use crate::{
geometry::{
Coordinate, Coordinates,
mesh::{Connectivity, Mesh, differential::laplace::Weighting},
},
math::{
Scalar, Tensor,
test::{TestError, assert_eq_within_tols},
},
};
fn tri() -> Mesh<3> {
Mesh::from((
vec![Connectivity::Triangular(vec![[0_usize, 1, 2]].into())],
Coordinates::from([
Coordinate::const_from([0.0, 0.0, 0.0]),
Coordinate::const_from([2.0, 0.0, 0.0]),
Coordinate::const_from([0.0, 2.0, 0.0]),
]),
))
}
fn spread(mesh: &Mesh<3>) -> Scalar {
let coordinates = mesh.coordinates();
let center = mesh.coordinates().iter().sum::<Coordinate<3>>() / 3.0;
(0..3)
.map(|node| {
(0..3)
.map(|i| (coordinates[node][i] - center[i]).powi(2))
.sum::<Scalar>()
})
.sum()
}
#[test]
fn zero_iterations_is_identity() -> Result<(), TestError> {
let mut mesh = tri();
mesh.taubin_smooth(0, 0.1, 0.5, Weighting::Uniform, false, false);
let coordinates = mesh.coordinates();
assert_eq_within_tols(&coordinates[0], &[0.0, 0.0, 0.0].into())?;
assert_eq_within_tols(&coordinates[1], &[2.0, 0.0, 0.0].into())?;
assert_eq_within_tols(&coordinates[2], &[0.0, 2.0, 0.0].into())
}
#[test]
fn first_iteration_matches_laplace_deflate() -> Result<(), TestError> {
let mut laplace = tri();
laplace.laplace_smooth(1, 0.5, Weighting::Uniform, false, false);
let mut taubin = tri();
taubin.taubin_smooth(1, 0.1, 0.5, Weighting::Uniform, false, false);
(0..3).try_for_each(|node| {
assert_eq_within_tols(&laplace.coordinates()[node], &taubin.coordinates()[node])
})
}
#[test]
fn resists_shrinkage_relative_to_laplace() {
let mut laplace = tri();
laplace.laplace_smooth(2, 0.5, Weighting::Uniform, false, false);
let mut taubin = tri();
taubin.taubin_smooth(2, 0.1, 0.5, Weighting::Uniform, false, false);
assert!(spread(&taubin) > spread(&laplace));
}