### Archive

Archive for September 11, 2016

## 3D mathematics [book]

It’s not often I promote books, but this time I’ll make an exception: Mathematics for 3d programming and computer graphics.

A book worth every penny, even if you dont use 3d graphics very often

No matter if you are a Delphi programmer, Smart Pascal, Freepascal, C# or C++; sooner or later you are going to have to dip your fingers into what we may call “primal coding”. That means coding that was established some time ago, and that have since been isolated and standardized in APIS. This means that if you want to learn it, you are faced with the fact that everyone is teaching you how to use the API — not how to make it or how it works behind the scenes!

### 3D graphics

Once in a while I go on a retro-computer rant (I know, I know) talking about the good ol’ days. But there is a reason for this! And a good one at that. I grew up when things like 3d graphics didn’t exist. There were no 3d graphics on the Commodore 64 or the Amiga 500. The 80’s and early 90’s were purely 2d. So I have been lucky and followed the evolution of these things long before they became “standard” and isolated away in API’s.

Somewhere around the mid 80’s there was a shift from “top-down 2d graphics” in games and demo coding. From vanilla squares to isometric tiles (actually the first game that used it was Qbert, released in 1982). So rather than building up a level with 32 x 32 pixel squares – you built up games with 128 degrees tilted blocks (or indeed, hexagon shaped tiles).

This was the beginning of “3D for the masses” as we know it because it added a sense of depth to the game world.

Qbert, 1982, isometric view

With isometric graphics you suddenly had to take this depth factor into account. This became quite important when testing collisions between sprites. And it didn’t take long before the classical “X,Y,Z” formulas to become established.

As always, these things already existed (3D computation was common even back in the 70s). But their use in everyday lives were extremely rare. Suddenly 3d went from being the domain of architects and scientists – to being written and deployed by kids in bedrooms and code-shops. This is where the european demo scene really came to our aid.

### Back to school

This book is about the math. And it’s explained in such a way that you don’t have to be good in it. Rather than teaching you how to use OpenGL or Direct3D, this book teaches you the basics of 3D rotation, vectors, matrixes and how it all fits together.

Why is this useful? Because if you know something from scratch it makes you a better programmer. It’s like cars. Knowing how to drive is the most important thing, but a mechanic will always have a deeper insight into what the vehicle can and cannot do.

Every facet is explained both as theorem and practical example

This is the book you would want if you were to create OpenGL. Or like me, when you don’t really like math but want to brush up on old tricks. We used this in demo coding almost daily when I was 14-15 years old. But I have forgotten so much of it, and the information is quite hard to find in a clear, organized way.

Now I don’t expect anyone to want to write a new 3D engine, but 3D graphics is not just about that. Take something simple, like how an iPhone application transition between forms. Remember the cube effect? Looking at that effect and knowing some basic 3D formulas and voila, it’s not a big challenge to recreate it in Delphi, C++, C# or whatever language you enjoy the most.

I mean, adding OpenGL or WebGL dependencies just to spin a few cubes or position stuff in 3D space? That’s overkill. It’s actually less than 200 lines of code.