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Blender Math


math.pngWhile working with Blender it's easy to forget what a math processing powerhouse it really is. It's all hidden behind buttons and windows, but behind the screens there's a LOT of calculus going on. I ran into an article called 'Blender's Orientation Matrix' by Luma (the makers of the game Club Silo) which kind of puts things in perspective again.

From the introduction of the article:

It is often necessary to get some sense of the orientation of an ob ject for some game purpose. In Blender's Game Engine, the only information available is the orientation matrix, a rather intimidating 3 × 3 matrix of numbers, which seems hard to interpret and use. In this tutorial, I describe how the matrix works, and how it can be used for some common tasks. I also give Python code that implements most of the algorithms described here.

I have a degree in physics and math like this used to be (note the past tense) easy: I had tensor matrices for breakfast! However, just browsing through this paper was enough to re-install some respect for the Blender developers into me ;-)

Get the article from the 'Programming Tutorials' page on the Luma website (and while you're there, check out some of their other cool stuff).

About the Author

Avatar image for Bart Veldhuizen
Bart Veldhuizen

I have a LONG history with Blender - I wrote some of the earliest Blender tutorials, worked for Not a Number and helped run the crowdfunding campaign that open sourced Blender (the first one on the internet!). I founded BlenderNation in 2006 and have been editing it every single day since then ;-) I also run the Blender Artists forum and I'm Head of Community at Sketchfab.


  1. wow very cool, thx this will be interessting to read, always asked myself how to use this matrices in blender python scripts. THX

  2. I battled with the orientation matrix in Ozone Forces. Reading up on Euler rotation really made my head spin. I will read this when I'm feeling brave.. until then just the thought of jumping back into the euler matrix makes my stomach hurt. I hate it so much.

  3. Like you said it brother: "past tense". I have a bachelor degree in electrical engineering (specialized technical computer science). Math and C were long forgotten friends. But now I'm brushing up on those two skills again as I speak. My goal is to read those Siggraph papers like they were novels and implement those new technology in Blender right away.

    So , I hope that I can cut in starting at Blender 2.47 or something. I was wrestling with fast SSS though a few years back. It took me a quite a few months to understand Prof. Hendrik's paper and after that I started to write some code down. But then my new born son happened.

    In any case, I think that there will be lots of new potential developers for Blender waiting to strike, and when they do they'll come in waves :)

  4. i have a hard enough time understanding (and trying to explain) color math, much less matrix algerbra! Good job!! As a one-time SigGraph member (decades ago), I am amazed at when these research papers become reality. I think it takes a tremendous intelligence to understand the principles, realize the limitations of the medium (the programming language), and figure out how to turn A into B. You guys have my respect!!

  5. Just what I couldn't find anywhere and didn't know where to look for.

    I was just going to update my tutorial on shoulder deformation using pydrivers to include my solution to a pending problem by some creative cheating using constrained bones.

    Now with this reference, I might solve the problem by math alone.

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