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 C2, 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();
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> CubicNurbs<P>

pub fn new( control_points: impl Into<Vec<P>>, weights: Option<impl Into<Vec<f32>>>, knots: Option<impl Into<Vec<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 copy 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> FromReflect for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

fn from_reflect(reflect: &dyn Reflect) -> Option<Self>

Constructs a concrete instance of Self from a reflected value.

fn take_from_reflect( reflect: Box<dyn Reflect>, ) -> Result<Self, Box<dyn Reflect>>

Attempts to downcast the given value to Self using, constructing the value using from_reflect if that fails.

impl<P> GetTypeRegistration for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

fn get_type_registration() -> TypeRegistration

Returns the default TypeRegistration for this type.

fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this type.

impl<P: VectorSpace> RationalGenerator<P> for CubicNurbs<P>

fn to_curve(&self) -> RationalCurve<P>

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

impl<P> Reflect for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

fn get_represented_type_info(&self) -> Option<&'static TypeInfo>

Returns the TypeInfo of the type represented by this value.

fn into_any(self: Box<Self>) -> Box<dyn Any>

Returns the value as a Box<dyn Any>.

fn as_any(&self) -> &dyn Any

Returns the value as a &dyn Any.

fn as_any_mut(&mut self) -> &mut dyn Any

Returns the value as a &mut dyn Any.

fn into_reflect(self: Box<Self>) -> Box<dyn Reflect>

Casts this type to a boxed reflected value.

fn as_reflect(&self) -> &dyn Reflect

Casts this type to a reflected value.

fn as_reflect_mut(&mut self) -> &mut dyn Reflect

Casts this type to a mutable reflected value.

fn clone_value(&self) -> Box<dyn Reflect>

Clones the value as a Reflect trait object.

fn set(&mut self, value: Box<dyn Reflect>) -> Result<(), Box<dyn Reflect>>

Performs a type-checked assignment of a reflected value to this value.

fn try_apply(&mut self, value: &dyn Reflect) -> Result<(), ApplyError>

Tries to apply a reflected value to this value.

fn reflect_kind(&self) -> ReflectKind

Returns a zero-sized enumeration of “kinds” of type.

fn reflect_ref(&self) -> ReflectRef<'_>

Returns an immutable enumeration of “kinds” of type.

fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type.

fn reflect_owned(self: Box<Self>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type.

fn reflect_partial_eq(&self, value: &dyn Reflect) -> Option<bool>

Returns a “partial equality” comparison result.

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

Debug formatter for the value.

fn apply(&mut self, value: &(dyn Reflect + 'static))

Applies a reflected value to this value.

fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type).

fn serializable(&self) -> Option<Serializable<'_>>

Returns a serializable version of the value.

fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type.

impl<P> Struct for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

fn field(&self, name: &str) -> Option<&dyn Reflect>

Returns a reference to the value of the field named name as a &dyn Reflect.

fn field_mut(&mut self, name: &str) -> Option<&mut dyn Reflect>

Returns a mutable reference to the value of the field named name as a &mut dyn Reflect.

fn field_at(&self, index: usize) -> Option<&dyn Reflect>

Returns a reference to the value of the field with index index as a &dyn Reflect.

fn field_at_mut(&mut self, index: usize) -> Option<&mut dyn Reflect>

Returns a mutable reference to the value of the field with index index as a &mut dyn Reflect.

fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index index.

fn field_len(&self) -> usize

Returns the number of fields in the struct.

fn iter_fields(&self) -> FieldIter<'_>

Returns an iterator over the values of the reflectable fields for this struct.

fn clone_dynamic(&self) -> DynamicStruct

Clones the struct into a DynamicStruct.

impl<P> TypePath for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace,

fn type_path() -> &'static str

Returns the fully qualified path of the underlying type.

fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type.

fn type_ident() -> Option<&'static str>

Returns the name of the type, or None if it is anonymous.

fn crate_name() -> Option<&'static str>

Returns the name of the crate the type is in, or None if it is anonymous.

fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or None if it is anonymous.

impl<P> Typed for CubicNurbs<P>

where Self: Any + Send + Sync, P: TypePath + VectorSpace, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.