gemlab 2.0.0

Geometry and meshes laboratory for finite element analyses
Documentation 
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use russell_lab::{Matrix, Vector};

/// Defines a triangle with 3 nodes (linear edges)
///
/// ![tri3](https://raw.githubusercontent.com/cpmech/gemlab/main/data/figures/test_draw_shape_tri3.svg)
///
/// # Local IDs of nodes
///
/// ```text
/// s
/// |
/// 2, (0,1)
/// | ',
/// |   ',         node    r    s
/// |     ',          0  0.0  0.0
/// |       ',        1  1.0  0.0
/// |         ',      2  0.0  1.0
/// |           ',
/// |             ',
/// |               ',
/// | (0,0)           ', (1,0)
/// 0-------------------1 ---- r
/// ```
///
/// # Local IDs of edges
///
/// ```text
///   2,
///   | ',                 p0  p1
///   |   ',           e:0 [1, 0]
///   |     ',         e:1 [2, 1]
///   |       ', 1     e:2 [0, 2]
/// 2 |         ',
///   |           ',
///   |             ',
///   |               ',
///   |                 ',
///   0-------------------1
///             0
/// ```
///
/// # Notes
///
/// * The order of edge nodes is such that the normals are outward
/// * The order of edge nodes corresponds to [super::Lin2] nodes
/// * This shape is a lower-order version of [super::Tri6]
pub struct Tri3 {}

impl Tri3 {
    pub const GEO_NDIM: usize = 2;
    pub const NNODE: usize = 3;
    pub const NEDGE: usize = 3;
    pub const NFACE: usize = 0;
    pub const EDGE_NNODE: usize = 2;
    pub const FACE_NNODE: usize = 0;
    pub const FACE_NEDGE: usize = 0;
    pub const TRIANGULATE_NTRIANGLE: usize = 1;

    #[rustfmt::skip]
    pub const EDGE_NODE_IDS: [[usize; Tri3::EDGE_NNODE]; Tri3::NEDGE] = [
        [1, 0],
        [2, 1],
        [0, 2],
    ];

    #[rustfmt::skip]
    pub const EDGE_NODE_IDS_INWARD: [[usize; Tri3::EDGE_NNODE]; Tri3::NEDGE] = [
        [0, 1],
        [1, 2],
        [2, 0],
    ];

    #[rustfmt::skip]
    pub const NODE_REFERENCE_COORDS: [[f64; Tri3::GEO_NDIM]; Tri3::NNODE] = [
        [0.0, 0.0],
        [1.0, 0.0],
        [0.0, 1.0],
    ];

    #[rustfmt::skip]
    pub const TRIANGULATE_TRIANGLES: [[usize; 3]; Tri3::TRIANGULATE_NTRIANGLE] = [
        [0, 1, 2],
    ];

    /// Computes the interpolation functions
    ///
    /// # Output
    ///
    /// * `interp` -- interpolation function evaluated at ksi (nnode)
    ///
    /// # Input
    ///
    /// * `ksi` -- reference coordinates with length ≥ geo_ndim
    pub fn calc_interp(interp: &mut Vector, ksi: &[f64]) {
        let (r, s) = (ksi[0], ksi[1]);

        interp[0] = 1.0 - r - s;
        interp[1] = r;
        interp[2] = s;
    }

    /// Computes the derivatives of interpolation functions with respect to the reference coordinates
    ///
    /// # Output
    ///
    /// * `deriv` -- derivatives of the interpolation function with respect to
    ///   the reference coordinates ksi, evaluated at ksi (nnode,geo_ndim)
    ///
    /// # Input
    ///
    /// * `ksi` -- reference coordinates with length ≥ geo_ndim
    pub fn calc_deriv(deriv: &mut Matrix, _: &[f64]) {
        deriv.set(0, 0, -1.0);
        deriv.set(1, 0, 1.0);
        deriv.set(2, 0, 0.0);

        deriv.set(0, 1, -1.0);
        deriv.set(1, 1, 0.0);
        deriv.set(2, 1, 1.0);
    }
}