Struct Simplex3 

pub struct Simplex3 { /* private fields */ }

The hull of any 4 noncoplanar points in three dimensions.

Examples

A Simplex3, or equivalently a (nonuniform) tetrahedron, is the simplest faceted three-dimensional geometry. Because a simplex has an intrinsic idea of its position in space (defined by its barycenter), this struct provides implementations for spatial translation and a center of mass.

A uniform tetrahedron with edge length 2*sqrt(2), centered at the origin Vertices are defined by 3-length positive-signed permutations of [1,-1]

use hoomd_geometry::{IntersectsAt, Volume, shape::Simplex3};
use hoomd_vector::{Cartesian, Rotation, Versor};

let tet = Simplex3::default();

assert_eq!(tet.vertices()[0], [1.0; 3].into());
assert_eq!(tet.centroid(), [0.0; 3].into());

assert_eq!(tet.volume(), 8.0 / 3.0);

assert_eq!(
    tet.get_edge_vectors()[0],
    tet.vertices()[1] - tet.vertices()[0]
);

Simplex3 instances support a fast intersection detection algorithm:

let other_tet = Simplex3::default();
let displacement = [2.0, 2.0, 0.0].into();
let q_ij = Versor::identity();

assert!(tet.intersects_at(&other_tet, &displacement, &q_ij));

assert!(!tet.intersects_at(&other_tet, &[2.001, 2.0, 0.0].into(), &q_ij));

Although generally advised, Simplex3 tetrahedra are not required to be convex:

let planar_tetrahedron = Simplex3::from(
    [[0.0; 3], [0.0; 3], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0]]
        .map(Cartesian::from),
);

assert_eq!(planar_tetrahedron.volume(), 0.0);
assert_eq!(planar_tetrahedron.centroid(), [1.0, 1.0, 0.0].into());

Implementations

impl Simplex3

pub fn vertices(&self) -> [Cartesian<3>; 4]

The vertices of the simplex.

pub fn translate_by(&mut self, rhs: &Cartesian<3>) -> Self

Translate a simplex via rowwise addition of a Cartesian3

pub fn centroid(&self) -> Cartesian<3>

The center of mass of the tetrahedron.

pub fn get_edges(&self) -> [[Cartesian<3>; 2]; 5]

Get the edges of the tetrahedron as edge endpoint coordinates. In vertex index form, this returns values in the order [(1, 0), (2, 0), (3, 0), (2, 1), (3, 2)]

pub fn get_edge_vectors(&self) -> [Cartesian<3>; 5]

Edge vectors, in the same order as get_edges and pointing left to right.

Trait Implementations

impl Clone for Simplex3

fn clone(&self) -> Simplex3

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Simplex3

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Simplex3

fn default() -> Self

A uniform tetrahedron, centered on the origin with edges bisecting half of the faces of a cube on their diagonals.

impl<'de> Deserialize<'de> for Simplex3

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Simplex3

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl From<[[f64; 3]; 4]> for Simplex3

fn from(arrs: [[f64; 3]; 4]) -> Self

Converts to this type from the input type.

impl From<[Cartesian<3>; 4]> for Simplex3

fn from(vertices: [Cartesian<3>; 4]) -> Self

Converts to this type from the input type.

impl<R> IntersectsAt<Simplex3, Cartesian<3>, R> for Simplex3

where R: Rotation + Rotate<Cartesian<3>>, RotationMatrix<3>: From<R>,

fn intersects_at(&self, other: &Simplex3, v_ij: &Cartesian<3>, o_ij: &R) -> bool

Original C code of algorithm: https://web.archive.org/web/20030907000716/http://www.acm.org/jgt/papers/GanovelliPonchioRocchini02/tet_a_tet.html

Recent Clojure reimplementation that orients shapes: https://gist.github.com/postspectacular/9021724

fn approximate_separation_distance( &self, other: &S, v_ij: &V, o_ij: &R, resolution: PositiveReal, ) -> f64

where V: InnerProduct,

Approximate the amount of overlap between two shapes.

impl<R> IntersectsAtGlobal<Simplex3, Cartesian<3>, R> for Simplex3

where R: Rotation + Rotate<Cartesian<3>>, RotationMatrix<3>: From<R>,

fn intersects_at_global( &self, other: &Simplex3, r_self: &Cartesian<3>, o_self: &R, r_other: &Cartesian<3>, o_other: &R, ) -> bool

Test whether the set of points in one shape intersects with the set of another (in the global frame).

impl PartialEq for Simplex3

fn eq(&self, other: &Simplex3) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for Simplex3

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl SupportMapping<Cartesian<3>> for Simplex3

fn support_mapping(&self, n: &Cartesian<3>) -> Cartesian<3>

Return the furthest extent of a shape in the direction of n.

impl Volume for Simplex3

fn volume(&self) -> f64

The N-hypervolume of a geometry.

impl StructuralPartialEq for Simplex3