Struct QuadraticBezierSegment

pub struct QuadraticBezierSegment<S> {
    pub from: Point2D<S, UnknownUnit>,
    pub ctrl: Point2D<S, UnknownUnit>,
    pub to: Point2D<S, UnknownUnit>,
}

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 + t² * to

Fields

from: Point2D<S, UnknownUnit>

ctrl: Point2D<S, UnknownUnit>

to: Point2D<S, UnknownUnit>

Implementations

impl<S> QuadraticBezierSegment<S>

where S: Scalar,

pub fn cast<NewS>(self) -> QuadraticBezierSegment<NewS>

where NewS: NumCast,

pub fn sample(&self, t: S) -> Point2D<S, UnknownUnit>

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) -> Vector2D<S, UnknownUnit>

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) -> QuadraticBezierSegment<S>

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>) -> QuadraticBezierSegment<S>

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_a_point(&self, tolerance: S) -> bool

Returns whether the curve can be approximated with a single point, given a tolerance threshold.

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

Returns true if the curve can be approximated with a single line segment given a tolerance threshold.

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>(&self, transform: &T) -> QuadraticBezierSegment<S>

where T: Transformation<S>,

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(&LineSegment<S>),

Approximates the curve with sequence of line segments.

The tolerance parameter defines the maximum distance between the curve and its approximation.

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

where F: FnMut(&LineSegment<S>, Range<S>),

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

The tolerance parameter defines the maximum distance between the curve and its approximation.

The end of the t parameter range at the final segment is guaranteed to be equal to 1.0.

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_range<F>(&self, cb: &mut 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(&QuadraticBezierSegment<S>),

Invokes a callback for each monotonic part of the segment.

pub fn for_each_y_monotonic_range<F>(&self, cb: &mut F)

where F: FnMut(Range<S>),

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

pub fn for_each_y_monotonic<F>(&self, cb: &mut F)

where F: FnMut(&QuadraticBezierSegment<S>),

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

pub fn for_each_x_monotonic_range<F>(&self, cb: &mut F)

where F: FnMut(Range<S>),

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

pub fn for_each_x_monotonic<F>(&self, cb: &mut F)

where F: FnMut(&QuadraticBezierSegment<S>),

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

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

Returns a triangle containing this curve segment.

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

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, UnknownUnit>

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 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<Point2D<S, UnknownUnit>, 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 and 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) -> Point2D<S, UnknownUnit>

pub fn to(&self) -> Point2D<S, UnknownUnit>

pub fn line_segment_intersections( &self, segment: &LineSegment<S>, ) -> ArrayVec<Point2D<S, UnknownUnit>, 2>

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

pub fn closest_point(&self, pos: Point2D<S, UnknownUnit>) -> S

Analytic solution to finding the closest point on the curve to pos.

pub fn distance_to_point(&self, pos: Point2D<S, UnknownUnit>) -> S

Returns the shortest distance between this segment and a point.

pub fn square_distance_to_point(&self, pos: Point2D<S, UnknownUnit>) -> S

Returns the shortest squared distance between this segment and a point.

May be useful to avoid the cost of a square root when comparing against a distance that can be squared instead.

pub fn drag( &self, t: S, new_position: Point2D<S, UnknownUnit>, ) -> QuadraticBezierSegment<S>

pub fn length(&self) -> S

Computes the length of this segment.

Implements Raph Levien’s analytical approach described in https://raphlinus.github.io/curves/2018/12/28/bezier-arclength.html

pub fn to_f32(&self) -> QuadraticBezierSegment<f32>

pub fn to_f64(&self) -> QuadraticBezierSegment<f64>

pub fn polynomial_form(&self) -> QuadraticBezierPolynomial<S>

Trait Implementations

impl<S> Clone for QuadraticBezierSegment<S>

where S: Clone,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<S> Debug for QuadraticBezierSegment<S>

where S: Debug,

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

Formats the value using the given formatter.

impl<S> PartialEq for QuadraticBezierSegment<S>

where S: PartialEq,

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

where S: Scalar,

type Scalar = S

fn from(&self) -> Point2D<S, UnknownUnit>

Start of the curve.

fn to(&self) -> Point2D<S, UnknownUnit>

End of the curve.

fn sample(&self, t: S) -> Point2D<S, UnknownUnit>

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) -> Vector2D<S, UnknownUnit>

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) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)

Split this curve into two sub-curves.

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

Return the curve before the split point.

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

Return the curve after the split point.

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

Return the curve inside a given range of t.

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

Swap the direction of the segment.

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

Compute the length of the segment using a flattened approximation.

fn for_each_flattened_with_t( &self, tolerance: <QuadraticBezierSegment<S> as Segment>::Scalar, callback: &mut dyn FnMut(&LineSegment<S>, Range<S>), )

Approximates the curve with sequence of line segments.

impl<S> Copy for QuadraticBezierSegment<S>

where S: Copy,

impl<S> StructuralPartialEq for QuadraticBezierSegment<S>