# Glossary

The canonical language for this course. Lessons, figures, and code all use these terms; where
several words exist for one idea, one is chosen and the rest are listed as aliases to avoid.

A term is added here once a lesson has established it. Terms are promoted, not pre-loaded — so
this file also serves as a record of ground covered.

## Bases and conventions

**Basis**:
Three direction vectors that coordinates are measured against. A coordinate triple is
meaningless without one.
_Avoid_: Coordinate system (too vague — say basis, convention, or frame), axes

**Frame**:
A basis together with an origin. "World frame", "joint frame", "sensor frame". Use *frame* when
position matters, *basis* when only direction does.
_Avoid_: Space, coordinate space

**Convention**:
A named, documented package of choices: handedness, which axis is up, which axis is forward,
units, and quaternion component order. Unity and glTF are conventions.
_Avoid_: Format, standard

**Handedness**:
The one bit distinguishing the two possible arrangements of three axes. Curl the fingers of one
hand from **+X** toward **+Y**; if the *right* thumb points along **+Z** the basis is
right-handed, if the *left* thumb does it is left-handed. Not a statement about which axis is up.
_Avoid_: Orientation (means something else here), winding

**Chirality**:
The handedness of an *object* rather than of a basis — whether a body's right hand is genuinely
its right hand. Rotations preserve chirality; reflections reverse it. This is the property
violated by a mirrored skeleton. Measured as the triple product `(forward × up) · right` of the
body's semantic axes — but note the *sign* is a statement about the body **and** the frame it is
written in: a correct body reads `+1` in a right-handed frame and `−1` in a left-handed one, so
only compare poses expressed in the same convention.
_Avoid_: Mirroring, flipped-ness

**Semantic axis**:
What an axis *means* for the thing being described — up, forward, or the body's own right — as
opposed to which letter it is called. Conversions have to be judged against semantic axes,
because that is what a pose actually is.
_Avoid_: Logical axis, meaning of the axis

**Handedness conversion**:
The transform crossing between a left-handed and a right-handed convention. Between Unity and
glTF it is `(x, y, z) → (−x, y, z)` for positions and directions, and
`(x, y, z, w) → (x, −y, −z, w)` for rotation quaternions — note that the two negate *opposite*
components. Reversing handedness requires a reflection, so no rotation can substitute for it.
_Avoid_: Axis flip, the sign fix, converting coordinate systems

## Rotations

**Quaternion**:
A four-component encoding of a rotation, written **XYZW** in this course with W the scalar part,
matching the glTF spec. `q` and `−q` denote the same rotation.
_Avoid_: Quat when writing prose (fine in code), rotation vector

---

### Not yet established

Terms the mission needs that no lesson has earned yet — listed so they are defined consistently
when their lesson arrives, not defined ad hoc before then: *local* vs *world* transform,
**TRS**, multiply order / pre- vs post-multiplication, *bind pose*, *inverse bind matrix*,
*sensor-to-segment calibration*, *drift*, *slerp*, *gimbal lock*.