Triangle and tetrahedron mesh generators

Introduction

This crate implements Triangle and Tetrahedron mesh generators by wrapping the best tools around, namely, Triangle and Tetgen.

Here, all the data structures accessed by the C/C++ codes are allocated on the "C-side" by (carefully) using "malloc/new." 😅 We then make use of Valgrind and tests to make sure that there are no leaks. In this way, there is no performance loss of the C-code while enabling the convenience of Rust.

The resulting Rust interface to Triangle and Tetgen is somewhat low-level. However, other projects could use this interface to make higher-level functions.

The code works in multithreaded applications---not exhaustively verified but tested. See, for example, the comprehensive tests in mem_check_triangle_build.rs and mem_check_tetgen_build.rs

A higher-level crate is available for mesh generation (and more): Gemlab: Geometry, meshes, and numerical integration for finite element analyses.

See the documentation for further information:

Tritet documentation - Contains the API reference and examples

Installation

Install some libraries:

sudo apt install build-essential

Setting Cargo.toml

👆 Check the crate version and update your Cargo.toml accordingly:

[dependencies]
tritet = "*"

Examples

Note: set SAVE_FIGURE to true to generate the figures.

2D Delaunay triangulation

use plotpy::Plot;
use tritet::{StrError, Trigen};

const SAVE_FIGURE: bool = false;

fn main() -> Result<(), StrError> {
    // allocate data for 10 points
    let mut trigen = Trigen::new(10, None, None, None)?;

    // set points
    trigen
        .set_point(0, 0, 0.478554, 0.00869692)?
        .set_point(1, 0, 0.13928, 0.180603)?
        .set_point(2, 0, 0.578587, 0.760349)?
        .set_point(3, 0, 0.903726, 0.975904)?
        .set_point(4, 0, 0.0980015, 0.981755)?
        .set_point(5, 0, 0.133721, 0.348832)?
        .set_point(6, 0, 0.648071, 0.369534)?
        .set_point(7, 0, 0.230951, 0.558482)?
        .set_point(8, 0, 0.0307942, 0.459123)?
        .set_point(9, 0, 0.540745, 0.331184)?;

    // generate Delaunay triangulation
    trigen.generate_delaunay(false)?;

    // draw triangles
    if SAVE_FIGURE {
        let mut plot = Plot::new();
        trigen.draw_triangles(&mut plot, true, true, true, true, None, None, None);
        plot.set_equal_axes(true)
            .set_figure_size_points(600.0, 600.0)
            .save("/tmp/tritet/doc_triangle_delaunay_1.svg")?;
    }
    Ok(())
}

2D Voronoi tessellation

use plotpy::Plot;
use tritet::{StrError, Trigen};

const SAVE_FIGURE: bool = false;

fn main() -> Result<(), StrError> {
    // allocate data for 10 points
    let mut trigen = Trigen::new(10, None, None, None)?;

    // set points
    trigen
        .set_point(0, 0, 0.478554, 0.00869692)?
        .set_point(1, 0, 0.13928, 0.180603)?
        .set_point(2, 0, 0.578587, 0.760349)?
        .set_point(3, 0, 0.903726, 0.975904)?
        .set_point(4, 0, 0.0980015, 0.981755)?
        .set_point(5, 0, 0.133721, 0.348832)?
        .set_point(6, 0, 0.648071, 0.369534)?
        .set_point(7, 0, 0.230951, 0.558482)?
        .set_point(8, 0, 0.0307942, 0.459123)?
        .set_point(9, 0, 0.540745, 0.331184)?;

    // generate Voronoi tessellation
    trigen.generate_voronoi(false)?;

    // draw Voronoi diagram
    if SAVE_FIGURE {
        let mut plot = Plot::new();
        trigen.draw_voronoi(&mut plot);
        plot.set_equal_axes(true)
            .set_figure_size_points(600.0, 600.0)
            .save("/tmp/tritet/doc_triangle_voronoi_1.svg")?;
    }
    Ok(())
}

2D mesh generation

use plotpy::Plot;
use tritet::{StrError, Trigen};

const SAVE_FIGURE: bool = false;

fn main() -> Result<(), StrError> {
    // allocate data for 12 points, 10 segments, 2 regions, and 1 hole
    let mut trigen = Trigen::new(12, Some(10), Some(2), Some(1))?;

