Struct stroke::cubic_bezier::CubicBezier

pub struct CubicBezier<P> { /* private fields */ }

A 2d cubic Bezier curve defined by four points: the starting point, two successive control points and the ending point. The curve is defined by equation: ∀ t ∈ [0..1], P(t) = (1 - t)³ * start + 3 * (1 - t)² * t * ctrl1 + 3 * t² * (1 - t) * ctrl2 + t³ * end

Implementations

impl<P> CubicBezier<P>where P: Point,

pub fn new(start: P, ctrl1: P, ctrl2: P, end: P) -> Self

pub fn eval(&self, t: P::Scalar) -> P

Evaluate a CubicBezier curve at t by direct evaluation of the polynomial (not numerically stable)

pub fn eval_casteljau(&self, t: P::Scalar) -> P

Evaluate a CubicBezier curve at t using the numerically stable De Casteljau algorithm

pub fn control_points(&self) -> [P; 4]

pub fn axis(&self, t: P::Scalar, axis: usize) -> P::Scalar

Returns the x coordinate of the curve evaluated at t Convenience shortcut for bezier.eval(t).x()

pub fn arclen(&self, nsteps: usize) -> P::Scalar

Approximates the arc length of the curve by flattening it with straight line segments. Remember arclen also works by linear approximation, not the integral, so we have to accept error! This approximation is unfeasable if desired accuracy is greater than 2 decimal places

pub fn split(&self, t: P::Scalar) -> (Self, Self)

pub fn derivative(&self) -> QuadraticBezier<P>

Return the derivative curve. The derivative is also a bezier curve but of degree n-1 (cubic->quadratic) Since it returns the derivative function, eval() needs to be called separately

pub fn dd(&self, t: P::Scalar, axis: usize) -> P::Scalar

Direct Derivative - Sample the axis coordinate at ‘axis’ of the curve’s derivative at t without creating a new curve. This is a convenience function for .derivative().eval(t).axis(n)
Parameters: t: the sampling parameter on the curve interval [0..1] axis: the index of the coordinate axis [0..N] Returns: Scalar value of the points own type type F
May be deprecated in the future.
This function can cause out of bounds panic when axis is larger than dimension of P

pub fn distance_to_point(&self, point: P) -> P::Scalar

Calculates the minimum distance between given ‘point’ and the curve. Uses two passes with the same amount of steps in t:

1. coarse search over the whole curve
2. fine search around the minimum yielded by the coarse search

pub fn baseline(&self) -> LineSegment<P>

pub fn is_linear(&self, tolerance: P::Scalar) -> bool

pub fn is_a_point(&self, tolerance: P::Scalar) -> bool

pub fn bounding_box(&self) -> [(P::Scalar, P::Scalar); P::DIM]

Return the bounding box of the curve as an array of (min, max) tuples for each dimension (its index)

Trait Implementations

impl<P: Clone> Clone for CubicBezier<P>

fn clone(&self) -> CubicBezier<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: Debug> Debug for CubicBezier<P>

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

Formats the value using the given formatter.

impl<P> From<CubicBezier<P>> for BezierSegment<P>where P: Point,

fn from(s: CubicBezier<P>) -> Self

Converts to this type from the input type.

impl<P: PartialEq> PartialEq<CubicBezier<P>> for CubicBezier<P>

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

This method tests for self and other values to be equal, and is used by ==.

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.

impl<P: Copy> Copy for CubicBezier<P>

impl<P> StructuralPartialEq for CubicBezier<P>