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Triangle and tetrahedron mesh generators
Contents
<a name="introduction"></a> 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
<a name="installation"></a> Installation
Install some libraries:
sudo apt install build-essential
<a name="cargo"></a> Setting Cargo.toml
👆 Check the crate version and update your Cargo.toml accordingly:
[dependencies]
tritet = "*"
<a name="examples"></a> 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(())
}
<a name="developers"></a> For developers
Install cargo-valgrind:
cargo install cargo-valgrind
Then check for memory leaks (none ;-):
bash memcheck.bash