pub struct QuadraticBezierSegment<S> {
pub from: Point2D<S, UnknownUnit>,
pub ctrl: Point2D<S, UnknownUnit>,
pub to: Point2D<S, UnknownUnit>,
}
Expand description
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§
Source§impl<S> QuadraticBezierSegment<S>where
S: Scalar,
impl<S> QuadraticBezierSegment<S>where
S: Scalar,
pub fn cast<NewS>(self) -> QuadraticBezierSegment<NewS>where
NewS: NumCast,
Sourcepub fn sample(&self, t: S) -> Point2D<S, UnknownUnit>
pub fn sample(&self, t: S) -> Point2D<S, UnknownUnit>
Sample the curve at t (expecting t between 0 and 1).
Sourcepub fn x(&self, t: S) -> S
pub fn x(&self, t: S) -> S
Sample the x coordinate of the curve at t (expecting t between 0 and 1).
Sourcepub fn y(&self, t: S) -> S
pub fn y(&self, t: S) -> S
Sample the y coordinate of the curve at t (expecting t between 0 and 1).
Sourcepub fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>
pub fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>
Sample the curve’s derivative at t (expecting t between 0 and 1).
Sourcepub fn dx(&self, t: S) -> S
pub fn dx(&self, t: S) -> S
Sample the x coordinate of the curve’s derivative at t (expecting t between 0 and 1).
Sourcepub fn dy(&self, t: S) -> S
pub fn dy(&self, t: S) -> S
Sample the y coordinate of the curve’s derivative at t (expecting t between 0 and 1).
Sourcepub fn flip(&self) -> QuadraticBezierSegment<S>
pub fn flip(&self) -> QuadraticBezierSegment<S>
Swap the beginning and the end of the segment.
Sourcepub fn y_maximum_t(&self) -> S
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.
Sourcepub fn y_minimum_t(&self) -> S
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.
Sourcepub fn local_y_extremum_t(&self) -> Option<S>
pub fn local_y_extremum_t(&self) -> Option<S>
Return the y inflection point or None if this curve is y-monotonic.
Sourcepub fn x_maximum_t(&self) -> S
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.
Sourcepub fn x_minimum_t(&self) -> S
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.
Sourcepub fn local_x_extremum_t(&self) -> Option<S>
pub fn local_x_extremum_t(&self) -> Option<S>
Return the x inflection point or None if this curve is x-monotonic.
Sourcepub fn split_range(&self, t_range: Range<S>) -> QuadraticBezierSegment<S>
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.
Sourcepub fn split(
&self,
t: S,
) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)
pub fn split( &self, t: S, ) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)
Split this curve into two sub-curves.
Sourcepub fn before_split(&self, t: S) -> QuadraticBezierSegment<S>
pub fn before_split(&self, t: S) -> QuadraticBezierSegment<S>
Return the curve before the split point.
Sourcepub fn after_split(&self, t: S) -> QuadraticBezierSegment<S>
pub fn after_split(&self, t: S) -> QuadraticBezierSegment<S>
Return the curve after the split point.
Sourcepub fn to_cubic(&self) -> CubicBezierSegment<S>
pub fn to_cubic(&self) -> CubicBezierSegment<S>
Elevate this curve to a third order bézier.
pub fn baseline(&self) -> LineSegment<S>
Sourcepub fn is_a_point(&self, tolerance: S) -> bool
pub fn is_a_point(&self, tolerance: S) -> bool
Returns whether the curve can be approximated with a single point, given a tolerance threshold.
Sourcepub fn is_linear(&self, tolerance: S) -> bool
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.
Sourcepub fn fat_line(&self) -> (LineEquation<S>, LineEquation<S>)
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.
Sourcepub fn transformed<T>(&self, transform: &T) -> QuadraticBezierSegment<S>where
T: Transformation<S>,
pub fn transformed<T>(&self, transform: &T) -> QuadraticBezierSegment<S>where
T: Transformation<S>,
Applies the transform to this curve and returns the results.
Sourcepub fn flattening_step(&self, tolerance: S) -> S
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.
Sourcepub fn for_each_flattened<F>(&self, tolerance: S, callback: &mut F)where
F: FnMut(&LineSegment<S>),
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.
