## startin

A Delaunay triangulator for terrains

### 21 releases

 0.8.0 Jul 16, 2024 Dec 14, 2023 Aug 16, 2023 Jan 4, 2023 Jul 30, 2019

#216 in Algorithms

105KB
2K SLoC

# startin

A Delaunay triangulator where the input are 2.5D points, the DT is computed in 2D but the elevation of the vertices are kept. This is used mostly for the modelling of terrains. Constructing a 2D Delaunay triangulation is also possible.

The construction algorithm used is an incremental insertion based on flips, and the data structure is a cheap implementation of the star-based structure defined in Blandford et al. (2003), cheap because the link of each vertex is stored a simple array (`Vec`) and not in an optimised blob like they did. It results in a pretty fast library (comparison will come at some point), but it uses more space than the optimised one.

The deletion of a vertex is also possible. The algorithm implemented is a modification of the one of Mostafavi, Gold, and Dakowicz (2003). The ears are filled by flipping, so it's in theory more robust. I have also extended the algorithm to allow the deletion of vertices on the boundary of the convex hull. The algorithm is sub-optimal, but in practice the number of neighbours of a given vertex in a DT is only 6, so it doesn't really matter.

Robust arithmetic for the geometric predicates are used (Shewchuk's predicates, well the Rust port of the code (robust crate)), so startin is robust and shouldn't crash (touch wood).

There are a few interpolation functions implemented: (1) nearest-neighbour, (2) linear in TIN, (3) Laplace, (4) natural neighbour (aka Sibson's interpolation), (5) IDW with search-radius.

# Python bindings

I also made Python bindings, called "startinpy": https://github.com/hugoledoux/startinpy/.

There are a few more functions (eg reading GeoTIFF, LAZ can be read easily), the docs is better, and it all input/output are NumPy arrays.

# Web-demo with WebAssembly

Rust can be compiled to WebAssembly, and you can see a demo of some of the possibilities of startin (all computations are done locally and it's fast!).

--> web-demo

# C interface

A basic C interface is available in `src/c_interface.rs`, to compile it:

``````cargo build --features c_api
``````

# Documentation

You can read the complete documentation here

# Usage

``````extern crate startin;
fn main() {
let mut pts: Vec<[f64; 3]> = Vec::new();
pts.push([20.0, 30.0, 2.0]);
pts.push([120.0, 33.0, 12.5]);
pts.push([124.0, 222.0, 7.65]);
pts.push([20.0, 133.0, 21.0]);
pts.push([60.0, 60.0, 33.0]);
let mut dt = startin::Triangulation::new();
dt.insert(&pts, startin::InsertionStrategy::AsIs);
println!("{}", dt);
//-- print all the vertices
for (i, each) in dt.all_vertices().iter().enumerate() {
// skip the first one, the infinite vertex
if i > 0 {
println!("#{}: ({:.3}, {:.3}, {:.3})", i, each[0], each[1], each[2]);
}
}
//-- insert a new vertex
let re = dt.insert_one_pt(22.2, 33.3, 4.4);
match re {
Ok(_v) => println!(
"Inserted new point, now the DT has {} vertices",
dt.number_of_vertices()
),
Err(v) => println!("Duplicate of vertex #{}, not inserted", v),
}
//-- remove it
match dt.remove(6) {
Ok(num) => println!("Vertex deleted, now the DT has {} vertices", num),
Err(why) => println!("!!! Deletion error: {:?}", why),
}
//-- get the convex hull
let ch = dt.convex_hull();
println!("Convex hull: {:?}", ch);
//-- fetch triangle containing (x, y)
match dt.locate(50.0, 50.0) {
Ok(tr) => println!("The triangle is {}", tr),
Err(why) => println!("Error: {:?}", why),
}
//-- interpolate with Laplace interpolation at 2 locations
let locs = vec![[51.0, 22.0], [50.3, 19.9]];
let interpolant = startin::interpolation::Laplace {};
let zs = startin::interpolation::interpolate(&interpolant, &mut dt, &locs);
for z in &zs {
match z {
Ok(value) => println!("z = {}", value),
Err(why) => println!("Interplation impossible: {:?}", why),
}
}
//-- save the triangulation in OBJ for debug purposes
let _re = dt.write_obj("/home/elvis/tr.obj".to_string());
}
``````

~1.7–2.6MB
~44K SLoC