Struct KnotVec 

pub struct KnotVec<N: ScalarT> { /* private fields */ }

Vector of knots in non-decreasing order.

Knot values exist in the parameter space of a NURBS curve. They partition the total 1D parameter range into regions over which the interpolating polynomials of the NURBS curve are active. Thus, in combination with the degree of a NURBS curve, they define the non-uniform B-spline basis functions.

Implementations

impl<N: ScalarT> KnotVec<N>

pub fn new(knots: Vec<N>) -> Option<Self>

Creates a new knot vector if possible.

A new knot vector must satisfy the following criteria:

• it must contain >= 2 elements
• it must be sorted (non-decreasing)
• it must represent a non-zero span (the last knot cannot be equal to the first)

Parameters

• knots - a vector of knot values in non-decreasing order

Example

let knots = KnotVec::new(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]).unwrap();

pub fn len(&self) -> usize

Returns the number of knots in the knot vector.

Example

let knots = KnotVec::new(vec![0.0, 0.0, 1.0, 1.0]).unwrap();
assert_eq!(knots.len(), 4);

pub fn is_clamped(&self, degree: usize) -> bool

Checks if a knot vector is clamped.

A knot vector is clamped if the first knot value is repeated degree + 1 times at the start of the knot vector (ie. its multiplicity is degree + 1), and if the last knot is repeated degree + 1 times at the end of the knot vector.

Parameters

• degree - degree of the NURBS curve

pub fn is_empty(&self) -> bool

Checks if the knot vector is empty (always returns false).

pub fn min_u(&self) -> N

Returns the minimum parameter value contained in this knot vector.

pub fn max_u(&self) -> N

Returns the maximum parameter value contained in this knot vector.

pub fn clamp(&self, u: N) -> N

Clamp a parameter value to the allowed range of the parameter.

Parameters

• u - the parameter value to clamp in the range min_u <= u <= max_u

pub fn find_span(&self, u: N) -> usize

Finds the index of the span inside the knot vector which contains the parameter value u.

Each pair of knots in the knot vector defines a span. Spans are zero length for knots with a multiplicity > 1. Given a parameter value, u, this function returns the index of the knot span which contains u.

The knot span index, i = knots.find_span(u), which contains u, satisfies the relationship that:

knots[i] <= u < knots[i+1], when u < knots.max_u()
knots[i] < u == knots[i+1], when u == knots.max_u()

Parameters

• u - the parameter value for which to find the span

Examples

let knots = KnotVec::new(vec![0.0, 0.0, 0.5, 1.0, 1.0]).unwrap();
assert_eq!(knots.find_span(0.0), 1);
assert_eq!(knots.find_span(0.6), 2);
assert_eq!(knots.find_span(1.0), 2); // note u=knots.max_u() is a bit special

Panics

Panics if the parameter u is outside the allowed range of the knot vector.

Trait Implementations

impl<N: Clone + ScalarT> Clone for KnotVec<N>

fn clone(&self) -> KnotVec<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<N: Debug + ScalarT> Debug for KnotVec<N>

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

Formats the value using the given formatter.

impl<N: ScalarT> Index<usize> for KnotVec<N>

type Output = N

The returned type after indexing.

fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<N: PartialEq + ScalarT> PartialEq for KnotVec<N>

fn eq(&self, other: &KnotVec<N>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<N: PartialEq + ScalarT> StructuralPartialEq for KnotVec<N>