Struct lyon_geom::QuadraticBezierSegment
source · pub struct QuadraticBezierSegment<S> {
pub from: Point<S>,
pub ctrl: Point<S>,
pub to: Point<S>,
}
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: Point<S>
§ctrl: Point<S>
§to: Point<S>
Implementations§
source§impl<S: Scalar> QuadraticBezierSegment<S>
impl<S: Scalar> QuadraticBezierSegment<S>
pub fn cast<NewS: NumCast>(self) -> QuadraticBezierSegment<NewS>
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) -> Vector<S>
pub fn derivative(&self, t: S) -> Vector<S>
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 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>) -> Self
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.
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: Transformation<S>>(&self, transform: &T) -> Self
pub fn transformed<T: Transformation<S>>(&self, transform: &T) -> Self
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.
This implements the algorithm described by Raph Levien at https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html
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
.
This implements the algorithm described by Raph Levien at https://raphlinus.github.io/graphics/curves/2019/12/23/flatten-quadbez.html
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>
pub fn fast_bounding_box(&self) -> Box2D<S>
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>
pub fn bounding_box(&self) -> Box2D<S>
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<Point<S>, 2>
pub fn line_intersections(&self, line: &Line<S>) -> ArrayVec<Point<S>, 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) -> Point<S>
pub fn to(&self) -> Point<S>
sourcepub fn line_segment_intersections(
&self,
segment: &LineSegment<S>,
) -> ArrayVec<Point<S>, 2>
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.
sourcepub fn closest_point(&self, pos: Point<S>) -> S
pub fn closest_point(&self, pos: Point<S>) -> S
Analytic solution to finding the closest point on the curve to pos
.
sourcepub fn distance_to_point(&self, pos: Point<S>) -> S
pub fn distance_to_point(&self, pos: Point<S>) -> S
Returns the shortest distance between this segment and a point.
sourcepub fn square_distance_to_point(&self, pos: Point<S>) -> S
pub fn square_distance_to_point(&self, pos: Point<S>) -> 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: Point<S>) -> Self
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>
Trait Implementations§
source§impl<S: Clone> Clone for QuadraticBezierSegment<S>
impl<S: Clone> Clone for QuadraticBezierSegment<S>
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> Debug for QuadraticBezierSegment<S>
impl<S: Debug> Debug for QuadraticBezierSegment<S>
source§impl<S: PartialEq> PartialEq for QuadraticBezierSegment<S>
impl<S: PartialEq> PartialEq for QuadraticBezierSegment<S>
source§impl<S: Scalar> Segment for QuadraticBezierSegment<S>
impl<S: Scalar> Segment for QuadraticBezierSegment<S>
type Scalar = S
source§fn derivative(&self, t: S) -> Vector<S>
fn derivative(&self, t: S) -> Vector<S>
source§fn before_split(&self, t: S) -> Self
fn before_split(&self, t: S) -> Self
source§fn after_split(&self, t: S) -> Self
fn after_split(&self, t: S) -> Self
source§fn split_range(&self, t_range: Range<S>) -> Self
fn split_range(&self, t_range: Range<S>) -> Self
source§fn approximate_length(&self, tolerance: S) -> S
fn approximate_length(&self, tolerance: S) -> S
source§fn for_each_flattened_with_t(
&self,
tolerance: Self::Scalar,
callback: &mut dyn FnMut(&LineSegment<S>, Range<S>),
)
fn for_each_flattened_with_t( &self, tolerance: Self::Scalar, callback: &mut dyn FnMut(&LineSegment<S>, Range<S>), )
impl<S: Copy> Copy for QuadraticBezierSegment<S>
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,
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> CloneToUninit for Twhere
T: Clone,
impl<T> CloneToUninit for Twhere
T: Clone,
source§unsafe fn clone_to_uninit(&self, dst: *mut T)
unsafe fn clone_to_uninit(&self, dst: *mut T)
clone_to_uninit
)