Struct bevy::math::prelude::CubicSegment

pub struct CubicSegment<P>
where P: VectorSpace,
{ pub coeff: [P; 4], }
Expand description

A segment of a cubic curve, used to hold precomputed coefficients for fast interpolation. Can be evaluated as a parametric curve over the domain [0, 1).

Segments can be chained together to form a longer compound curve.

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§coeff: [P; 4]

Coefficients of the segment

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impl<P> CubicSegment<P>
where P: VectorSpace,

pub fn position(&self, t: f32) -> P

Instantaneous position of a point at parametric value t.

pub fn velocity(&self, t: f32) -> P

Instantaneous velocity of a point at parametric value t.

pub fn acceleration(&self, t: f32) -> P

Instantaneous acceleration of a point at parametric value t.

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impl CubicSegment<Vec2>

The CubicSegment<Vec2> can be used as a 2-dimensional easing curve for animation.

The x-axis of the curve is time, and the y-axis is the output value. This struct provides methods for extremely fast solves for y given x.

pub fn new_bezier( p1: impl Into<Vec2>, p2: impl Into<Vec2>, ) -> CubicSegment<Vec2>

Construct a cubic Bezier curve for animation easing, with control points p1 and p2. A cubic Bezier easing curve has control point p0 at (0, 0) and p3 at (1, 1), leaving only p1 and p2 as the remaining degrees of freedom. The first and last control points are fixed to ensure the animation begins at 0, and ends at 1.

This is a very common tool for UI animations that accelerate and decelerate smoothly. For example, the ubiquitous “ease-in-out” is defined as (0.25, 0.1), (0.25, 1.0).

pub fn ease(&self, time: f32) -> f32

Given a time within 0..=1, returns an eased value that follows the cubic curve instead of a straight line. This eased result may be outside the range 0..=1, however it will always start at 0 and end at 1: ease(0) = 0 and ease(1) = 1.

let cubic_bezier = CubicSegment::new_bezier((0.25, 0.1), (0.25, 1.0));
assert_eq!(cubic_bezier.ease(0.0), 0.0);
assert_eq!(cubic_bezier.ease(1.0), 1.0);
§How cubic easing works

Easing is generally accomplished with the help of “shaping functions”. These are curves that start at (0,0) and end at (1,1). The x-axis of this plot is the current time of the animation, from 0 to 1. The y-axis is how far along the animation is, also from 0 to 1. You can imagine that if the shaping function is a straight line, there is a 1:1 mapping between the time and how far along your animation is. If the time = 0.5, the animation is halfway through. This is known as linear interpolation, and results in objects animating with a constant velocity, and no smooth acceleration or deceleration at the start or end.

y
│         ●
│       ⬈
│     ⬈    
│   ⬈
│ ⬈
●─────────── x (time)

Using cubic Beziers, we have a curve that starts at (0,0), ends at (1,1), and follows a path determined by the two remaining control points (handles). These handles allow us to define a smooth curve. As time (x-axis) progresses, we now follow the curve, and use the y value to determine how far along the animation is.

y
         ⬈➔●
│      ⬈   
│     ↑      
│     ↑
│    ⬈
●➔⬈───────── x (time)

To accomplish this, we need to be able to find the position y on a curve, given the x value. Cubic curves are implicit parametric functions like B(t) = (x,y). To find y, we first solve for t that corresponds to the given x (time). We use the Newton-Raphson root-finding method to quickly find a value of t that is very near the desired value of x. Once we have this we can easily plug that t into our curve’s position function, to find the y component, which is how far along our animation should be. In other words:

Given time in 0..=1

Use Newton’s method to find a value of t that results in B(t) = (x,y) where x == time

Once a solution is found, use the resulting y value as the final result

Trait Implementations§

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impl<P> Clone for CubicSegment<P>
where P: Clone + VectorSpace,

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fn clone(&self) -> CubicSegment<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 CubicSegment<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> Default for CubicSegment<P>
where P: Default + VectorSpace,

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fn default() -> CubicSegment<P>

Returns the “default value” for a type. Read more
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impl<P> Extend<CubicSegment<P>> for CubicCurve<P>
where P: VectorSpace,

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fn extend<T>(&mut self, iter: T)
where T: IntoIterator<Item = CubicSegment<P>>,

