# Triangle and tetrahedron mesh generators
[](https://codecov.io/gh/cpmech/tritet)
This project presents a Rust code to generate triangle and tetrahedron meshes by calling
[Triangle](https://www.cs.cmu.edu/~quake/triangle.html) and
[Tetgen (1.4)](http://tetgen.org/).
A critical aspect of this crate is that all the data structures accessed by the C-code
are allocated on the "C-side" by (carefully) using "malloc/new." 😅
We then make use of [Valgrind](https://valgrind.org/) and tests to make sure that all is (hopefully) well.
The code should work fine in multithreaded applications (not exhaustively verified, though!).
See, for example, the comprehensive tests in
[mem_check_triangle_build.rs](https://github.com/cpmech/tritet/blob/main/src/bin/mem_check_triangle_build.rs)
and
[mem_check_tetgen_build.rs](https://github.com/cpmech/tritet/blob/main/src/bin/mem_check_tetgen_build.rs)
The resulting Rust interface to Triangle and Tetgen is a lightweight, low-level set of functions.
However, other projects could use this interface to make higher-level functions.
For example, this crate is used by [Gemlab: Geometry, meshes, and numerical integration for finite element analyses](https://github.com/cpmech/gemlab).
## Documentation
[Tritet documentation on docs.rs](https://docs.rs/tritet)
## Installation
Install some libraries:
```bash
sudo apt install build-essential
```
Add this to your Cargo.toml:
```toml
[dependencies]
tritet = "0.1"
```
## Examples
### 2D Delaunay triangulation
```rust
use plotpy::Plot;
use tritet::{StrError, Triangle};
fn main() -> Result<(), StrError> {
// allocate data for 10 points
let mut triangle = Triangle::new(10, None, None, None)?;
// set points
triangle
.set_point(0, 0.478554, 0.00869692)?
.set_point(1, 0.13928, 0.180603)?
.set_point(2, 0.578587, 0.760349)?
.set_point(3, 0.903726, 0.975904)?
.set_point(4, 0.0980015, 0.981755)?
.set_point(5, 0.133721, 0.348832)?
.set_point(6, 0.648071, 0.369534)?
.set_point(7, 0.230951, 0.558482)?
.set_point(8, 0.0307942, 0.459123)?
.set_point(9, 0.540745, 0.331184)?;
// generate Delaunay triangulation
triangle.generate_delaunay(false)?;
// draw triangles
let mut plot = Plot::new();
// triangle.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
```rust
use plotpy::Plot;
use tritet::{StrError, Triangle};
fn main() -> Result<(), StrError> {
// allocate data for 10 points
let mut triangle = Triangle::new(10, None, None, None)?;
// set points
triangle
.set_point(0, 0.478554, 0.00869692)?
.set_point(1, 0.13928, 0.180603)?
.set_point(2, 0.578587, 0.760349)?
.set_point(3, 0.903726, 0.975904)?
.set_point(4, 0.0980015, 0.981755)?
.set_point(5, 0.133721, 0.348832)?
.set_point(6, 0.648071, 0.369534)?
.set_point(7, 0.230951, 0.558482)?
.set_point(8, 0.0307942, 0.459123)?
.set_point(9, 0.540745, 0.331184)?;
// generate Voronoi tessellation
triangle.generate_voronoi(false)?;
// draw Voronoi diagram
let mut plot = Plot::new();
// triangle.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
```rust
use plotpy::Plot;
use tritet::{StrError, Triangle};
fn main() -> Result<(), StrError> {
// allocate data for 12 points, 10 segments, 2 regions, and 1 hole
let mut triangle = Triangle::new(12, Some(10), Some(2), Some(1))?;
// set points
triangle
.set_point(0, 0.0, 0.0)?
.set_point(1, 1.0, 0.0)?
.set_point(2, 1.0, 1.0)?
.set_point(3, 0.0, 1.0)?
.set_point(4, 0.2, 0.2)?
.set_point(5, 0.8, 0.2)?
.set_point(6, 0.8, 0.8)?
.set_point(7, 0.2, 0.8)?
.set_point(8, 0.0, 0.5)?
.set_point(9, 0.2, 0.5)?
.set_point(10, 0.8, 0.5)?
.set_point(11, 1.0, 0.5)?;
// set segments
triangle
.set_segment(0, 0, 1)?
.set_segment(1, 1, 2)?
.set_segment(2, 2, 3)?
.set_segment(3, 3, 0)?
.set_segment(4, 4, 5)?
.set_segment(5, 5, 6)?
.set_segment(6, 6, 7)?
.set_segment(7, 7, 4)?
.set_segment(8, 8, 9)?
.set_segment(9, 10, 11)?;
// set regions
triangle
.set_region(0, 0.1, 0.1, 1, None)?
.set_region(1, 0.1, 0.9, 2, None)?;
// set holes
triangle.set_hole(0, 0.5, 0.5)?;
// generate o2 mesh without constraints
triangle.generate_mesh(false, true, None, None)?;
assert_eq!(triangle.ntriangle(), 14);
// draw mesh
let mut plot = Plot::new();
// triangle.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
```rust
use plotpy::Plot;
use tritet::{StrError, Tetgen};
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)?
.set_point(1, 1.0, 0.0, 0.0)?
.set_point(2, 1.0, 1.0, 0.0)?
.set_point(3, 0.0, 1.0, 0.0)?
.set_point(4, 0.0, 0.0, 1.0)?
.set_point(5, 1.0, 0.0, 1.0)?
.set_point(6, 1.0, 1.0, 1.0)?
.set_point(7, 0.0, 1.0, 1.0)?;
// generate Delaunay triangulation
tetgen.generate_delaunay(false)?;
// draw edges of tetrahedra
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
```rust
use plotpy::Plot;
use tritet::{write_tet_vtu, StrError, Tetgen};
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)?
.set_point(1, 1.0, 0.0, 0.0)?
.set_point(2, 1.0, 1.0, 0.0)?
.set_point(3, 0.0, 1.0, 0.0)?
.set_point(4, 0.0, 0.0, 1.0)?
.set_point(5, 1.0, 0.0, 1.0)?
.set_point(6, 1.0, 1.0, 1.0)?
.set_point(7, 0.0, 1.0, 1.0)?;
// outer cube
tetgen
.set_point(8, -1.0, -1.0, -1.0)?
.set_point(9, 2.0, -1.0, -1.0)?
.set_point(10, 2.0, 2.0, -1.0)?
.set_point(11, -1.0, 2.0, -1.0)?
.set_point(12, -1.0, -1.0, 2.0)?
.set_point(13, 2.0, -1.0, 2.0)?
.set_point(14, 2.0, 2.0, 2.0)?
.set_point(15, -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, -0.9, -0.9, -0.9, 1, None)?;
tetgen.set_hole(0, 0.5, 0.5, 0.5)?;
// generate mesh
tetgen.generate_mesh(false, false, None, None)?;
// generate file for Paraview
// write_tet_vtu(&tetgen, "/tmp/tritet/example_tetgen_mesh_1.vtu")?;
// draw edges of tetrahedra
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(())
}
```
