feat(nvsim): source.rs Biot–Savart synthesis [nvsim:pass2]
Pass 2 of the implementation plan. Adds magnetic-field synthesis at arbitrary sensor locations, all in f64 for near-field stability per plan §7-1. Public API (re-exported from lib.rs): - dipole_field(&DipoleSource, sensor_pos) -> ([f64; 3], near_field_flag) Closed-form analytic dipole: B = (μ₀ / 4π r³)[3(m·r̂)r̂ − m] (Jackson 3e §5.6). - current_loop_field(&CurrentLoop, sensor_pos) -> (Vec3, flag) Numerical Biot–Savart over n_segments straight chords (default 64); flag fires if any chord midpoint < R_MIN_M (1 mm) of sensor. - ferrous_field(&FerrousObject, ambient_b, sensor_pos) -> (Vec3, flag) Linear induced moment m = χ·V·H_ambient (Cullity & Graham 2e §2), re-radiates as a dipole. - scene_field_at(&Scene, sensor_pos) -> (Vec3, flag) — aggregate. - scene_field_at_sensors(&Scene) -> Vec<(Vec3, flag)> — for every sensor. - R_MIN_M = 1 mm — near-field clamp constant. Pass 2 acceptance per plan §3 — n=8 RMS gate ≤ 0.5%. Test `dipole_n8_directions_within_half_percent_rms` independently recomputes the formula in-test rather than calling the implementation twice, so the gate guards against an implementation that accidentally agrees with a buggy reference. 7 new tests: - on-axis dipole matches B_z = μ₀ m / (2π z³) - equatorial dipole matches B_z = -μ₀ m / (4π r³) - n=8 directions RMS ≤ 0.5% — Pass 2 acceptance gate - on-axis current loop matches μ₀ I a² / [2(a²+z²)^(3/2)] - near-field r < 1 mm clamps to (0, flag=true) - zero-ambient ferrous object emits zero field - two opposite dipoles aggregate to zero at colocated sensor Validated: - cargo test -p nvsim → 19 passed (was 12; +7). - cargo test --workspace --no-default-features → 1,594 passed, 0 failed, 8 ignored (was 1,587; +7). - ESP32-S3 on COM7 streaming live CSI (cb #8900). Co-Authored-By: claude-flow <ruv@ruv.net>
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@ -29,9 +29,14 @@
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pub mod frame;
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pub mod scene;
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pub mod source;
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pub use frame::{MagFrame, MAG_FRAME_MAGIC, MAG_FRAME_VERSION};
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pub use scene::{CurrentLoop, DipoleSource, EddyCurrent, FerrousObject, Scene};
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pub use source::{
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current_loop_field, dipole_field, ferrous_field, scene_field_at, scene_field_at_sensors,
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R_MIN_M,
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};
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/// Top-level simulator error type.
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#[derive(Debug, thiserror::Error)]
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@ -0,0 +1,314 @@
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//! Magnetic-field synthesis at sensor location(s) — Pass 2 of the implementation plan.
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//!
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//! Implements the analytic magnetic-dipole field formula, numerical
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//! Biot–Savart integration over current loops, and linearly-induced
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//! moments for ferrous objects. All operations in `f64` for near-field
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//! stability per plan §7-1 (float-precision risk).
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//!
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//! # Primary sources
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//! - Jackson, *Classical Electrodynamics* 3e (1999) §5.4–5.6 — Biot–Savart, dipole.
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//! - Cullity & Graham, *Introduction to Magnetic Materials* 2e (2009) Ch. 2 — χ_steel.
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//! - Ortner & Bandeira, *SoftwareX* 11, 100466 (2020) — Magpylib reference impl.
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//!
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//! # API
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//!
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//! Free functions ([`dipole_field`], [`current_loop_field`],
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//! [`ferrous_field`], [`scene_field_at`]) keep the math testable in
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//! isolation; the convenience method [`crate::scene::Scene::field_at`]
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//! aggregates a single sensor sample.
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use crate::scene::{CurrentLoop, DipoleSource, FerrousObject, Scene, Vec3};
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use crate::MU_0;
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/// Minimum source–sensor distance below which the dipole / Biot–Savart
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/// formulae are clamped to zero. Plan §2.1: 1 mm. Below this, the field
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/// formula's `1/r³` factor dominates float rounding and the dipole model
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/// itself is meaningless (real magnets have finite extent).
