Struct CubicNurbs 

pub struct CubicNurbs<P: VectorSpace> {
    pub control_points: Vec<P>,
    pub weights: Vec<f32>,
    pub knots: Vec<f32>,
}

Non-uniform Rational B-Splines (NURBS) are a powerful generalization of the CubicBSpline which can represent a much more diverse class of curves (like perfect circles and ellipses).

Non-uniformity

The ‘NU’ part of NURBS stands for “Non-Uniform”. This has to do with a parameter called ‘knots’. The knots are a non-decreasing sequence of floating point numbers. The first and last three pairs of knots control the behavior of the curve as it approaches its endpoints. The intermediate pairs each control the length of one segment of the curve. Multiple repeated knot values are called “knot multiplicity”. Knot multiplicity in the intermediate knots causes a “zero-length” segment, and can create sharp corners.

Rationality

The ‘R’ part of NURBS stands for “Rational”. This has to do with NURBS allowing each control point to be assigned a weighting, which controls how much it affects the curve compared to the other points.

Interpolation

The curve will not pass through the control points except where a knot has multiplicity four.

Tangency

Tangents are automatically computed based on the position of control points.

Continuity

When there is no knot multiplicity, the curve is C2 continuous, meaning it has no holes or jumps and the tangent vector changes smoothly along the entire curve length. Like the CubicBSpline, the acceleration continuity makes it useful for camera paths. Knot multiplicity of 2 in intermediate knots reduces the continuity to C1, and knot multiplicity of 3 reduces the continuity to C0. The curve is always at least C0, meaning it has no jumps or holes.

Usage

let points = [
    vec2(-1.0, -20.0),
    vec2(3.0, 2.0),
    vec2(5.0, 3.0),
    vec2(9.0, 8.0),
];
let weights = [1.0, 1.0, 2.0, 1.0];
let knots = [0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 5.0];
let nurbs = CubicNurbs::new(points, Some(weights), Some(knots))
    .expect("NURBS construction failed!")
    .to_curve()
    .unwrap();
let positions: Vec<_> = nurbs.iter_positions(100).collect();

Fields

control_points: Vec<P>

The control points of the NURBS

weights: Vec<f32>

Weights

knots: Vec<f32>

Knots

Implementations

impl<P: VectorSpace<Scalar = f32>> CubicNurbs<P>

pub fn new( control_points: impl IntoIterator<Item = P>, weights: Option<impl IntoIterator<Item = f32>>, knots: Option<impl IntoIterator<Item = f32>>, ) -> Result<Self, CubicNurbsError>

Build a Non-Uniform Rational B-Spline.

If provided, weights must be the same length as the control points. Defaults to equal weights.

If provided, the number of knots must be n + 4 elements, where n is the amount of control points. Defaults to open uniform knots: Self::open_uniform_knots. Knots cannot all be equal.

At least 4 points must be provided, otherwise an error will be returned.

pub fn uniform_knots(control_points: usize) -> Option<Vec<f32>>

Generates uniform knots that will generate the same curve as CubicBSpline.

“Uniform” means that the difference between two subsequent knots is the same.

Will return None if there are less than 4 control points.

pub fn open_uniform_knots(control_points: usize) -> Option<Vec<f32>>

Generates open uniform knots, which makes the ends of the curve pass through the start and end points.

The start and end knots have multiplicity 4, and intermediate knots have multiplicity 0 and difference of 1.

Will return None if there are less than 4 control points.

Trait Implementations

impl<P: Clone + VectorSpace> Clone for CubicNurbs<P>

fn clone(&self) -> CubicNurbs<P>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<P: Debug + VectorSpace> Debug for CubicNurbs<P>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<P: VectorSpace<Scalar = f32>> RationalGenerator<P> for CubicNurbs<P>

Available on crate feature alloc only.

type Error = InsufficientDataError

An error type indicating why construction might fail.

fn to_curve(&self) -> Result<RationalCurve<P>, Self::Error>

Build a RationalCurve by computing the interpolation coefficients for each curve segment.