Extends a collection with the contents of an iterator. Read more
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fn extend_one(&mut self, item: A)

🔬This is a nightly-only experimental API. (extend_one)
Extends a collection with exactly one element.
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fn extend_reserve(&mut self, additional: usize)

🔬This is a nightly-only experimental API. (extend_one)
Reserves capacity in a collection for the given number of additional elements. Read more
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impl<P> From<CubicSegment<P>> for RationalSegment<P>
where P: VectorSpace,

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fn from(value: CubicSegment<P>) -> RationalSegment<P>

Converts to this type from the input type.
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impl<P> FromReflect for CubicSegment<P>
where P: VectorSpace + TypePath, CubicSegment<P>: Any + Send + Sync, [P; 4]: FromReflect + TypePath + RegisterForReflection,

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fn from_reflect(reflect: &(dyn Reflect + 'static)) -> Option<CubicSegment<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 CubicSegment<P>
where P: VectorSpace + TypePath, CubicSegment<P>: Any + Send + Sync, [P; 4]: 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> PartialEq for CubicSegment<P>

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fn eq(&self, other: &CubicSegment<P>) -> bool

This method tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<P> Reflect for CubicSegment<P>
where P: VectorSpace + TypePath, CubicSegment<P>: Any + Send + Sync, [P; 4]: 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<CubicSegment<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<CubicSegment<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<CubicSegment<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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fn apply(&mut self, value: &(dyn Reflect + 'static))

Applies a reflected value to this value. Read more
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fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type). Read more
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fn serializable(&self) -> Option<Serializable<'_>>

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 CubicSegment<P>
where P: VectorSpace + TypePath, CubicSegment<P>: Any + Send + Sync, [P; 4]: 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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fn field_mut(&mut self, name: &str) -> Option<&mut (dyn Reflect + 'static)>

Returns a mutable reference to the value of the field named name as a &mut dyn Reflect.
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fn field_at(&self, index: usize) -> Option<&(dyn Reflect + 'static)>

Returns a reference to the value of the field with index index as a &dyn Reflect.
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fn field_at_mut(&mut self, index: usize) -> Option<&mut (dyn Reflect + 'static)>

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

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 CubicSegment<P>

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fn type_path() -> &'static str

Returns the fully qualified path of the underlying type. Read more
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fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type. Read more
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fn type_ident() -> Option<&'static str>

Returns the name of the type, or None if it is anonymous. Read more
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fn crate_name() -> Option<&'static str>

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 CubicSegment<P>
where P: VectorSpace + TypePath, CubicSegment<P>: Any + Send + Sync, [P; 4]: 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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impl<P> Copy for CubicSegment<P>
where P: Copy + VectorSpace,

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impl<P> StructuralPartialEq for CubicSegment<P>
where P: VectorSpace,

Auto Trait Implementations§

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impl<P> Freeze for CubicSegment<P>
where P: Freeze,

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impl<P> RefUnwindSafe for CubicSegment<P>
where P: RefUnwindSafe,

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impl<P> Send for CubicSegment<P>
where P: Send,

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impl<P> Sync for CubicSegment<P>
where P: Sync,

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impl<P> Unpin for CubicSegment<P>
where P: Unpin,

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impl<P> UnwindSafe for CubicSegment<P>
where P: UnwindSafe,

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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where U: ShaderType, &'a T: for<'a> Into<U>,

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fn as_bind_group_shader_type(&self, _images: &RenderAssets<GpuImage>) -> U

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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Immutably borrows from an owned value. Read more
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Mutably borrows from an owned value. Read more
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default unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> CloneToUninit for T
where T: Copy,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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fn downcast(&self) -> &T

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impl<T> Downcast for T
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Convert Box<dyn Trait> (where Trait: Downcast) to Box<dyn Any>. Box<dyn Any> can then be further downcast into Box<ConcreteType> where ConcreteType implements Trait.
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Convert Rc<Trait> (where Trait: Downcast) to Rc<Any>. Rc<Any> can then be further downcast into Rc<ConcreteType> where ConcreteType implements Trait.
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Convert &Trait (where Trait: Downcast) to &Any. This is needed since Rust cannot generate &Any’s vtable from &Trait’s.
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Convert &mut Trait (where Trait: Downcast) to &Any. This is needed since Rust cannot generate &mut Any’s vtable from &mut Trait’s.
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