Crate axiolid_tetrahedralize 

Exact 3D Delaunay tetrahedralization.

Delaunay3 is an incremental Bowyer-Watson triangulation of a point set in space. Its guarantees are stated and tested, not hoped for:

• every tetrahedron is positively oriented, decided by the exact orient3d;
• no point lies strictly inside any tetrahedron’s circumsphere, decided by the exact insphere;
• the boundary faces are exactly the convex hull, kept with an infinite vertex rather than a bounding box, so nothing outside the input is inserted;
• degenerate input – cospherical points such as a cubic grid, points in the plane of a hull face, exact duplicates – is handled by a symbolic perturbation (simulation of simplicity) that depends only on the coordinates, so the triangulation is the same for every insertion order.

What is refused

• Points spanning fewer than three dimensions have no tetrahedra: Delaunay3::from_points reports Delaunay3Error::NotFullDimensional (a coplanar set belongs to axiolid-triangulate).
• Non-finite coordinates, and non-zero coordinates whose magnitude lies outside [2^-100, 2^100], where the degree-5 and degree-6 exact predicates would leave binary64’s normal range.
• Weighted (regular) triangulation, and constraints: neither input segments nor input faces are recovered (#126).

Example

use axiolid_core::Point3;
use axiolid_tetrahedralize::Delaunay3;

// The eight corners of a cube are cospherical: several Delaunay
// tetrahedralizations exist, and the perturbation picks one of them.
let corners: Vec<Point3> = (0..8)
    .map(|i| Point3::new(f64::from(i & 1), f64::from((i >> 1) & 1), f64::from(i >> 2)))
    .collect();
let delaunay = Delaunay3::from_points(&corners)?;
let mesh = delaunay.tetrahedra();
assert!(mesh.tetrahedra.len() == 5 || mesh.tetrahedra.len() == 6);
assert_eq!(delaunay.hull_triangles().len(), 12);

Structs

Delaunay3

An incremental 3D Delaunay triangulation of a point set.

Tetrahedra

The finite tetrahedra of a triangulation, with their adjacency.

Enums

Delaunay3Error

Why a point or a point set was refused.

Insertion

What Delaunay3::insert did with a point.

Constants

MAX_COORDINATE

Largest coordinate magnitude accepted: 2^100.

MIN_COORDINATE

Smallest non-zero coordinate magnitude accepted: 2^-100.