Curvo

Curvo is a NURBS curve / surface modeling library for Rust.

Visualization on Bevy

This library enables not only the creation of NURBS curves from control points, knot vectors, and weights associated with each control point, but also supports generating curves that precisely pass through the given control points and creating periodic curves. Additionally, it allows for the construction of NURBS surfaces through operations such as extruding and lofting based on NURBS curves as inputs.

The modeling operations for NURBS surfaces supported by this library currently include the following:

• Extrude
• Loft
• Sweep
• Revolve

The supported features also include finding the closest point on NURBS curves, finding intersections between two NURBS curves, and dividing based on arc length.

Additional features

Usage

use curvo::prelude::*;
use nalgebra::{Point3, Rotation3, Translation3, Vector3};
use std::f64::consts::FRAC_PI_2;

fn main() {
  // Create a set of points to interpolate
  let points = vec![
      Point3::new(-1.0, -1.0, 0.),
      Point3::new(1.0, -1.0, 0.),
      Point3::new(1.0, 1.0, 0.),
      Point3::new(-1.0, 1.0, 0.),
      Point3::new(-1.0, 2.0, 0.),
      Point3::new(1.0, 2.5, 0.),
  ];

  // Create a NURBS curve that interpolates the given points with degree 3
  // You can also specify the precision of the curve by generic type (f32 or f64)
  let interpolated = NurbsCurve3D::<f64>::try_interpolate(&points, 3).unwrap();

  // NURBS curve & surface can be transformed by nalgebra's matrix
  let rotation = Rotation3::from_axis_angle(&Vector3::z_axis(), FRAC_PI_2);
  let translation = Translation3::new(0., 0., 3.);
  let transform_matrix = translation * rotation; // nalgebra::Isometry3

  // Transform the curve by the given matrix (nalgebra::Isometry3 into nalgebra::Matrix4)
  let offsetted = interpolated.transformed(&transform_matrix.into());

  // Create a NURBS surface by lofting two NURBS curves
  let lofted = NurbsSurface::try_loft(
    &[interpolated, offsetted],
    Some(3), // degree of v direction
  ).unwrap();

  // Tessellate the surface in adaptive manner about curvature for efficient rendering
  let option = AdaptiveTessellationOptions {
      norm_tolerance: 1e-4,
      ..Default::default()
  };
  let tessellation = lofted.tessellate(Some(option));
}

Dependencies

• nalgebra: this library heavily relies on nalgebra, a linear algebra library, to perform its computations.

References

• The NURBS Book by Piegl and Tiller

Feature development sponsored by VUILD Inc.

The NURBS boolean operations feature in this project was developed at the request of VUILD.
They supported the development as a sponsor by funding the feature's implementation.