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//! waves trait implementation
//!
//! defines the Waves trait and related functionality for wave propagation modeling
use crate::{angle::Angle, geonum_mod::Geonum};
pub trait Waves: Sized {
/// propagates waves through spacetime using wave equation principles
/// conventional: numerical wave propagation with spatial/temporal discretization O(n²)
/// geonum: direct phase evolution via angle rotation O(1)
fn propagate(&self, time: Self, position: Self, velocity: Self) -> Self;
/// creates dispersive waves with wavenumber and frequency
/// conventional: wave packet construction with fourier transforms O(n log n)
/// geonum: direct dispersion relation encoding O(1)
fn disperse(position: Self, time: Self, wavenumber: Self, frequency: Self) -> Self;
/// computes frequency as a geometric number from temporal phase evolution
/// conventional: scalar frequency extraction via division
/// geonum: directional frequency preserving temporal geometry O(1)
fn frequency(&self, other: &Self, time_interval: Self) -> Self;
/// computes wavenumber as a geometric number from spatial phase evolution
/// conventional: scalar wavenumber extraction via division
/// geonum: directional wavenumber preserving spatial geometry O(1)
fn wavenumber(&self, other: &Self, spatial_interval: Self) -> Self;
}
impl Waves for Geonum {
fn propagate(&self, time: Self, position: Self, velocity: Self) -> Self {
// compute phase based on position and time using geometric operations
let velocity_time = velocity * time;
let phase = position - velocity_time;
// create new geometric number with same magnitude but adjusted angle
Geonum::new_with_angle(self.mag, self.angle + phase.angle)
}
fn disperse(position: Self, time: Self, wavenumber: Self, frequency: Self) -> Self {
// compute phase based on dispersion relation: φ = kx - ωt
let k_x = wavenumber * position;
let omega_t = frequency * time;
let phase = k_x - omega_t;
// create new geometric number with unit magnitude and phase angle
Geonum::new_with_angle(1.0, phase.angle)
}
fn frequency(&self, other: &Self, time_interval: Self) -> Self {
// compute temporal phase difference
let phase_diff = *self - *other;
// frequency is phase difference per unit time
let magnitude = phase_diff.mag / time_interval.mag;
Geonum::new_with_angle(magnitude, Angle::new(1.0, 2.0))
}
fn wavenumber(&self, other: &Self, spatial_interval: Self) -> Self {
// compute spatial phase difference
let phase_diff = *self - *other;
// wavenumber is phase difference per unit distance
let magnitude = phase_diff.mag / spatial_interval.mag;
Geonum::new_with_angle(magnitude, Angle::new(1.0, 2.0))
}
}
#[cfg(test)]
mod tests {
use super::*;
use std::f64::consts::PI;
#[test]
fn it_propagates() {
// create a geometric number representing a wave
let wave = Geonum::new(1.0, 0.0, 1.0);
// define wave parameters as geonums
let velocity = Geonum::new(3.0e8, 0.0, 1.0); // speed of light
let time_1 = Geonum::new(0.0, 0.0, 1.0);
let time_2 = Geonum::new(1.0e-9, 0.0, 1.0); // 1 nanosecond later
let position = Geonum::new(0.0, 0.0, 1.0);
// propagate wave at two different time points
let wave_t1 = wave.propagate(time_1, position, velocity);
let wave_t2 = wave.propagate(time_2, position, velocity);
// prove magnitude is preserved during propagation
assert_eq!(wave_t1.mag, wave.mag, "propagation preserves amplitude");
assert_eq!(wave_t2.mag, wave.mag, "propagation preserves amplitude");
// compute actual phase changes from the propagate method
// phase = position - velocity * time as Geonum operations
let velocity_time_1 = velocity * time_1;
