Struct lyon_geom::QuadraticBezierSegment

pub struct QuadraticBezierSegment<S> {
    pub from: Point<S>,
    pub ctrl: Point<S>,
    pub to: Point<S>,
}

A 2d curve segment defined by three points: the beginning of the segment, a control point and the end of the segment.

The curve is defined by equation: ∀ t ∈ [0..1], P(t) = (1 - t)² * from + 2 * (1 - t) * t * ctrl + 2 * t² * to

Fields

from: Point<S>

ctrl: Point<S>

to: Point<S>

Implementations

impl<S: Scalar> QuadraticBezierSegment<S>

pub fn sample(&self, t: S) -> Point<S>

Sample the curve at t (expecting t between 0 and 1).

pub fn x(&self, t: S) -> S

Sample the x coordinate of the curve at t (expecting t between 0 and 1).

pub fn y(&self, t: S) -> S

Sample the y coordinate of the curve at t (expecting t between 0 and 1).

pub fn derivative(&self, t: S) -> Vector<S>

Sample the curve’s derivative at t (expecting t between 0 and 1).

pub fn dx(&self, t: S) -> S

Sample the x coordinate of the curve’s derivative at t (expecting t between 0 and 1).

pub fn dy(&self, t: S) -> S

Sample the y coordinate of the curve’s derivative at t (expecting t between 0 and 1).

pub fn flip(&self) -> Self

Swap the beginning and the end of the segment.

pub fn y_maximum_t(&self) -> S

Find the advancement of the y-most position in the curve.

This returns the advancement along the curve, not the actual y position.

pub fn y_minimum_t(&self) -> S

Find the advancement of the y-least position in the curve.

This returns the advancement along the curve, not the actual y position.

pub fn local_y_extremum_t(&self) -> Option<S>

Return the y inflection point or None if this curve is y-monotonic.

pub fn x_maximum_t(&self) -> S

Find the advancement of the x-most position in the curve.

This returns the advancement along the curve, not the actual x position.

pub fn x_minimum_t(&self) -> S

Find the advancement of the x-least position in the curve.

This returns the advancement along the curve, not the actual x position.

pub fn local_x_extremum_t(&self) -> Option<S>

Return the x inflection point or None if this curve is x-monotonic.

pub fn split_range(&self, t_range: Range<S>) -> Self

Return the sub-curve inside a given range of t.

This is equivalent splitting at the range’s end points.

pub fn split(
    &self,
    t: S
) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)

Split this curve into two sub-curves.

pub fn before_split(&self, t: S) -> QuadraticBezierSegment<S>

Return the curve before the split point.

pub fn after_split(&self, t: S) -> QuadraticBezierSegment<S>

Return the curve after the split point.

pub fn to_cubic(&self) -> CubicBezierSegment<S>

Elevate this curve to a third order bézier.

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

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

pub fn fat_line(&self) -> (LineEquation<S>, LineEquation<S>)

Computes a “fat line” of this segment.

A fat line is two conservative lines between which the segment is fully contained.

pub fn transformed<T: Transformation<S>>(&self, transform: &T) -> Self

Applies the transform to this curve and returns the results.

pub fn flattening_step(&self, tolerance: S) -> S

Find the interval of the beginning of the curve that can be approximated with a line segment.

pub fn for_each_flattened<F>(&self, tolerance: S, callback: &mut F) where
    F: FnMut(Point<S>), 

Compute a flattened approximation of the curve, invoking a callback at each step.

The callback takes the point on the curve at each step.

This implements the algorithm described by Raph Levien at https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html

pub fn for_each_flattened_t<F>(&self, tolerance: S, callback: &mut F) where
    F: FnMut(S), 

Compute a flattened approximation of the curve, invoking a callback at each step.

The callback takes the curve parameter at each step.

This implements the algorithm described by Raph Levien at https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html

pub fn for_each_flattened_with_t<F>(&self, tolerance: S, callback: &mut F) where
    F: FnMut(Point<S>, S), 

Compute a flattened approximation of the curve, invoking a callback at each step.

The callback takes the point and corresponding curve parameter at each step.

This implements the algorithm described by Raph Levien at https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html

pub fn flattened(&self, tolerance: S) -> Flattened<S>

Returns the flattened representation of the curve as an iterator, starting after the current point.

pub fn flattened_t(&self, tolerance: S) -> FlattenedT<S>

Returns the flattened representation of the curve as an iterator, starting after the current point.

pub fn for_each_monotonic_t<F>(&self, cb: F) where
    F: FnMut(S), 

Invokes a callback between each monotonic part of the segment.

pub fn for_each_monotonic_range<F>(&self, cb: F) where
    F: FnMut(Range<S>), 

Invokes a callback for each monotonic part of the segment..

