Impractical Instruments

get your learn on

Whaternion?

Interactive lessons on 3d math built around the bugs that actually break sensor <-> skeleton pipelines.

When a pose comes out twisted, mirrored, or drifting we debug it by permuting signs until it looks right. That means wrong fixes survive. This course replaces sign-permutation with reasoning you can check against a specification. See docs/rules/course-scope.md for what we are aiming at.

How to use this

Work through the lessons in any order. Each is short, self-contained, and ends with a quiz.

The reference sheets compress each lesson into a cheat sheet.

Lessons

Lesson 001 · ~12 min Handedness is chirality, not which way is up
Unity and glTF agree that +Y is up and +Z is forward, and a skeleton copied between them still comes out mirrored. Why that is inevitable, and which single sign flip fixes it.

Reference sheets

Reference 001 Conventions & conversions
Unity ⇄ glTF in one table, both conversion rules, the two tests worth memorising, and a symptom-to-cause guide. Prints to one sheet, front and back.

Where this is going

Planned, in roughly this order. Four main failure classes: twisted limbs, mirrored motion, multiply-order confusion, and drift.

NextSkill it buys you
002 · The rotation that follows the flip See a reflection reverse the sense of a rotation, so the quaternion rule stops being a memorised sign pattern. Closes out the mirrored-motion bug.
003 · Local, world, and which side to multiply on Read T * R * S and parent * local and know what each product means — the highest-frequency confusion of the four.
004 · Reading a quaternion by eye Recover axis and angle from four numbers; know why q and −q are the same rotation and when that bites.
005 · Building a basis from three points The optical/vision spine: turn joint positions into a frame, and orthonormalize it without introducing a twist.
006 · Sensor-to-segment calibration See the calibration offset as a fixed change of basis rather than a magic quaternion. This is the twisted-limb bug.
007 · Drift, normalization, and reference frames Why poses degrade, why gravity is a reference frame, and what a T-pose calibration actually pins down.
Order is not fixed — it follows whatever the team most needs next. Ask for a topic and it can jump the queue.

What is in this repo

lessons/One self-contained HTML page per lesson. Start here.
reference/Printable cheat sheets — the compressed, durable part.
assets/Shared components: the stylesheet, a dependency-free 3D renderer, the convention definitions, controls, and the quiz widget.
assets/brand/The Impractical Instruments design system — tokens and fonts, vendored verbatim so the course still opens offline.
docs/rules/Why the course exists and what it leaves out, how a lesson is built and styled, and the canonical vocabulary lessons adhere to.
RESOURCES.mdTrusted sources, annotated — plus explicit gaps.
learning-records/What the team has established, and what that changes about what to teach next.