Struct rasterize::Quad

pub struct Quad(pub [Point; 3]);

Quadratic bezier curve

Polynomial form: (1 - t) ^ 2 * p0 + 2 * (1 - t) * t * p1 + t ^ 2 * p2 Matrix from:

            ┌          ┐ ┌    ┐
┌         ┐ │  1  0  0 │ │ p0 │
│ 1 t t^2 │ │ -2  2  0 │ │ p1 │
└         ┘ │  1 -2  1 │ │ p2 │
            └          ┘ └    ┘

Tuple Fields

0: [Point; 3]

Implementations

impl Quad

pub fn new(
    p0: impl Into<Point>,
    p1: impl Into<Point>,
    p2: impl Into<Point>
) -> Self

Create new quadratic bezier curve

pub fn points(&self) -> [Point; 3]

Points defining quadratic bezier curve

pub fn ends(&self) -> (Line, Line)

Tangent lines at the ends of the quadratic bezier curve

pub fn smooth(&self) -> Point

Find smooth point used by SVG parser

Trait Implementations

impl Clone for Quad

fn clone(&self) -> Quad

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Curve for Quad

fn flatness(&self) -> Scalar

Flatness criteria for the cubic curve

It is equal to f = max d(t) where d(t) = |q(t) - l(t)|, l(t) = (1 - t) * p0 + t * p2 for q(t) bezier2 curve with p{0..2} control points, in other words maximum distance from parametric line to bezier2 curve for the same parameter t.

Line can be represented as bezier2 curve, if p1 = (p0 + p2) / 2.0. Grouping polynomial coefficients:

    q(t) = t^2 p2 + 2 (1 - t) t p1 + (1 - t)^2 p0
    l(t) = t^2 p2 + (1 - t) t (p0 + p2) + (1 - t)^2 p0
    d(t) = |q(t) - l(t)| = (1 - t) t |2 * p1 - p0 - p2|
    f    = 1 / 4 * | 2 p1 - p0 - p2 |
    f^2  = 1/16 |2 * p1 - p0 - p2|^2

fn split(&self) -> (Self, Self)

Optimized version of split_at(0.5)

fn transform(&self, tr: Transform) -> Self

Apply affine transformation to the curve

fn start(&self) -> Point

Point at which curve starts

fn end(&self) -> Point

Point at which curve ends

fn at(&self, t: Scalar) -> Point

Evaluate curve at parameter value t in (0.0..=1.0)

fn deriv(&self) -> Segment

Derivative with respect to t, deriv(t) = [curve'(t)_x, curve'(t)_y]

fn split_at(&self, t: Scalar) -> (Self, Self)

Split the curve at parameter value t

fn cut(&self, a: Scalar, b: Scalar) -> Self

Create sub-curve specified starting at parameter value a and ending at value b

fn bbox(&self, init: Option<BBox>) -> BBox

Extend provided init bounding box with the bounding box of the curve

fn offset(&self, dist: Scalar, out: &mut impl Extend<Segment>)

Offset the curve by distance dist, result is inserted into out container

fn reverse(&self) -> Self

Identical curve but directed from end to start, instead of start to end.

fn roots(&self) -> CurveRoots

Find roots of the equation curve(t)_y = 0. Values of the parameter at which curve crosses y axis.

fn extremities(&self) -> CurveExtremities

Find all extremities of the curve curve'(t)_x = 0 || curve'(t)_y = 0

fn length(&self, t0: Scalar, t1: Scalar) -> Scalar

Calculate length of the curve from t0 to t1

fn flatten(&self, tr: Transform, flatness: Scalar) -> CurveFlattenIter

Convert curve to an iterator over line segments with desired flatness

fn param_at_length(&self, l: Scalar, error: Option<Scalar>) -> Scalar

Find value of parameter t given desired l length of the segment

impl Debug for Quad

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

Formats the value using the given formatter.

impl Display for Quad

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

Formats the value using the given formatter.

impl From<Quad> for Cubic

fn from(quad: Quad) -> Self

Converts to this type from the input type.

impl From<Quad> for Segment

fn from(quad: Quad) -> Self

Converts to this type from the input type.

impl FromStr for Quad

type Err = SvgParserError

The associated error which can be returned from parsing.

fn from_str(text: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl PartialEq<Quad> for Quad

fn eq(&self, other: &Quad) -> bool

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

fn ne(&self, other: &Quad) -> bool

This method tests for !=.

impl Copy for Quad

impl StructuralPartialEq for Quad