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use nalgebra::SMatrix;
use super::{Scalar, N, Point, Vector};
type ProjectionMatrix = SMatrix<Scalar, N, N>;
pub struct Subspace<const DIM: usize> {
point: Point,
vectors: [Vector; DIM],
projection_matrix: ProjectionMatrix,
}
pub type Line = Subspace<1>;
pub type Plane = Subspace<2>;
impl<const DIM: usize> Subspace<DIM> {
pub fn new(point: Point, mut vectors: [Vector; DIM]) -> Self {
for vector in &mut vectors {
vector.normalize_mut();
}
Self {
point,
vectors,
projection_matrix: {
let v = SMatrix::<Scalar, N, DIM>::from_columns(&vectors);
let transpose = v.transpose();
let inverse = (transpose * v).try_inverse().unwrap();
v * inverse * transpose
}
}
}
pub fn project_point(&self, point: Point) -> Point {
self.projection_matrix * (point - self.point.coords) + self.point.coords
}
pub fn distance(&self, point: Point) -> Scalar {
let projected = self.project_point(point);
(projected - point).norm()
}
}
#[cfg(test)]
mod tests {
use crate::algebra::{subspace::Line, Point, Vector};
#[test]
fn test_projection_onto_line() {
let line = Line::new(Point::new(1.0, 0.0), [Vector::new(3.0, 1.0)]);
let point = Point::new(3.0, 4.0);
let matrix = line.projection_matrix;
{
let diff = matrix * matrix - matrix;
assert!(diff.norm() < 0.001, "Projection matrix squared should be equal to itself: {}, {}", matrix, matrix* matrix);
}
{
let diff = matrix - matrix.transpose();
assert!(diff.norm() < 0.001, "Projection matrix transpose should be equal to itself: {}, {}", matrix, matrix.transpose());
}
{
let projected = line.project_point(point);
let diff = projected - Point::new(4.0, 1.0);
assert!(diff.norm() < 0.001, "Point projected incorrectly");
}
}
}
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