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pub const R_MIN_M: f64 = 1.0e-3;
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// ────────────────────── public entry points ──────────────────────────────
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/// Field at `sensor_pos` due to a magnetic dipole.
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///
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/// Closed-form: `B = (μ₀ / 4π r³) · [3(m·r̂)r̂ − m]`. Returns `(B, near_field_flag)`
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/// where `near_field_flag = true` indicates `|r| < R_MIN_M` and the field has
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/// been clamped to zero. The caller is responsible for raising the
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/// `SATURATION_NEAR_FIELD` flag on the emitted [`crate::MagFrame`].
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pub fn dipole_field(dipole: &DipoleSource, sensor_pos: Vec3) -> (Vec3, bool) {
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let r = vec3_sub(sensor_pos, dipole.position);
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let r_norm = vec3_norm(r);
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if r_norm < R_MIN_M {
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return ([0.0; 3], true);
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}
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let r_hat = vec3_scale(r, 1.0 / r_norm);
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let m_dot_r = vec3_dot(dipole.moment, r_hat);
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let bracket = vec3_sub(vec3_scale(r_hat, 3.0 * m_dot_r), dipole.moment);
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let coef = MU_0 / (4.0 * std::f64::consts::PI * r_norm.powi(3));
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(vec3_scale(bracket, coef), false)
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}
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/// Field at `sensor_pos` due to a planar circular current loop.
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///
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/// Discretised over `loop_.n_segments` straight chords:
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/// `dB = (μ₀/4π) · (I dl × r̂) / r²`. Returns `(B, near_field_flag)` where the
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/// flag fires if any chord midpoint is within [`R_MIN_M`] of the sensor.
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pub fn current_loop_field(loop_: &CurrentLoop, sensor_pos: Vec3) -> (Vec3, bool) {
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let n = loop_.n_segments.max(8) as usize;
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let normal = vec3_normalise(loop_.normal);
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let (u, v) = orthonormal_basis(normal);
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let mut sum: Vec3 = [0.0; 3];
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let two_pi = 2.0 * std::f64::consts::PI;
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let mut saturation = false;
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for i in 0..n {
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let theta_a = (i as f64 / n as f64) * two_pi;
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let theta_b = ((i + 1) as f64 / n as f64) * two_pi;
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let p_a = vec3_add(
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loop_.centre,
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vec3_add(
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vec3_scale(u, loop_.radius * theta_a.cos()),
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vec3_scale(v, loop_.radius * theta_a.sin()),
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),
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);
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let p_b = vec3_add(
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loop_.centre,
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vec3_add(
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vec3_scale(u, loop_.radius * theta_b.cos()),
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vec3_scale(v, loop_.radius * theta_b.sin()),
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),
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);
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let mid = vec3_scale(vec3_add(p_a, p_b), 0.5);
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let dl = vec3_sub(p_b, p_a);
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let r = vec3_sub(sensor_pos, mid);
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let r_norm = vec3_norm(r);
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if r_norm < R_MIN_M {
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saturation = true;
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continue;
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}
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let r_hat = vec3_scale(r, 1.0 / r_norm);
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let cross = vec3_cross(dl, r_hat);
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let coef = MU_0 * loop_.current / (4.0 * std::f64::consts::PI * r_norm.powi(2));
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sum = vec3_add(sum, vec3_scale(cross, coef));
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}
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(sum, saturation)
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}
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/// Field at `sensor_pos` due to a ferrous object's linearly-induced moment.
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///
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/// `m_induced = χ · V · H_ambient`, with `H = B/μ₀` (SI). Default χ = 5000
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/// for low-carbon steel per Cullity & Graham 2e §2. Output then radiates as a
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/// dipole at the object's position.
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pub fn ferrous_field(obj: &FerrousObject, ambient_b: Vec3, sensor_pos: Vec3) -> (Vec3, bool) {
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let h_ambient = vec3_scale(ambient_b, 1.0 / MU_0);
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let m_induced = vec3_scale(h_ambient, obj.susceptibility * obj.volume);
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let induced_dipole = DipoleSource::new(obj.position, m_induced);
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dipole_field(&induced_dipole, sensor_pos)
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}
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/// Total field at `sensor_pos` from every primitive in `scene`. Returns
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/// `(B, saturation)` where `saturation` is `true` if any source clamped to
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/// zero in the near-field. The caller emits the corresponding flag.
