'll explore: but the same ideas are used in 2D games occasionally as well. Generally we will be talking about 3D games. The article will refer to some examples of popular computer games which you may have played. The purpose of this article is to have a look at how mathematics is used in computer games. ![]()
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