arctk 2.0.10

Numerical simulations of physical systems
Documentation 
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//! Electro-magnetic boundary crossing calculator.

use nalgebra::{Unit, Vector3};

/// Optical interface crossing information.
/// Calculates trajectory information.
pub struct Crossing {
    /// Probability of reflection.
    pub ref_prob: f64,
    /// Reflection direction.
    pub ref_dir: Unit<Vector3<f64>>,
    /// Transmission (refraction) direction.
    pub trans_dir: Option<Unit<Vector3<f64>>>,
}

impl Crossing {
    /// Construct a new instance.
    #[inline]
    #[must_use]
    pub fn new(
        inc: &Unit<Vector3<f64>>,
        norm: &Unit<Vector3<f64>>,
        n_curr: f64,
        n_next: f64,
    ) -> Self {
        debug_assert!(n_curr >= 1.0);
        debug_assert!(n_next >= 1.0);
        debug_assert!(inc.dot(norm) < 0.0);

        let ci = -inc.dot(norm);
        let n = n_curr / n_next;

        let crit_ang = if n_curr <= n_next {
            None
        } else {
            Some((n_next / n_curr).asin())
        };

        let (ref_prob, trans_dir) = if crit_ang.is_some()
            && (ci.acos() >= crit_ang.expect("Failed to determine critical angle."))
        {
            (1.0, None)
        } else {
            let s2t = (n * n) * ci.mul_add(-ci, 1.0);
            let ct = (1.0 - s2t).sqrt();

            (
                Self::init_ref_prob(n_curr, n_next, ci, ct),
                Some(Self::init_trans_dir(inc, norm, n, ci, ct)),
            )
        };

        Self {
            ref_prob,
            ref_dir: Self::init_ref_dir(inc, norm, ci),
            trans_dir,
        }
    }

    /// Calculate the reflection probability.
    #[inline]
    #[must_use]
    fn init_ref_prob(n1: f64, n2: f64, ci: f64, ct: f64) -> f64 {
        debug_assert!(n1 >= 0.0);
        debug_assert!(n2 >= 0.0);

        let n1_c_i = n1 * ci;
        let n2_c_t = n2 * ct;
        let r_norm_sqrt = (n1_c_i - n2_c_t) / (n1_c_i + n2_c_t);
        let r_norm = r_norm_sqrt * r_norm_sqrt;

        let n2_c_i = n2 * ci;
        let n1_c_t = n1 * ct;
        let r_tran_sqrt = (n2_c_i - n1_c_t) / (n2_c_i + n1_c_t);
        let r_tran = r_tran_sqrt * r_tran_sqrt;

        (r_norm + r_tran) / 2.0
    }

    /// Calculate the reflection direction.
    #[inline]
    #[must_use]
    fn init_ref_dir(
        inc: &Unit<Vector3<f64>>,
        norm: &Unit<Vector3<f64>>,
        ci: f64,
    ) -> Unit<Vector3<f64>> {
        Unit::new_unchecked(inc.into_inner() + (2.0 * ci * norm.into_inner()))
    }

    /// Calculate the reflection direction and the required constant.
    #[inline]
    #[must_use]
    pub fn calc_ref_dir(inc: &Unit<Vector3<f64>>, norm: &Unit<Vector3<f64>>) -> Unit<Vector3<f64>> {
        Self::init_ref_dir(inc, norm, -inc.dot(norm))
    }

    /// Calculate the transmission direction.
    #[inline]
    #[must_use]
    fn init_trans_dir(
        inc: &Unit<Vector3<f64>>,
        norm: &Unit<Vector3<f64>>,
        n: f64,
        ci: f64,
        ct: f64,
    ) -> Unit<Vector3<f64>> {
        Unit::new_unchecked((n * inc.into_inner()) + n.mul_add(ci, -ct) * norm.into_inner())
    }

    /// Get the transmission probability.
    #[inline]
    #[must_use]
    pub fn trans_prob(&self) -> f64 {
        1.0 - self.ref_prob
    }
}