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pub fn scene_field_at(scene: &Scene, sensor_pos: Vec3) -> (Vec3, bool) {
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let mut total: Vec3 = [0.0; 3];
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let mut sat = false;
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for d in &scene.dipoles {
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let (b, s) = dipole_field(d, sensor_pos);
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total = vec3_add(total, b);
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sat |= s;
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}
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for l in &scene.loops {
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let (b, s) = current_loop_field(l, sensor_pos);
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total = vec3_add(total, b);
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sat |= s;
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}
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for f in &scene.ferrous {
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let (b, s) = ferrous_field(f, scene.ambient_field, sensor_pos);
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total = vec3_add(total, b);
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sat |= s;
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}
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(total, sat)
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}
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/// Total field at every sensor location in a scene, in scene order.
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pub fn scene_field_at_sensors(scene: &Scene) -> Vec<(Vec3, bool)> {
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scene.sensors.iter().map(|&p| scene_field_at(scene, p)).collect()
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}
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// ────────────────────── vec3 helpers ─────────────────────────────────────
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#[inline]
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fn vec3_add(a: Vec3, b: Vec3) -> Vec3 {
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[a[0] + b[0], a[1] + b[1], a[2] + b[2]]
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}
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#[inline]
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fn vec3_sub(a: Vec3, b: Vec3) -> Vec3 {
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[a[0] - b[0], a[1] - b[1], a[2] - b[2]]
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}
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#[inline]
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fn vec3_scale(a: Vec3, s: f64) -> Vec3 {
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[a[0] * s, a[1] * s, a[2] * s]
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}
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#[inline]
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fn vec3_dot(a: Vec3, b: Vec3) -> f64 {
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a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
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}
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#[inline]
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fn vec3_cross(a: Vec3, b: Vec3) -> Vec3 {
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[
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a[1] * b[2] - a[2] * b[1],
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a[2] * b[0] - a[0] * b[2],
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a[0] * b[1] - a[1] * b[0],
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]
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}
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#[inline]
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fn vec3_norm(a: Vec3) -> f64 {
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vec3_dot(a, a).sqrt()
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}
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#[inline]
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fn vec3_normalise(a: Vec3) -> Vec3 {
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let n = vec3_norm(a);
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if n < 1e-20 {
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[0.0, 0.0, 1.0]
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} else {
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vec3_scale(a, 1.0 / n)
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}
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}
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/// Build two orthonormal vectors `u, v` perpendicular to `n` (which must be
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/// approximately unit). Stable across all input directions including ±ẑ.
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fn orthonormal_basis(n: Vec3) -> (Vec3, Vec3) {
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let pick = if n[0].abs() < 0.9 {
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[1.0, 0.0, 0.0]
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} else {
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[0.0, 1.0, 0.0]
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};
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let u = vec3_normalise(vec3_cross(pick, n));
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let v = vec3_cross(n, u);
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(u, v)
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}
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// ─────────────────────────── tests ────────────────────────────────────────
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#[cfg(test)]
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mod tests {
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use super::*;
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use approx::assert_relative_eq;
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#[test]
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fn dipole_on_axis_matches_closed_form() {
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// On-axis (along +ẑ for a dipole moment along +ẑ):
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// B_z = μ₀ m / (2π z³) (Jackson 3e §5.6 specialisation).
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let m = 1.0e-3;
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let z = 0.5;
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let dipole = DipoleSource::new([0.0; 3], [0.0, 0.0, m]);
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let (b, sat) = dipole_field(&dipole, [0.0, 0.0, z]);
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assert!(!sat);
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let expected_bz = MU_0 * m / (2.0 * std::f64::consts::PI * z.powi(3));
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assert_relative_eq!(b[2], expected_bz, max_relative = 1e-12);
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assert_relative_eq!(b[0], 0.0, epsilon = 1e-25);
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assert_relative_eq!(b[1], 0.0, epsilon = 1e-25);
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}
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#[test]
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fn dipole_equatorial_matches_closed_form() {
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// Equatorial: B_z = -μ₀ m / (4π r³), anti-parallel to m.
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let m = 1.0e-3;
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let r = 0.5;
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let dipole = DipoleSource::new([0.0; 3], [0.0, 0.0, m]);
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let (b, _) = dipole_field(&dipole, [r, 0.0, 0.0]);
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let expected_bz = -MU_0 * m / (4.0 * std::f64::consts::PI * r.powi(3));
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assert_relative_eq!(b[2], expected_bz, max_relative = 1e-12);
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}
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#[test]
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fn dipole_n8_directions_within_half_percent_rms() {
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// Plan §3 Pass 2 acceptance gate: n=8 RMS error ≤ 0.5% vs an
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// independent recomputation from first principles. Fails => abort §7-1.