let phase_1 = position - velocity_time_1;
let velocity_time_2 = velocity * time_2;
let phase_2 = position - velocity_time_2;
// test that wave angles are correctly updated
assert_eq!(
wave_t1.angle,
wave.angle + phase_1.angle,
"phase at t1 evolves according to position - velocity * time"
);
assert_eq!(
wave_t2.angle,
wave.angle + phase_2.angle,
"phase at t2 evolves according to position - velocity * time"
);
// prove phase difference between two time points
let phase_diff = wave_t2.angle - wave_t1.angle;
let expected_phase_diff = phase_2.angle - phase_1.angle;
assert_eq!(
phase_diff, expected_phase_diff,
"phase difference matches expected value"
);
// prove propagation in space
let position_2 = Geonum::new(1.0, 0.0, 1.0); // 1 meter away
let wave_p2 = wave.propagate(time_1, position_2, velocity);
let phase_p2 = position_2 - velocity_time_1;
assert_eq!(
wave_p2.angle,
wave.angle + phase_p2.angle,
"phase at p2 evolves according to position - velocity * time"
);
}
#[test]
fn it_disperses() {
// define wave parameters as geonums
let wavenumber = Geonum::new(2.0 * PI, 0.0, 1.0); // 2π rad/m (wavelength = 1m)
let frequency = Geonum::new(3.0e8 * 2.0 * PI, 0.0, 1.0); // ω = c·k for light
let position_1 = Geonum::new(0.0, 0.0, 1.0);
let position_2 = Geonum::new(0.5, 0.0, 1.0); // half a wavelength
let time_1 = Geonum::new(0.0, 0.0, 1.0);
let time_2 = Geonum::new(1.0 / (3.0e8 * 2.0 * PI / (2.0 * PI)), 0.0, 1.0); // one period
// create waves at different positions and times
let wave_x1_t1 = Geonum::disperse(position_1, time_1, wavenumber, frequency);
let wave_x2_t1 = Geonum::disperse(position_2, time_1, wavenumber, frequency);
let wave_x1_t2 = Geonum::disperse(position_1, time_2, wavenumber, frequency);
// prove all waves have unit amplitude
assert_eq!(wave_x1_t1.mag, 1.0, "dispersed waves have unit amplitude");
// prove phase at origin and t=0 has blade 2 from 0-0 subtraction
assert_eq!(
wave_x1_t1.angle,
Angle::new_with_blade(2, 0.0, 1.0),
"phase at origin and t=0 has blade 2 from subtraction"
);
// prove spatial phase difference after half a wavelength
// compute the actual phase difference from the disperse operations
let actual_phase_diff = wave_x2_t1.angle - wave_x1_t1.angle;
// compute phase difference using geonum operations
// (at half wavelength this represents π radians or blade 2 geometrically)
let k_x1 = wavenumber * position_1;
let k_x2 = wavenumber * position_2;
let omega_t = frequency * time_1;
let phase_1 = k_x1 - omega_t;
let phase_2 = k_x2 - omega_t;
let expected_phase_diff = phase_2.angle - phase_1.angle;
assert_eq!(
actual_phase_diff, expected_phase_diff,
"spatial phase difference equals wavenumber times distance"
);
// prove temporal phase difference after one period
// compute actual phase difference between t2 and t1
let k_x = wavenumber * position_1;
let omega_t1 = frequency * time_1;
let omega_t2 = frequency * time_2;
let phase_t1 = k_x - omega_t1;
let phase_t2 = k_x - omega_t2;
// the phase difference should complete a full cycle (2π)
let phase_diff_angle = wave_x1_t2.angle - wave_x1_t1.angle;
let expected_temporal_diff = phase_t2.angle - phase_t1.angle;
// test that blade difference is 4 (full rotation) or equivalent
assert_eq!(
phase_diff_angle, expected_temporal_diff,
"temporal phase evolution matches expected value"
);
// prove dispersion relation by comparing wave phase velocities
// For k=2π, ω=2πc, wave speed should be c
let wave_speed = frequency.mag / wavenumber.mag;
let expected_speed = 3.0e8; // speed of light
assert!(
(wave_speed - expected_speed).abs() / expected_speed < 1e-10,
"dispersion relation yields correct wave speed"
);
}
}