Angles as points¶

A heading, a rotor position or a phase against a reference is a point on a circle. Its origin has a modulus: points stay within one turn, and the difference of two points is the shortest way round.

A heading¶

use exact_units::{Bam16, Point, origins::Angle, units::Turn};

type Heading = Point<Angle<Turn>, Bam16>;

let a = Heading::from_raw(0xf000); // 337.5°
let b = Heading::from_raw(0x1000); //  22.5°
assert_eq!((b - a).get(), 0x2000); // +45°: across 0, the short way
assert_eq!((a - b).get(), -0x2000); // −45°: the difference is signed

The difference of two Bam16 points is an i16: positive is counter-clockwise, negative clockwise. Exactly half a turn is \(-\tfrac12\) turn.

Other periods¶

A period that isn't \(2^{\text{bits}}\) steps works too. Hundredths of a degree wrap every 36 000 steps:

use exact_units::{Fixed, Point, origins::Angle, prefix::Centi, units::Degree};

type CentiDeg = Point<Angle<Degree>, Fixed<Degree, Centi, u16>>;

// 350° + 20° = 10°
assert_eq!((CentiDeg::from_raw(35_000) + Fixed::new(2_000)).raw(), 1_000);

How it wraps, for an \(n\)-bit storage and a period of \(M\) steps:

• \(M = 2^{n}\) (a binary angle): the storage's own wrapping add. Free.
• Any other \(M\): rem_euclid in a wider integer.
• A period that isn't a whole number of steps doesn't compile.

An unsigned storage keeps points in \([0, M)\), a signed one in \([-M/2, M/2)\).

Your own reference¶

An encoder's index pulse or north are origins of their own. Declare one with origin! and modulus: Modulo<..>: Your own units.