    // set points
    trigen
        .set_point(0, 0, 0.0, 0.0)?
        .set_point(1, 0, 1.0, 0.0)?
        .set_point(2, 0, 1.0, 1.0)?
        .set_point(3, 0, 0.0, 1.0)?
        .set_point(4, 0, 0.2, 0.2)?
        .set_point(5, 0, 0.8, 0.2)?
        .set_point(6, 0, 0.8, 0.8)?
        .set_point(7, 0, 0.2, 0.8)?
        .set_point(8, 0, 0.0, 0.5)?
        .set_point(9, 0, 0.2, 0.5)?
        .set_point(10, 0, 0.8, 0.5)?
        .set_point(11, 0, 1.0, 0.5)?;

    // set segments
    trigen
        .set_segment(0, -1, 0, 1)?
        .set_segment(1, -1, 1, 2)?
        .set_segment(2, -1, 2, 3)?
        .set_segment(3, -1, 3, 0)?
        .set_segment(4, -1, 4, 5)?
        .set_segment(5, -1, 5, 6)?
        .set_segment(6, -1, 6, 7)?
        .set_segment(7, -1, 7, 4)?
        .set_segment(8, -1, 8, 9)?
        .set_segment(9, -1, 10, 11)?;

    // set regions
    trigen
        .set_region(0, 1, 0.1, 0.1, None)?
        .set_region(1, 2, 0.1, 0.9, None)?;

    // set holes
    trigen.set_hole(0, 0.5, 0.5)?;

    // generate o2 mesh without constraints
    trigen.generate_mesh(false, true, false, None, None)?;

    // draw mesh
    if SAVE_FIGURE {
        let mut plot = Plot::new();
        trigen.draw_triangles(&mut plot, true, true, true, true, None, None, None);
        plot.set_equal_axes(true)
            .set_figure_size_points(600.0, 600.0)
            .save("/tmp/tritet/doc_triangle_mesh_1.svg")?;
    }
    Ok(())
}

3D Delaunay triangulation

use plotpy::Plot;
use tritet::{StrError, Tetgen};

const SAVE_FIGURE: bool = false;

fn main() -> Result<(), StrError> {
    // allocate data for 8 points
    let mut tetgen = Tetgen::new(8, None, None, None)?;

    // set points
    tetgen
        .set_point(0, 0, 0.0, 0.0, 0.0)?
        .set_point(1, 0, 1.0, 0.0, 0.0)?
        .set_point(2, 0, 1.0, 1.0, 0.0)?
        .set_point(3, 0, 0.0, 1.0, 0.0)?
        .set_point(4, 0, 0.0, 0.0, 1.0)?
        .set_point(5, 0, 1.0, 0.0, 1.0)?
        .set_point(6, 0, 1.0, 1.0, 1.0)?
        .set_point(7, 0, 0.0, 1.0, 1.0)?;

    // generate Delaunay triangulation
    tetgen.generate_delaunay(false)?;

    // draw edges of tetrahedra
    if SAVE_FIGURE {
        let mut plot = Plot::new();
        tetgen.draw_wireframe(&mut plot, true, true, true, true, None, None, None);
        plot.set_equal_axes(true)
            .set_figure_size_points(600.0, 600.0)
            .save("/tmp/tritet/example_tetgen_delaunay_1.svg")?;
    }
    Ok(())
}

3D mesh generation

Note: set SAVE_VTU_FILE to true to generate Paraview file.

use plotpy::Plot;
use tritet::{StrError, Tetgen};

const SAVE_VTU_FILE: bool = false;
const SAVE_FIGURE: bool = false;

fn main() -> Result<(), StrError> {
    // allocate data for 16 points and 12 facets
    // (one cube/hole inside another cube)
    let mut tetgen = Tetgen::new(
        16,
        Some(vec![
            4, 4, 4, 4, 4, 4, // inner cube
            4, 4, 4, 4, 4, 4, // outer cube
        ]),
        Some(1),
        Some(1),
    )?;

    // inner cube
    tetgen
        .set_point(0, 0, 0.0, 0.0, 0.0)?
        .set_point(1, 0, 1.0, 0.0, 0.0)?
        .set_point(2, 0, 1.0, 1.0, 0.0)?
        .set_point(3, 0, 0.0, 1.0, 0.0)?
        .set_point(4, 0, 0.0, 0.0, 1.0)?
        .set_point(5, 0, 1.0, 0.0, 1.0)?
        .set_point(6, 0, 1.0, 1.0, 1.0)?
        .set_point(7, 0, 0.0, 1.0, 1.0)?;

