Patch the vectors, matrices and quaternions behind 3D graphics yourself.
2 Sessions at 3 hours, live in English language
Recordings will become available the day after the live lesson.
Maths for artists who use computers. Particularly anyone who finds themselves transforming things in game-engine / GPU-powered worlds.
Over two sessions the goal is to learn the relevant mathematical concepts not just conceptually, but to start developing a kind of intuitive understanding that enables playful exploration. Then you too can frolic among the matrices and quaternions like a pony in a field of clover.
It works both ways. On one side, the applied and concrete: vectors, dot and cross products, matrices and transforms, orientation and quaternions — put to work building your own cameras, wrestling gimbal lock, and driving teapots (aggressively). On the other, the fun of visualizing abstract theory until it stops being abstract: signed distance fields, scalar and vector fields, gradient and curl.
It builds on the maths patches Toby K published in VL.ExtendedTutorials and goes further — we patch it all ourselves in Skia and Stride, with exercises to grow the intuition, and dip a toe into VL.Fuse. You help steer, too: propose a topic or two at the end of session one and we cover them in session two.
By the end, the matrices aren’t something to survive. They are somewhere to play.
What you will learn
- Vectors and Unit Vector
- Dot Product
- Matrices
- Stride entity system and transforms
- Cross Product
- The many ways to describe orientation
- Up vectors
- Gimbal lock
- Quaternions
- Screen space vs World space vs Foobar space
- Camera transforms
- How to make your own cameras
- SDFs
- Scalar Fields
- Vector fields
- Gradient and Curl of fields
Requirements
- Windows computer with latest vvvv gamma installed
- 3 button mouse recommended
- Second monitor recommended
- VL.Fuse pack matching your vvvv version (compatibility chart: https://thegraybook.vvvv.org/changelog/nuget-compatibility-chart.html)
- A suitable GPU for running VL.Fuse (run some help patches to test)
Course Outline
Session 1 – 10.11.2026
We will cover the lower level concepts and patch it all ourselves in skia & stride.
Does some specific mathematical abstraction confound you? There is the opportunity at the end of the first session to propose a couple of topics to be included in the second session.
Session 2 – 17.11.2026
We put the knowledge from session 1 together to make fun stuff like cameras and aggressively driven teapots. Plus we try to demystify VL.Fuse a little bit. Finally we will have time for a topic or two chosen by students at the end of session 1.