Sourcepub fn for_each_flattened_with_t<F>(&self, tolerance: S, callback: &mut F)
pub fn for_each_flattened_with_t<F>(&self, tolerance: S, callback: &mut F)
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
.
Sourcepub fn flattened(&self, tolerance: S) -> Flattened<S> ⓘ
pub fn flattened(&self, tolerance: S) -> Flattened<S> ⓘ
Returns the flattened representation of the curve as an iterator, starting after the current point.
Sourcepub fn flattened_t(&self, tolerance: S) -> FlattenedT<S> ⓘ
pub fn flattened_t(&self, tolerance: S) -> FlattenedT<S> ⓘ
Returns the flattened representation of the curve as an iterator, starting after the current point.
Sourcepub fn for_each_monotonic_range<F>(&self, cb: &mut F)
pub fn for_each_monotonic_range<F>(&self, cb: &mut F)
Invokes a callback for each monotonic part of the segment.
Sourcepub fn for_each_monotonic<F>(&self, cb: &mut F)where
F: FnMut(&QuadraticBezierSegment<S>),
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.
Sourcepub fn for_each_y_monotonic_range<F>(&self, cb: &mut F)
pub fn for_each_y_monotonic_range<F>(&self, cb: &mut F)
Invokes a callback for each y-monotonic part of the segment.
Sourcepub fn for_each_y_monotonic<F>(&self, cb: &mut F)where
F: FnMut(&QuadraticBezierSegment<S>),
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.
Sourcepub fn for_each_x_monotonic_range<F>(&self, cb: &mut F)
pub fn for_each_x_monotonic_range<F>(&self, cb: &mut F)
Invokes a callback for each x-monotonic part of the segment.
Sourcepub fn for_each_x_monotonic<F>(&self, cb: &mut F)where
F: FnMut(&QuadraticBezierSegment<S>),
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.
Sourcepub fn bounding_triangle(&self) -> Triangle<S>
pub fn bounding_triangle(&self) -> Triangle<S>
Returns a triangle containing this curve segment.
Sourcepub fn fast_bounding_box(&self) -> Box2D<S, UnknownUnit>
pub fn fast_bounding_box(&self) -> Box2D<S, UnknownUnit>
Returns a conservative rectangle that contains the curve.
Sourcepub fn fast_bounding_range_x(&self) -> (S, S)
pub fn fast_bounding_range_x(&self) -> (S, S)
Returns a conservative range of x that contains this curve.
Sourcepub fn fast_bounding_range_y(&self) -> (S, S)
pub fn fast_bounding_range_y(&self) -> (S, S)
Returns a conservative range of y that contains this curve.
Sourcepub fn bounding_box(&self) -> Box2D<S, UnknownUnit>
pub fn bounding_box(&self) -> Box2D<S, UnknownUnit>
Returns the smallest rectangle the curve is contained in
Sourcepub fn bounding_range_x(&self) -> (S, S)
pub fn bounding_range_x(&self) -> (S, S)
Returns the smallest range of x that contains this curve.
Sourcepub fn bounding_range_y(&self) -> (S, S)
pub fn bounding_range_y(&self) -> (S, S)
Returns the smallest range of y that contains this curve.
Sourcepub fn is_x_monotonic(&self) -> bool
pub fn is_x_monotonic(&self) -> bool
Returns whether this segment is monotonic on the x axis.
Sourcepub fn is_y_monotonic(&self) -> bool
pub fn is_y_monotonic(&self) -> bool
Returns whether this segment is monotonic on the y axis.
Sourcepub fn is_monotonic(&self) -> bool
pub fn is_monotonic(&self) -> bool
Returns whether this segment is fully monotonic.
Sourcepub fn line_intersections_t(&self, line: &Line<S>) -> ArrayVec<S, 2>
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.
Sourcepub fn line_intersections(
&self,
line: &Line<S>,
) -> ArrayVec<Point2D<S, UnknownUnit>, 2>
pub fn line_intersections( &self, line: &Line<S>, ) -> ArrayVec<Point2D<S, UnknownUnit>, 2>
Computes the intersection points (if any) between this segment a line.