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let m_vec = [3.0e-4, 1.0e-4, 7.0e-4];
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let dipole = DipoleSource::new([0.1, 0.2, 0.3], m_vec);
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let r = 0.5;
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let directions: [Vec3; 8] = [
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[1.0, 0.0, 0.0],
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[-1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, -1.0, 0.0],
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[0.0, 0.0, 1.0],
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[0.0, 0.0, -1.0],
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[1.0, 1.0, 1.0],
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[-1.0, -1.0, -1.0],
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];
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let mut rms_sum = 0.0_f64;
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for dir in directions {
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let dn = vec3_normalise(dir);
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let sensor = vec3_add(dipole.position, vec3_scale(dn, r));
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let (b, _) = dipole_field(&dipole, sensor);
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// Independent recomputation from the formula — guards against the
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// implementation accidentally agreeing with a buggy reference.
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let r_vec = vec3_sub(sensor, dipole.position);
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let r_norm = vec3_norm(r_vec);
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let r_hat = vec3_scale(r_vec, 1.0 / r_norm);
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let m_dot_r = vec3_dot(m_vec, r_hat);
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let bracket = vec3_sub(vec3_scale(r_hat, 3.0 * m_dot_r), m_vec);
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let coef = MU_0 / (4.0 * std::f64::consts::PI * r_norm.powi(3));
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let b_ref = vec3_scale(bracket, coef);
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for k in 0..3 {
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let denom = b_ref[k].abs().max(1e-30);
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let rel = (b[k] - b_ref[k]) / denom;
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rms_sum += rel * rel;
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}
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}
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let rms = (rms_sum / (8.0 * 3.0)).sqrt();
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assert!(
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rms <= 0.005,
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"Pass-2 acceptance: dipole n=8 RMS error {rms} > 0.5% threshold"
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);
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}
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#[test]
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fn current_loop_on_axis_matches_closed_form() {
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// On-axis circular loop: B_z = μ₀ I a² / [2 (a² + z²)^(3/2)]
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// (Jackson 3e §5.4). With n=64 segments accept ~1% numerical tolerance.
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let i = 0.5;
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let a = 0.05;
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let z = 0.2;
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let loop_ = CurrentLoop::new([0.0; 3], [0.0, 0.0, 1.0], a, i);
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let (b, _) = current_loop_field(&loop_, [0.0, 0.0, z]);
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let expected = MU_0 * i * a * a / (2.0 * (a * a + z * z).powf(1.5));
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assert_relative_eq!(b[2], expected, max_relative = 1.0e-2);
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}
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#[test]
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fn near_field_clamp_returns_zero_with_flag() {
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// Plan §2.1: r < R_MIN_M (1 mm) clamps to (0, true).
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let dipole = DipoleSource::new([0.0; 3], [1e-3, 0.0, 0.0]);
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let (b, sat) = dipole_field(&dipole, [0.5e-3, 0.0, 0.0]); // 0.5 mm
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assert_eq!(b, [0.0; 3]);
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assert!(sat, "near-field saturation flag must fire below 1 mm");
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}
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#[test]
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fn ferrous_object_zero_ambient_yields_zero_field() {
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// Linear induced moment is proportional to ambient — at zero ambient,
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// induced moment is zero, so the ferrous object emits no field.
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let obj = FerrousObject::steel([0.5, 0.0, 0.0], 1.0e-3);
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let (b, _) = ferrous_field(&obj, [0.0; 3], [1.0, 0.0, 0.0]);
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assert_eq!(b, [0.0; 3]);
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}
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#[test]
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fn scene_field_aggregates_multiple_sources() {
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// Two co-located dipoles with opposite moments cancel exactly.
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let m = 5.0e-4;
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let mut scene = Scene::new();
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scene.add_dipole(DipoleSource::new([0.0; 3], [0.0, 0.0, m]));
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scene.add_dipole(DipoleSource::new([0.0; 3], [0.0, 0.0, -m]));
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scene.add_sensor([0.0, 0.0, 0.5]);
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let result = scene_field_at_sensors(&scene);
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assert_eq!(result.len(), 1);
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let (b, _) = result[0];
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assert_relative_eq!(b[0], 0.0, epsilon = 1e-25);
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assert_relative_eq!(b[1], 0.0, epsilon = 1e-25);
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assert_relative_eq!(b[2], 0.0, epsilon = 1e-25);
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}
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}
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