Struct CubicBezier3

pub struct CubicBezier3<T> {
    pub start: Vec3<T>,
    pub ctrl0: Vec3<T>,
    pub ctrl1: Vec3<T>,
    pub end: Vec3<T>,
}

A 3D Bézier curve with two control points.

3x3 and 4x4 matrices can be multiplied by a Bézier curve to transform all of its points.

Fields

start: Vec3<T>

Starting point of the curve.

ctrl0: Vec3<T>

First control point of the curve, associated with start.

ctrl1: Vec3<T>

Second control point of the curve, associated with end.

end: Vec3<T>

End point of the curve.

Implementations

impl<T> CubicBezier3<T>

where T: Real,

pub fn evaluate(self, t: T) -> Vec3<T>

Evaluates the position of the point lying on the curve at interpolation factor t.

This is one of the most important Bézier curve operations, because, in one way or another, it is used to render a curve to the screen. The common use case is to successively evaluate a curve at a set of values that range from 0 to 1, to approximate the curve as an array of line segments which are then rendered.

pub fn evaluate_derivative(self, t: T) -> Vec3<T>

Evaluates the derivative tangent at interpolation factor t, which happens to give a non-normalized tangent vector.

See also normalized_tangent().

pub fn matrix() -> Mat4<T>

Returns the constant matrix M such that, given T = [1, t*t, t*t*t, t*t*t*t] and P the vector of control points, dot(T * M, P) evalutes the Bezier curve at ‘t’.

This function name is arguably dubious.

pub fn split(self, t: T) -> [CubicBezier3<T>; 2]

Splits this cubic Bézier curve into two curves, at interpolation factor t.

pub fn unit_quarter_circle() -> CubicBezier3<T>

Gets the cubic Bézier curve that approximates a unit quarter circle.

You can build a good-looking circle out of 4 curves by applying symmetries to this curve.

pub fn unit_circle() -> [CubicBezier3<T>; 4]

Gets the 4 cubic Bézier curves that, used together, approximate a unit quarter circle.

The returned tuple is (north-east, north-west, south-west, south-east).

impl<T> CubicBezier3<T>

pub fn reversed(self) -> CubicBezier3<T>

Gets this curve reversed, i.e swaps start with end and ctrl0 with ctrl1.

pub fn reverse(&mut self)

Reverses this curve, i.e swaps start with end and ctrl0 with ctrl1.

pub fn into_vec4(self) -> Vec4<Vec3<T>>

Converts this curve into a Vec4 of points.

pub fn into_tuple(self) -> (Vec3<T>, Vec3<T>, Vec3<T>, Vec3<T>)

Converts this curve into a tuple of points.

pub fn into_array(self) -> [Vec3<T>; 4]

Converts this curve into an array of points.

impl<T> CubicBezier3<T>

where T: Real,

pub fn x_inflections(self) -> Option<(T, Option<T>)>

Returns the evaluation factor that gives an inflection point along the X axis, if any.

pub fn min_x(self) -> T

Returns the evaluation factor that gives the point on the curve which X coordinate is the minimum.

pub fn max_x(self) -> T

Returns the evaluation factor that gives the point on the curve which X coordinate is the maximum.

pub fn x_bounds(self) -> (T, T)

Returns the evaluation factors that give the points on the curve which X coordinates are the respective minimum and maximum.

impl<T> CubicBezier3<T>

where T: Real,

pub fn y_inflections(self) -> Option<(T, Option<T>)>

Returns the evaluation factor that gives an inflection point along the Y axis, if any.

pub fn min_y(self) -> T

Returns the evaluation factor that gives the point on the curve which Y coordinate is the minimum.

pub fn max_y(self) -> T

Returns the evaluation factor that gives the point on the curve which Y coordinate is the maximum.

pub fn y_bounds(self) -> (T, T)

Returns the evaluation factors that give the points on the curve which Y coordinates are the respective minimum and maximum.

impl<T> CubicBezier3<T>

where T: Real,

pub fn z_inflections(self) -> Option<(T, Option<T>)>

Returns the evaluation factor that gives an inflection point along the Z axis, if any.

pub fn min_z(self) -> T

Returns the evaluation factor that gives the point on the curve which Z coordinate is the minimum.

pub fn max_z(self) -> T

Returns the evaluation factor that gives the point on the curve which Z coordinate is the maximum.

pub fn z_bounds(self) -> (T, T)

Returns the evaluation factors that give the points on the curve which Z coordinates are the respective minimum and maximum.

impl<T> CubicBezier3<T>

where T: Real,

pub fn normalized_tangent(self, t: T) -> Vec3<T>

where T: Add<Output = T>,

Evaluates the normalized tangent at interpolation factor t.

pub fn length_by_discretization(self, step_count: u16) -> T

where T: Add<Output = T> + From<u16>,

Approximates the curve’s length by subdividing it into step_count+1 segments.

pub fn aabr(self) -> Aabr<T>

Gets the Axis-Aligned Bounding Rectangle for this curve.