    // outer cube
    tetgen
        .set_point(8,  0, -1.0, -1.0, -1.0)?
        .set_point(9,  0, 2.0, -1.0, -1.0)?
        .set_point(10, 0, 2.0, 2.0, -1.0)?
        .set_point(11, 0, -1.0, 2.0, -1.0)?
        .set_point(12, 0, -1.0, -1.0, 2.0)?
        .set_point(13, 0, 2.0, -1.0, 2.0)?
        .set_point(14, 0, 2.0, 2.0, 2.0)?
        .set_point(15, 0, -1.0, 2.0, 2.0)?;

    // inner cube
    tetgen
        .set_facet_point(0, 0, 0)?
        .set_facet_point(0, 1, 4)?
        .set_facet_point(0, 2, 7)?
        .set_facet_point(0, 3, 3)?;
    tetgen
        .set_facet_point(1, 0, 1)?
        .set_facet_point(1, 1, 2)?
        .set_facet_point(1, 2, 6)?
        .set_facet_point(1, 3, 5)?;
    tetgen
        .set_facet_point(2, 0, 0)?
        .set_facet_point(2, 1, 1)?
        .set_facet_point(2, 2, 5)?
        .set_facet_point(2, 3, 4)?;
    tetgen
        .set_facet_point(3, 0, 2)?
        .set_facet_point(3, 1, 3)?
        .set_facet_point(3, 2, 7)?
        .set_facet_point(3, 3, 6)?;
    tetgen
        .set_facet_point(4, 0, 0)?
        .set_facet_point(4, 1, 3)?
        .set_facet_point(4, 2, 2)?
        .set_facet_point(4, 3, 1)?;
    tetgen
        .set_facet_point(5, 0, 4)?
        .set_facet_point(5, 1, 5)?
        .set_facet_point(5, 2, 6)?
        .set_facet_point(5, 3, 7)?;

    // outer cube
    tetgen
        .set_facet_point(6, 0, 8 + 0)?
        .set_facet_point(6, 1, 8 + 4)?
        .set_facet_point(6, 2, 8 + 7)?
        .set_facet_point(6, 3, 8 + 3)?;
    tetgen
        .set_facet_point(7, 0, 8 + 1)?
        .set_facet_point(7, 1, 8 + 2)?
        .set_facet_point(7, 2, 8 + 6)?
        .set_facet_point(7, 3, 8 + 5)?;
    tetgen
        .set_facet_point(8, 0, 8 + 0)?
        .set_facet_point(8, 1, 8 + 1)?
        .set_facet_point(8, 2, 8 + 5)?
        .set_facet_point(8, 3, 8 + 4)?;
    tetgen
        .set_facet_point(9, 0, 8 + 2)?
        .set_facet_point(9, 1, 8 + 3)?
        .set_facet_point(9, 2, 8 + 7)?
        .set_facet_point(9, 3, 8 + 6)?;
    tetgen
        .set_facet_point(10, 0, 8 + 0)?
        .set_facet_point(10, 1, 8 + 3)?
        .set_facet_point(10, 2, 8 + 2)?
        .set_facet_point(10, 3, 8 + 1)?;
    tetgen
        .set_facet_point(11, 0, 8 + 4)?
        .set_facet_point(11, 1, 8 + 5)?
        .set_facet_point(11, 2, 8 + 6)?
        .set_facet_point(11, 3, 8 + 7)?;

    // set region and hole
    tetgen.set_region(0, 1, -0.9, -0.9, -0.9, None)?;
    tetgen.set_hole(0, 0.5, 0.5, 0.5)?;

    // generate mesh
    tetgen.generate_mesh(false, false, None, None)?;

    // generate file for Paraview
    if SAVE_VTU_FILE {
        tetgen.write_vtu("/tmp/tritet/example_tetgen_mesh_1.vtu")?;
    }

    // draw edges of tetrahedra
    if SAVE_FIGURE {
        let mut plot = Plot::new();
        tetgen.draw_wireframe(&mut plot, true, true, true, true, None, None, None);
        plot.set_equal_axes(true)
            .set_figure_size_points(600.0, 600.0)
            .save("/tmp/tritet/example_tetgen_mesh_1.svg")?;
    }
    Ok(())
}