neco-nurbs

日本語

2D and 3D rational NURBS curves, surfaces, and regions for CAD boundaries, profile geometry, and exact smooth-curve work.

A Japanese mathematical note is available in MATH-ja.md.

Curve and region operations

NurbsCurve2D represents weighted B-spline curves and supports validation, evaluation, sampling, knot insertion, Bezier decomposition, and splitting. Rational circles are provided out of the box, so exact circular profiles can stay analytic.

NurbsRegion groups piecewise closed curves into an outer boundary plus optional holes. It works well for 2D CAD domains and as input to meshing or B-Rep construction.

Usage

Create and evaluate a curve

use neco_nurbs::NurbsCurve2D;

let curve = NurbsCurve2D::new(
    2,
    vec![[0.0, 0.0], [1.0, 2.0], [3.0, 2.0], [4.0, 0.0]],
    vec![0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0],
);
curve.validate().unwrap();

let point = curve.evaluate(0.5);

Sample and refine a curve

let uniform = curve.sample(100);
let adaptive = curve.adaptive_sample(0.1);
let refined = curve.insert_knot(0.25);
let (left, right) = refined.split_at(0.5);
# let _ = (uniform, adaptive, left, right);

Build a region

use neco_nurbs::{NurbsCurve2D, NurbsRegion};

let region = NurbsRegion {
    outer: vec![NurbsCurve2D::circle([0.0, 0.0], 5.0)],
    holes: vec![vec![NurbsCurve2D::circle([1.0, 0.0], 1.0)]],
};

let points = region.outer_adaptive_sample(0.2);
# let _ = points;

API

Item	Description
`NurbsCurve2D`	Rational 2D NURBS curve
`NurbsCurve3D` / `NurbsSurface3D`	Rational 3D NURBS curve and surface types
`NurbsCurve2D::new` / `new_rational`	Construct non-rational or rational curves
`NurbsCurve2D::circle`	Create an exact circle
`validate` / `evaluate`	Check consistency and evaluate a point
`sample` / `adaptive_sample` / `evaluate_samples`	Uniform, adaptive, and batched evaluation
`insert_knot` / `split_at` / `split_at_params`	Refine or split a curve
`to_bezier_spans` / `reverse` / `bounding_box` / `is_closed`	Curve utilities
`NurbsRegion`	Outer boundary plus optional holes
`NurbsRegion::outer_adaptive_sample`	Sample region boundaries for downstream use
`fit_nurbs_curve(...)`	Optional nalgebra-backed curve fitting utility (`fitting`)

Optional features

Feature	Description
`polynomial-highorder`	Enable nalgebra-backed high-order polynomial routines
`fitting`	Enables nalgebra-backed curve fitting utilities

License

MIT

neco-nurbs 0.1.0