geopoint

conformal geometric algebra built on top of the O(1) geonum crate

features

• conformal point representation for euclidean geometry
• geometric primitives: points, lines, planes, spheres, circles
• geometric operations: containment tests, distance computation
• conformal transformations: translation, rotation, dilation, inversion
• versor implementation for efficient transformations

use

cargo add geopoint

basic

use geopoint::*;
use geonum::Multivector;

// create a euclidean point
let point = Multivector::point(&[1.0, 2.0, 3.0]);

// convert to conformal representation
let conf_point = point.to_conformal_point();

// extract euclidean point from conformal representation
let euclidean_point = conf_point.extract_euclidean();

// create a sphere
let center = Multivector::point(&[0.0, 0.0, 0.0]);
let sphere = Multivector::sphere(&center, 2.0);

// test if point is inside sphere
let is_inside = sphere.contains_point(&point);

// compute distance to sphere
let distance = sphere.distance_to_point(&point);

// apply translation
let translation = Multivector::point(&[1.0, 0.0, 0.0]);
let translated_point = point.translate(&translation);

// apply uniform scaling
let scaled_point = point.dilate(2.0);

custom standard angle

use geopoint::ZeroVector;
use std::f64::consts::PI as pi;

// create a zero vector with a custom standard angle (pi/4 angle)
let custom_metric = ZeroVector::new(3, pi/4.0);

// work with this custom standard angle
let point = custom_metric.point(&[1.0, 2.0, 3.0]);

// standard angle (pi/2) matches euclidean geometry
let standard = ZeroVector::standard(3);

// conformal angle (0.0) for conformal transformations
let conformal = ZeroVector::conformal(3);

see:

• tests/lib_test.rs for examples of basic usage
• tests/zero_vector_test.rs for examples with custom metrics
• tests/conformal_test.rs for a complete demonstration

benches

geopoint maintains geonums O(1) computational advantage in high dimensional spaces

core operations (nanoseconds)

dimension scaling

geopoint demonstrates excellent performance with operations completing in hundreds of nanoseconds. high-dimensional operations scale efficiently, showing only a small increase in execution time as dimensions grow - a key advantage of the underlying O(1) representation from geonum

test

cargo fmt --check # format
cargo clippy # lint
cargo test --lib # unit
cargo test --test "*" # feature
cargo bench # bench
cargo llvm-cov # coverage

docs

cargo doc --open

todo

• complete coordinate extraction for all dimensions
• fix rotation with custom angle
• implement meet and join operations
• add blade identification
• optimize high-dimensional operations