On 3D curves, this discards the z values.

pub fn flipped_x(self) -> CubicBezier3<T>

Returns this curve, flipping the x coordinate of each of its points.

pub fn flipped_y(self) -> CubicBezier3<T>

Returns this curve, flipping the y coordinate of each of its points.

pub fn flip_x(&mut self)

Flips the x coordinate of all points of this curve.

pub fn flip_y(&mut self)

Flips the y coordinate of all points of this curve.

pub fn binary_search_point_by_steps( self, p: Vec3<T>, steps: u16, epsilon: T, ) -> (T, Vec3<T>)

where T: Add<Output = T> + From<u16>,

Searches for the point lying on this curve that is closest to p.

steps is the number of points to sample in the curve for the “broad phase” that takes place before the binary search.

epsilon denotes the desired precision for the result. The higher it is, the sooner the algorithm will finish, but the result would be less satisfactory.

Panics

Panics if epsilon is less than or equal to T::epsilon().
epsilon must be positive and not approximately equal to zero.

pub fn binary_search_point<I>( self, p: Vec3<T>, coarse: I, half_interval: T, epsilon: T, ) -> (T, Vec3<T>)

where T: Add<Output = T>, I: IntoIterator<Item = (T, Vec3<T>)>,

Searches for the point lying on this curve that is closest to p.

For an example usage, see the source code of binary_search_point_by_steps().

coarse is an iterator over pairs of (interpolation_value, point) that are assumed to, together, represent a discretization of the curve.
This parameter is used for a “broad phase” - the point yielded by coarse that is closest to p is the starting point for the binary search.
coarse may very well yield a single pair; Also, it was designed so that, if you already have the values handy, there is no need to recompute them.
This function doesn’t panic if coarse yields no element, but then it would be very unlikely for the result to be satisfactory.

half_interval is the starting value for the half of the binary search interval.

epsilon denotes the desired precision for the result. The higher it is, the sooner the algorithm will finish, but the result would be less satisfactory.

Panics

Panics if epsilon is less than or equal to T::epsilon().
epsilon must be positive and not approximately equal to zero.

impl<T> CubicBezier3<T>

where T: Real,

pub fn aabb(self) -> Aabb<T>

Gets the Axis-Aligned Bounding Box for this curve.

pub fn flipped_z(self) -> CubicBezier3<T>

Returns this curve, flipping the y coordinate of each of its points.

pub fn flip_z(&mut self)

Flips the x coordinate of all points of this curve.

impl<T> CubicBezier3<T>

pub fn into_2d(self) -> CubicBezier2<T>

Converts this 3D curve to a 2D one, dropping the z elements.

Trait Implementations

impl<T> Clone for CubicBezier3<T>

where T: Clone,

fn clone(&self) -> CubicBezier3<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T> Debug for CubicBezier3<T>

where T: Debug,

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

Formats the value using the given formatter.

impl<T> Default for CubicBezier3<T>

where T: Default,

fn default() -> CubicBezier3<T>

Returns the “default value” for a type.

impl<'de, T> Deserialize<'de> for CubicBezier3<T>

where T: Deserialize<'de>,

fn deserialize<__D>( __deserializer: __D, ) -> Result<CubicBezier3<T>, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T> From<CubicBezier2<T>> for CubicBezier3<T>

where T: Zero,

fn from(c: CubicBezier2<T>) -> CubicBezier3<T>

Converts to this type from the input type.

impl<T> From<CubicBezier3<T>> for CubicBezier2<T>

fn from(c: CubicBezier3<T>) -> CubicBezier2<T>

Converts to this type from the input type.

impl<T> From<CubicBezier3<T>> for Vec4<Vec3<T>>

fn from(v: CubicBezier3<T>) -> Vec4<Vec3<T>>

Converts to this type from the input type.

impl<T> From<LineSegment3<T>> for CubicBezier3<T>

where T: Real + Lerp<T, Output = T>,

fn from(line_segment: LineSegment3<T>) -> CubicBezier3<T>

Converts to this type from the input type.

impl<T> From<QuadraticBezier3<T>> for CubicBezier3<T>

where T: Real,

fn from(b: QuadraticBezier3<T>) -> CubicBezier3<T>

Converts to this type from the input type.

impl<T> From<Range<Vec3<T>>> for CubicBezier3<T>

where T: Real + Lerp<T, Output = T>,

fn from(range: Range<Vec3<T>>) -> CubicBezier3<T>

Converts to this type from the input type.

impl<T> From<Vec4<Vec3<T>>> for CubicBezier3<T>

fn from(v: Vec4<Vec3<T>>) -> CubicBezier3<T>

Converts to this type from the input type.

impl<T> Hash for CubicBezier3<T>

where T: Hash,

fn hash<__H>(&self, state: &mut __H)

where __H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T> Mul<CubicBezier3<T>> for Mat4<T>

where T: Real + MulAdd<Output = T>,

type Output = CubicBezier3<T>

The resulting type after applying the * operator.

fn mul(self, rhs: CubicBezier3<T>) -> CubicBezier3<T>

Performs the * operation.

impl<T> PartialEq for CubicBezier3<T>

where T: PartialEq,

fn eq(&self, other: &CubicBezier3<T>) -> 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<T> Serialize for CubicBezier3<T>

where T: Serialize,

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<T> Copy for CubicBezier3<T>

where T: Copy,

impl<T> Eq for CubicBezier3<T>

where T: Eq,

impl<T> StructuralPartialEq for CubicBezier3<T>