The mathematical conventions Generally speaking, when we want to “render” something to the screen, it means we need to calculate the “color” of each pixel on the refreshing LCD in front of us, and then ask some hardware to fulfill those pixels with the color we specified. But typically what we have in our hard disk are just some mesh and texture data files, which only contain some basic information about the object we want to render, like how many vertexes they have, where the vertex’s position is in their own coordinate space, what the “color” of that vertex should look like and etc.. So, how to manipulate them until we get the final color that we could output to the screen’s pixel? Of course, we need some math, I assume you had already learned some basic linear algebra in theory and thus could understand what a matrix it is (or you could reference Wikipedia here for some sorts of overview).

Where is where? In our daily life, when someone asked for the help about how to reach the place they want to go, we would answer them like “walk toward north and turn left at the first corner”, and here we use some kind of coordinate system to represent the relativity of position in the world we are. And in our virtual world inside the computer, it would be awesome if we could use the same north and left concepts. But since the computer only knows 0 and 1, there are lots of difficulties to make a north really north.