pub fn for_each_monotonic<F>(&self, cb: &mut F) where
    F: FnMut(&Monotonic<QuadraticBezierSegment<S>>), 

pub fn approximate_length(&self, tolerance: S) -> S

Compute the length of the segment using a flattened approximation.

pub fn bounding_triangle(&self) -> Triangle<S>

Returns a triangle containing this curve segment.

pub fn fast_bounding_box(&self) -> Box2D<S>

Returns a conservative rectangle that contains the curve.

pub fn fast_bounding_rect(&self) -> Rect<S>

Returns a conservative rectangle that contains the curve.

pub fn fast_bounding_range_x(&self) -> (S, S)

Returns a conservative range of x that contains this curve.

pub fn fast_bounding_range_y(&self) -> (S, S)

Returns a conservative range of y that contains this curve.

pub fn bounding_box(&self) -> Box2D<S>

Returns the smallest rectangle the curve is contained in

pub fn bounding_rect(&self) -> Rect<S>

Returns the smallest rectangle the curve is contained in

pub fn bounding_range_x(&self) -> (S, S)

Returns the smallest range of x that contains this curve.

pub fn bounding_range_y(&self) -> (S, S)

Returns the smallest range of y that contains this curve.

pub fn assume_monotonic(&self) -> MonotonicQuadraticBezierSegment<S>

Cast this curve into a monotonic curve without checking that the monotonicity assumption is correct.

pub fn is_x_monotonic(&self) -> bool

Returns whether this segment is monotonic on the x axis.

pub fn is_y_monotonic(&self) -> bool

Returns whether this segment is monotonic on the y axis.

pub fn is_monotonic(&self) -> bool

Returns whether this segment is fully monotonic.

pub fn line_intersections_t(&self, line: &Line<S>) -> ArrayVec<[S; 2]>

Computes the intersections (if any) between this segment a line.

The result is provided in the form of the t parameters of each point along curve. To get the intersection points, sample the curve at the corresponding values.

pub fn line_intersections(&self, line: &Line<S>) -> ArrayVec<[Point<S>; 2]>

Computes the intersection points (if any) between this segment a line.

pub fn line_segment_intersections_t(
    &self,
    segment: &LineSegment<S>
) -> ArrayVec<[(S, S); 2]>

Computes the intersections (if any) between this segment a line segment.

The result is provided in the form of the t parameters of each point along curve and segment. To get the intersection points, sample the segments at the corresponding values.

pub fn from(&self) -> Point<S>

pub fn to(&self) -> Point<S>

pub fn line_segment_intersections(
    &self,
    segment: &LineSegment<S>
) -> ArrayVec<[Point<S>; 2]>

Computes the intersection points (if any) between this segment a line segment.

Trait Implementations

impl<S: Clone> Clone for QuadraticBezierSegment<S>

fn clone(&self) -> QuadraticBezierSegment<S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<S: Debug> Debug for QuadraticBezierSegment<S>

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

Formats the value using the given formatter.

impl<S> From<QuadraticBezierSegment<S>> for BezierSegment<S>

fn from(s: QuadraticBezierSegment<S>) -> Self

Converts to this type from the input type.

impl<S: PartialEq> PartialEq<QuadraticBezierSegment<S>> for QuadraticBezierSegment<S>

fn eq(&self, other: &QuadraticBezierSegment<S>) -> bool

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

fn ne(&self, other: &QuadraticBezierSegment<S>) -> bool

This method tests for !=.

impl<S: Scalar> Segment for QuadraticBezierSegment<S>

type Scalar = S

fn from(&self) -> Point<S>

Start of the curve.

fn to(&self) -> Point<S>

End of the curve.

fn sample(&self, t: S) -> Point<S>

Sample the curve at t (expecting t between 0 and 1).

fn x(&self, t: S) -> S

Sample x at t (expecting t between 0 and 1).

fn y(&self, t: S) -> S

Sample y at t (expecting t between 0 and 1).

fn derivative(&self, t: S) -> Vector<S>

Sample the derivative at t (expecting t between 0 and 1).

fn dx(&self, t: S) -> S

Sample x derivative at t (expecting t between 0 and 1).

fn dy(&self, t: S) -> S

Sample y derivative at t (expecting t between 0 and 1).

fn split(&self, t: S) -> (Self, Self)

Split this curve into two sub-curves.

fn before_split(&self, t: S) -> Self

Return the curve before the split point.

fn after_split(&self, t: S) -> Self

Return the curve after the split point.

fn split_range(&self, t_range: Range<S>) -> Self

Return the curve inside a given range of t.

fn flip(&self) -> Self

Swap the direction of the segment.

fn approximate_length(&self, tolerance: S) -> S

Compute the length of the segment using a flattened approximation.

impl<S: Copy> Copy for QuadraticBezierSegment<S>

impl<S> StructuralPartialEq for QuadraticBezierSegment<S>