Module vector 

Vector quantities: three components sharing one dimension.

A position, a velocity, a force and a field are all DVec3 to the compiler, and adding two of them is a bug the compiler cannot see. QVec3 carries the same seven exponents as Qty, so a displacement and a velocity stop being interchangeable.

Two of the operations are worth noticing, because they fall out of the dimensions rather than being decided:

• QVec3::normalize returns a bare DVec3. A direction has no dimension — dividing a length by a length leaves a pure number — so a unit vector is exactly the right type for “which way”, and a ray direction cannot be mistaken for a displacement.
• QVec3::length returns the scalar of the same dimension, which needs no exponent arithmetic and so works for every dimension at once.

dot and cross are missing on purpose: both change the dimension, and there is no way to express “the square of L” in a const generic parameter without unstable features. QVec3::along covers the case that actually comes up — projecting onto a unit direction, which preserves the dimension.

Structs

QVec3

Three components of one dimension, stored in SI base units.

Functions

centripetal

Force needed to hold mass in a circle — the check that a rotating stage’s bearing can take what a scan rate asks of it.

distance

Distance between two points, which is what a length actually measures.

free_travel

Speed acquired, and distance covered, under a constant acceleration.

kinetic_energy

Kinetic energy, ½mv². Needs the squared magnitude, so it is written out here rather than falling out of an operator.

momentum

Momentum of a moving mass.

newton_second

Newton’s second law, with the dimensions doing the checking.

Type Aliases

AccelerationVec

An acceleration, m·s⁻².

ForceVec

A force, newtons.

LengthVec

A position or a displacement, m. The same dimension, and deliberately the same type: the difference between them is a choice of origin, not of physics.

MomentumVec

A momentum, kg·m·s⁻¹. The vector a closed system conserves component by component — and see the note in the workspace README on why the smallest component is what binds a conservation audit.

VelocityVec

A velocity, m·s⁻¹.