Sourcepub fn line_segment_intersections_t(
&self,
segment: &LineSegment<S>,
) -> ArrayVec<(S, S), 2>
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>
Sourcepub fn line_segment_intersections(
&self,
segment: &LineSegment<S>,
) -> ArrayVec<Point2D<S, UnknownUnit>, 2>
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.
Sourcepub fn closest_point(&self, pos: Point2D<S, UnknownUnit>) -> S
pub fn closest_point(&self, pos: Point2D<S, UnknownUnit>) -> S
Analytic solution to finding the closest point on the curve to pos
.
Sourcepub fn distance_to_point(&self, pos: Point2D<S, UnknownUnit>) -> S
pub fn distance_to_point(&self, pos: Point2D<S, UnknownUnit>) -> S
Returns the shortest distance between this segment and a point.
Sourcepub fn square_distance_to_point(&self, pos: Point2D<S, UnknownUnit>) -> S
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>
Sourcepub fn length(&self) -> 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§
Source§impl<S> Clone for QuadraticBezierSegment<S>where
S: Clone,
impl<S> Clone for QuadraticBezierSegment<S>where
S: Clone,
Source§fn clone(&self) -> QuadraticBezierSegment<S>
fn clone(&self) -> QuadraticBezierSegment<S>
1.0.0 · Source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moreSource§impl<S> Debug for QuadraticBezierSegment<S>where
S: Debug,
impl<S> Debug for QuadraticBezierSegment<S>where
S: Debug,
Source§impl<S> PartialEq for QuadraticBezierSegment<S>where
S: PartialEq,
impl<S> PartialEq for QuadraticBezierSegment<S>where
S: PartialEq,
Source§impl<S> Segment for QuadraticBezierSegment<S>where
S: Scalar,
impl<S> Segment for QuadraticBezierSegment<S>where
S: Scalar,
type Scalar = S
Source§fn from(&self) -> Point2D<S, UnknownUnit>
fn from(&self) -> Point2D<S, UnknownUnit>
Source§fn to(&self) -> Point2D<S, UnknownUnit>
fn to(&self) -> Point2D<S, UnknownUnit>
Source§fn sample(&self, t: S) -> Point2D<S, UnknownUnit>
fn sample(&self, t: S) -> Point2D<S, UnknownUnit>
Source§fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>
fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>
Source§fn split(&self, t: S) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)
fn split(&self, t: S) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)
Source§fn before_split(&self, t: S) -> QuadraticBezierSegment<S>
fn before_split(&self, t: S) -> QuadraticBezierSegment<S>
Source§fn after_split(&self, t: S) -> QuadraticBezierSegment<S>
fn after_split(&self, t: S) -> QuadraticBezierSegment<S>
Source§fn split_range(&self, t_range: Range<S>) -> QuadraticBezierSegment<S>
fn split_range(&self, t_range: Range<S>) -> QuadraticBezierSegment<S>
Source§fn flip(&self) -> QuadraticBezierSegment<S>
fn flip(&self) -> QuadraticBezierSegment<S>
Source§fn approximate_length(&self, tolerance: S) -> S
fn approximate_length(&self, tolerance: S) -> S
Source§fn for_each_flattened_with_t(
&self,
tolerance: <QuadraticBezierSegment<S> as Segment>::Scalar,
callback: &mut dyn FnMut(&LineSegment<S>, Range<S>),
)
fn for_each_flattened_with_t( &self, tolerance: <QuadraticBezierSegment<S> as Segment>::Scalar, callback: &mut dyn FnMut(&LineSegment<S>, Range<S>), )
impl<S> Copy for QuadraticBezierSegment<S>where
S: Copy,
impl<S> StructuralPartialEq for QuadraticBezierSegment<S>
Auto Trait Implementations§
impl<S> Freeze for QuadraticBezierSegment<S>where
S: Freeze,
impl<S> RefUnwindSafe for QuadraticBezierSegment<S>where
S: RefUnwindSafe,
impl<S> Send for QuadraticBezierSegment<S>where
S: Send,
impl<S> Sync for QuadraticBezierSegment<S>where
S: Sync,
impl<S> Unpin for QuadraticBezierSegment<S>where
S: Unpin,
impl<S> UnwindSafe for QuadraticBezierSegment<S>where
S: UnwindSafe,
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