🔯 projgeom-rs

Projective geometry in Rust - A comprehensive library for projective, elliptic, hyperbolic, and Euclidean geometry computations.

🛠️ Installation

📦 Cargo

Install the rust toolchain in order to have cargo installed by following this guide.
run cargo install projgeom-rs

Add to your project

[dependencies]
projgeom-rs = "0.1"

📚 Usage Examples

Projective Geometry

use projgeom_rs::{PgPoint, PgLine, ProjectivePlane};

// Create two points in projective space
let p1 = PgPoint::new([1, 2, 3]);
let p2 = PgPoint::new([4, 5, 6]);

// Find the line through two points (meet operation)
let line = p1.meet(&p2);

// Check if a point lies on a line
assert!(line.incident(&p1));
assert!(line.incident(&p2));

// Parametrize a point on the line
let p3 = p1.parametrize(2, &p2, 3);
assert!(line.incident(&p3));

// Find the intersection of two lines
let l1 = PgLine::new([1, 0, 0]);
let l2 = PgLine::new([0, 1, 0]);
let intersection = l1.meet(&l2);

Elliptic Geometry

use projgeom_rs::{EllipticPoint, EllipticLine, CayleyKleinPlane};

// Create points in elliptic geometry
let a1 = EllipticPoint::new([1, 0, 0]);
let a2 = EllipticPoint::new([0, 1, 0]);
let a3 = EllipticPoint::new([0, 0, 1]);

// Compute perpendicular line
let perp_line = a1.perp();

// Compute orthocenter of a triangle
let triangle = [a1, a2, a3];
let orthocenter = orthocenter(&triangle);

// Compute altitudes
let altitudes = tri_altitude(&triangle);

Hyperbolic Geometry

use projgeom_rs::{HyperbolicPoint, HyperbolicLine, CayleyKleinPlane};

// Create points in hyperbolic geometry
let p1 = HyperbolicPoint::new([1, 0, 1]);
let p2 = HyperbolicPoint::new([0, 1, 1]);

// Find the line through two points
let line = p1.meet(&p2);

// Compute perpendicular
let perp = p1.perp();

Euclidean Geometry

use projgeom_rs::{EuclidPoint, EuclidLine, CayleyKleinPlane};

// Create points in Euclidean geometry
let p1 = EuclidPoint::new([1, 2, 1]);
let p2 = EuclidPoint::new([3, 4, 1]);

// Compute distance between points
let line = p1.meet(&p2);

// Reflect a point across a line
let mirror = EuclidLine::new([1, -1, 0]);
let reflected = reflect(&mirror, &p1);

Harmonic Conjugates

use projgeom_rs::{PgPoint, harm_conj};

// Compute harmonic conjugate
let a = PgPoint::new([1, 0, 0]);
let b = PgPoint::new([0, 1, 0]);
let c = PgPoint::new([1, 1, 0]);

let d = harm_conj(&a, &b, &c);
// d is the harmonic conjugate of c with respect to a and b

Projective Transformations

use projgeom_rs::{PgPoint, involution};

// Apply involution transformation
let origin = PgPoint::new([1, 0, 0]);
let mirror = PgLine::new([0, 1, 0]);
let point = PgPoint::new([1, 1, 1]);

let transformed = involution(&origin, &mirror, &point);

📜 License

Licensed under either of

Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

🤝 Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

See CONTRIBUTING.md.

Polyglot Implementations

projgeom-cpp - C++ version

Algorithm Polyglot

algorithm-polyglot - Meta-repo documenting the polyglot strategy