nalgebra/examples/dimensional_genericity.rs

extern crate alga;
extern crate nalgebra as na;

use alga::general::Real;
use alga::linear::FiniteDimInnerSpace;
use na::{Unit, ColumnVector, OwnedColumnVector, Vector2, Vector3};
use na::storage::Storage;
use na::dimension::{DimName, U1};

/// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, vector: &V) -> V
    where V: FiniteDimInnerSpace + Copy {
    let n = plane_normal.as_ref(); // Get the underlying vector of type `V`.
    *vector - *n * (n.dot(vector) * na::convert(2.0))
}


/// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
fn reflect_wrt_hyperplane_with_structural_genericity<N, D, S>(plane_normal: &Unit<ColumnVector<N, D, S>>,
                                                               vector:       &ColumnVector<N, D, S>)
                                                               -> OwnedColumnVector<N, D, S::Alloc>
    where N: Real,
          D: DimName,
          S: Storage<N, D, U1> {
    let n = plane_normal.as_ref(); // Get the underlying V.
    vector - n * (n.dot(vector) * na::convert(2.0))
}

/// Reflects a 2D vector wrt. the 2D line with normal `plane_normal`.
fn reflect_wrt_hyperplane2<N>(plane_normal: &Unit<Vector2<N>>,
                              vector:       &Vector2<N>)
                              -> Vector2<N>
    where N: Real {
    let n = plane_normal.as_ref(); // Get the underlying Vector2
    vector - n * (n.dot(vector) * na::convert(2.0))
}

/// Reflects a 3D vector wrt. the 3D plane with normal `plane_normal`.
/// /!\ This is an exact replicate of `reflect_wrt_hyperplane2, but for 3D.
fn reflect_wrt_hyperplane3<N>(plane_normal: &Unit<Vector3<N>>,
                              vector:       &Vector3<N>)
                              -> Vector3<N>
    where N: Real {
    let n = plane_normal.as_ref(); // Get the underlying Vector3
    vector - n * (n.dot(vector) * na::convert(2.0))
}


fn main() {
    let plane2 = Vector2::y_axis(); // 2D plane normal.
    let plane3 = Vector3::y_axis(); // 3D plane normal.

    let v2 = Vector2::new(1.0, 2.0);      // 2D vector to be reflected.
    let v3 = Vector3::new(1.0, 2.0, 3.0); // 3D vector to be reflected.

    // We can call the same function for 2D and 3D.
    assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane2, &v2).y, -2.0);
    assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane3, &v3).y, -2.0);

    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane2, &v2).y, -2.0);
    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane3, &v3).y, -2.0);

    // Call each specific implementation depending on the dimension.
    assert_eq!(reflect_wrt_hyperplane2(&plane2, &v2).y, -2.0);
    assert_eq!(reflect_wrt_hyperplane3(&plane3, &v3).y, -2.0);
}