## Math 3D - A simple vector and matrix library for C

Published

If you've done a bit of graphics programming with OpenGL you're probably familiar with vector and matrix math. Every point or direction in 3D space can be represented as a vector and most manipulations of those can be represented as matrices (moving them around, rotating them, projecting them on the screen, etc.).

I wasn't happy with the C math libraries I found so I wrote a new one (surprise!). Read on if you want to know why. But here is what using it looks like:

```
mat4_t projection = m4_perspective(60, 800.0 / 600.0, 1, 10);
vec3_t from = vec3(0, 0.5, 2), to = vec3(0, 0, 0), up = vec3(0, 1, 0);
mat4_t transform = m4_look_at(from, to, up);
vec3_t world_space = vec3(1, 1, -1);
mat4_t world_to_screen_space = m4_mul(projection, transform);
vec3_t screen_space = m4_mul_pos(world_to_screen_space, world_space);
```

OpenGL provides a lot of vector and matrix math for shaders that run on the GPU but on the CPU you have to do it yourself. I like it this way because it allows you to choose what kind of 3D math library you want: One that tries to optimize every last bit of performance but is complicated to use or one that is easy to use but lax on performance. Depending on the project you can pick what you need.

I do pretty much all of my low level graphics programming in C (I know, I'm weird, but OpenGL is a C API after all). And I haven't found a 3D math library I'm happy with for C. I don't know all of them but the ones I've looked at were complicated to use and vague on their semantics. Where they written with the OpenGL or Direct3D conventions in mind? How are matrices laid out in memory? Can I pass them into OpenGL directly or do I have to transpose them before hand?

There are good C++ math libraries that perfectly fit my purpose but I'm an awful C++ programmer. I spend way more time fiddling around with the language than I spend on solving the problem. So I stayed with C. Maybe someone else will find non-templated math code similarly appealing.

All this drove me to write my own small 3D math library for C. Just the basics, nothing fancy. A friend of mine joined in and together we started out from scratch. It was quite a nice learning experience. We spend a lot of time on the whiteboard, calculated a lot of the math by hand and wrote a lot of tests until we understood what the math should actually *mean*. It was just there that we realized that the perspective divide step in OpenGL is just an fixed function hack to fit a perspective projection into a 4x4 matrix. Kind of pointless with shaders...

Anyway, if you ever do OpenGL stuff in C and need a simple to use math library you can pick it up here: math_3d.h. It's a single header-file library in the style of stb_image.h so it's easy to integrate into projects.

It covers basic 3D vector math, transformation and camera matrices (translation, rotation, scaling and look at), projection matrices (orthographic and perspective) as well as basic matrix math (matrix-matrix, matrix-point and matrix-direction multiplication, inversion of affine transformations). The documentation is in the file itself so take a look if you're interested.

Happy programming. :)