Struct CubicBez

pub struct CubicBez {
    pub p0: Point,
    pub p1: Point,
    pub p2: Point,
    pub p3: Point,
}

A single cubic Bézier segment.

Fields

p0: Point

p1: Point

p2: Point

p3: Point

Implementations

impl CubicBez

pub fn new<P: Into<Point>>(p0: P, p1: P, p2: P, p3: P) -> CubicBez

Create a new cubic Bézier segment.

pub fn to_quads( &self, accuracy: f64, ) -> impl Iterator<Item = (f64, f64, QuadBez)>

Convert to quadratic Béziers.

The iterator returns the start and end parameter in the cubic of each quadratic segment, along with the quadratic.

Note that the resulting quadratic Béziers are not in general G1 continuous; they are optimized for minimizing distance error.

This iterator will always produce at least one QuadBez.

pub fn approx_spline(&self, accuracy: f64) -> Option<QuadSpline>

Return a QuadSpline approximating this cubic Bézier.

Returns None if no suitable approximation is found within the given tolerance.

pub fn is_finite(&self) -> bool

Is this cubic Bezier curve finite?

pub fn is_nan(&self) -> bool

Is this cubic Bezier curve NaN?

pub fn inflections(&self) -> ArrayVec<f64, 2>

Determine the inflection points.

Return value is t parameter for the inflection points of the curve segment. There are a maximum of two for a cubic Bézier.

See https://www.caffeineowl.com/graphics/2d/vectorial/cubic-inflexion.html for the theory.

pub fn tangents_to_point(&self, p: Point) -> ArrayVec<f64, 4>

Find points on the curve where the tangent line passes through the given point.

Result is array of t values such that the tangent line from the curve evaluated at that point goes through the argument point.

Trait Implementations

impl Clone for CubicBez

fn clone(&self) -> CubicBez

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for CubicBez

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

Formats the value using the given formatter.

impl From<CubicBez> for PathSeg

fn from(cubic_bez: CubicBez) -> PathSeg

Converts to this type from the input type.

impl Mul<CubicBez> for Affine

type Output = CubicBez

The resulting type after applying the * operator.

fn mul(self, c: CubicBez) -> CubicBez

Performs the * operation.

impl Mul<CubicBez> for TranslateScale

type Output = CubicBez

The resulting type after applying the * operator.

fn mul(self, other: CubicBez) -> CubicBez

Performs the * operation.

impl ParamCurve for CubicBez

fn subdivide(&self) -> (CubicBez, CubicBez)

Subdivide into halves, using de Casteljau.

fn eval(&self, t: f64) -> Point

Evaluate the curve at parameter t.

fn subsegment(&self, range: Range<f64>) -> CubicBez

Get a subsegment of the curve for the given parameter range.

fn start(&self) -> Point

The start point.

fn end(&self) -> Point

The end point.

impl ParamCurveArclen for CubicBez

fn arclen(&self, accuracy: f64) -> f64

Arclength of a cubic Bézier segment.

This is an adaptive subdivision approach using Legendre-Gauss quadrature in the base case, and an error estimate to decide when to subdivide.

fn inv_arclen(&self, arclen: f64, accuracy: f64) -> f64

Solve for the parameter that has the given arc length from the start.

impl ParamCurveArea for CubicBez

fn signed_area(&self) -> f64

Compute the signed area under the curve.

impl ParamCurveCurvature for CubicBez

fn curvature(&self, t: f64) -> f64

Compute the signed curvature at parameter t.

impl ParamCurveDeriv for CubicBez

type DerivResult = QuadBez

The parametric curve obtained by taking the derivative of this one.

fn deriv(&self) -> QuadBez

The derivative of the curve.

fn gauss_arclen(&self, coeffs: &[(f64, f64)]) -> f64

Estimate arclength using Gaussian quadrature.

impl ParamCurveExtrema for CubicBez

fn extrema(&self) -> ArrayVec<f64, MAX_EXTREMA>

Compute the extrema of the curve.

fn extrema_ranges(&self) -> ArrayVec<Range<f64>, { _ }>

Return parameter ranges, each of which is monotonic within the range.

fn bounding_box(&self) -> Rect

The smallest rectangle that encloses the curve in the range (0..1).

impl ParamCurveNearest for CubicBez

fn nearest(&self, p: Point, accuracy: f64) -> Nearest

Find the nearest point, using subdivision.

impl PartialEq for CubicBez

fn eq(&self, other: &CubicBez) -> 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 Shape for CubicBez

type PathElementsIter<'iter> = CubicBezIter

The iterator returned by the path_elements method.

fn path_elements(&self, _tolerance: f64) -> CubicBezIter

Returns an iterator over this shape expressed as PathEls; that is, as Bézier path elements.

fn area(&self) -> f64

Signed area.

fn perimeter(&self, accuracy: f64) -> f64

Total length of perimeter.

fn winding(&self, _pt: Point) -> i32

The winding number of a point.

fn bounding_box(&self) -> Rect

The smallest rectangle that encloses the shape.

fn to_path(&self, tolerance: f64) -> BezPath

Convert to a Bézier path.

fn into_path(self, tolerance: f64) -> BezPath

where Self: Sized,

Convert into a Bézier path.

fn path_segments(&self, tolerance: f64) -> Segments<Self::PathElementsIter<'_>>

Returns an iterator over this shape expressed as Bézier path segments (PathSegs).

fn contains(&self, pt: Point) -> bool

Returns true if the Point is inside this shape.

fn as_line(&self) -> Option<Line>

If the shape is a line, make it available.

fn as_rect(&self) -> Option<Rect>

If the shape is a rectangle, make it available.

fn as_rounded_rect(&self) -> Option<RoundedRect>

If the shape is a rounded rectangle, make it available.

fn as_circle(&self) -> Option<Circle>

If the shape is a circle, make it available.

fn as_path_slice(&self) -> Option<&[PathEl]>

If the shape is stored as a slice of path elements, make that available.

impl Copy for CubicBez

impl StructuralPartialEq for CubicBez