# Struct bevy::math::prelude::CubicNurbs

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

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§

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### impl<P> CubicNurbs<P>where P: VectorSpace,

#### pub fn new( control_points: impl Into<Vec<P>>, weights: Option<impl Into<Vec<f32>>>, knots: Option<impl Into<Vec<f32>>>, ) -> Result<CubicNurbs<P>, 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§

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### impl<P> Clone for CubicNurbs<P>where P: Clone + VectorSpace,

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

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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### impl<P> Debug for CubicNurbs<P>where P: Debug + VectorSpace,

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

Formats the value using the given formatter. Read more
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### impl<P> FromReflect for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

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#### fn from_reflect(reflect: &(dyn Reflect + 'static)) -> Option<CubicNurbs<P>>

Constructs a concrete instance of Self from a reflected value.
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#### 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. Read more
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### impl<P> GetTypeRegistration for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

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#### fn get_type_registration() -> TypeRegistration

Returns the default TypeRegistration for this type.
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#### fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this type. Read more
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### impl<P> RationalGenerator<P> for CubicNurbs<P>where P: VectorSpace,

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

Build a RationalCurve by computing the interpolation coefficients for each curve segment.
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### impl<P> Reflect for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

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

Returns the TypeInfo of the type represented by this value. Read more
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#### fn into_any(self: Box<CubicNurbs<P>>) -> Box<dyn Any>

Returns the value as a Box<dyn Any>.
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#### fn as_any(&self) -> &(dyn Any + 'static)

Returns the value as a &dyn Any.
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#### fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)

Returns the value as a &mut dyn Any.
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#### fn into_reflect(self: Box<CubicNurbs<P>>) -> Box<dyn Reflect>

Casts this type to a boxed reflected value.
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#### fn as_reflect(&self) -> &(dyn Reflect + 'static)

Casts this type to a reflected value.
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#### fn as_reflect_mut(&mut self) -> &mut (dyn Reflect + 'static)

Casts this type to a mutable reflected value.
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#### fn clone_value(&self) -> Box<dyn Reflect>

Clones the value as a Reflect trait object. Read more
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#### fn set(&mut self, value: Box<dyn Reflect>) -> Result<(), Box<dyn Reflect>>

Performs a type-checked assignment of a reflected value to this value. Read more
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#### fn try_apply( &mut self, value: &(dyn Reflect + 'static), ) -> Result<(), ApplyError>

Tries to apply a reflected value to this value. Read more
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#### fn reflect_kind(&self) -> ReflectKind

Returns a zero-sized enumeration of “kinds” of type. Read more
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#### fn reflect_ref(&self) -> ReflectRef<'_>

Returns an immutable enumeration of “kinds” of type. Read more
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#### fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type. Read more
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#### fn reflect_owned(self: Box<CubicNurbs<P>>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type. Read more
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#### fn reflect_partial_eq(&self, value: &(dyn Reflect + 'static)) -> Option<bool>

Returns a “partial equality” comparison result. Read more
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#### fn debug(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Debug formatter for the value. Read more
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Applies a reflected value to this value. Read more
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Returns a hash of the value (which includes the type). Read more
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Returns a serializable version of the value. Read more
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#### fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type. Read more
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### impl<P> Struct for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

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

Returns a reference to the value of the field named name as a &dyn Reflect.
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Returns a mutable reference to the value of the field named name as a &mut dyn Reflect.
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Returns a reference to the value of the field with index index as a &dyn Reflect.
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Returns a mutable reference to the value of the field with index index as a &mut dyn Reflect.
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#### fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index index.
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#### fn field_len(&self) -> usize

Returns the number of fields in the struct.
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Returns an iterator over the values of the reflectable fields for this struct.
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#### fn clone_dynamic(&self) -> DynamicStruct

Clones the struct into a DynamicStruct.
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### impl<P> TypePath for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync,

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#### fn type_path() -> &'static str

Returns the fully qualified path of the underlying type. Read more
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Returns a short, pretty-print enabled path to the type. Read more
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Returns the name of the type, or None if it is anonymous. Read more
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Returns the name of the crate the type is in, or None if it is anonymous. Read more
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#### fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or None if it is anonymous. Read more
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### impl<P> Typed for CubicNurbs<P>where P: VectorSpace + TypePath, CubicNurbs<P>: Any + Send + Sync, Vec<P>: FromReflect + TypePath + RegisterForReflection, Vec<f32>: FromReflect + TypePath + RegisterForReflection,

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#### fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.

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Return the T ShaderType for self. When used in AsBindGroup derives, it is safe to assume that all images in self exist.
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