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CubicBezierSegment

cosmic::iced::daemon::program::graphics::geometry::path::lyon_path::geom

Struct CubicBezierSegment 

pub struct CubicBezierSegment<S> {
    pub from: Point2D<S, UnknownUnit>,
    pub ctrl1: Point2D<S, UnknownUnit>,
    pub ctrl2: Point2D<S, UnknownUnit>,
    pub to: Point2D<S, UnknownUnit>,
}
Available on crate feature geometry only.
Expand description

A 2d curve segment defined by four points: the beginning of the segment, two control points and the end of the segment.

The curve is defined by equation:² ∀ t ∈ [0..1], P(t) = (1 - t)³ * from + 3 * (1 - t)² * t * ctrl1 + 3 * t² * (1 - t) * ctrl2 + t³ * to

Fields§

§from: Point2D<S, UnknownUnit>§ctrl1: Point2D<S, UnknownUnit>§ctrl2: Point2D<S, UnknownUnit>§to: Point2D<S, UnknownUnit>

Implementations§

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impl<S> CubicBezierSegment<S>
where S: Scalar,

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

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

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

pub fn solve_t_for_x(&self, x: S) -> ArrayVec<S, 3>

Available on crate feature canvas only.

Return the parameter values corresponding to a given x coordinate.

pub fn solve_t_for_y(&self, y: S) -> ArrayVec<S, 3>

Available on crate feature canvas only.

Return the parameter values corresponding to a given y coordinate.

pub fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

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

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

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

Available on crate feature canvas only.

Split this curve into two sub-curves.

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

Available on crate feature canvas only.

Return the curve before the split point.

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

Available on crate feature canvas only.

Return the curve after the split point.

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

Available on crate feature canvas only.

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

Available on crate feature canvas only.

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>)

Available on crate feature canvas only.

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) -> CubicBezierSegment<S>
where T: Transformation<S>,

Available on crate feature canvas only.

Applies the transform to this curve and returns the results.

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

Available on crate feature canvas only.

Swap the beginning and the end of the segment.

pub fn to_quadratic(&self) -> QuadraticBezierSegment<S>

Available on crate feature canvas only.

Approximate the curve with a single quadratic bézier segment.

This is terrible as a general approximation but works if the cubic curve does not have inflection points and is “flat” enough. Typically usable after subdividing the curve a few times.

pub fn to_quadratic_error(&self) -> S

Available on crate feature canvas only.

Evaluates an upper bound on the maximum distance between the curve and its quadratic approximation obtained using to_quadratic.

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

Available on crate feature canvas only.

Returns true if the curve can be safely approximated with a single quadratic bézier segment given the provided tolerance threshold.

Equivalent to comparing to_quadratic_error with the tolerance threshold, avoiding the cost of two square roots.

pub fn num_quadratics(&self, tolerance: S) -> u32

Available on crate feature canvas only.

Computes the number of quadratic bézier segments required to approximate this cubic curve given a tolerance threshold.

Derived by Raph Levien from section 10.6 of Sedeberg’s CAGD notes https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1000&context=facpub#section.10.6 and the error metric from the caffein owl blog post http://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html

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

Available on crate feature canvas only.

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>),

Available on crate feature canvas only.

Invokes a callback for each monotonic part of the segment.

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

Available on crate feature canvas only.

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>),

Available on crate feature canvas only.

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(&CubicBezierSegment<S>),

Available on crate feature canvas only.

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>),

Available on crate feature canvas only.

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(&CubicBezierSegment<S>),

Available on crate feature canvas only.

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

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

Available on crate feature canvas only.

Approximates the cubic bézier curve with sequence of quadratic ones, invoking a callback at each step.

pub fn for_each_quadratic_bezier_with_t<F>(&self, tolerance: S, cb: &mut F)
where F: FnMut(&QuadraticBezierSegment<S>, Range<S>),

Available on crate feature canvas only.

Approximates the cubic bézier curve with sequence of quadratic ones, invoking a callback at each step.

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

Available on crate feature canvas only.

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>),

Available on crate feature canvas only.

Approximates the curve with sequence of line segments.

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

Available on crate feature canvas only.

Compute the length of the segment using a flattened approximation.

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

Available on crate feature canvas only.

Invokes a callback at each inflection point if any.

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

Available on crate feature canvas only.

Return local x extrema or None if this curve is monotonic.

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

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

Available on crate feature canvas only.

Return local y extrema or None if this curve is monotonic.

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

pub fn y_maximum_t(&self) -> S

Available on crate feature canvas only.

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

Available on crate feature canvas only.

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 x_maximum_t(&self) -> S

Available on crate feature canvas only.

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

Available on crate feature canvas only.

Find the x-least position in the curve.

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

Available on crate feature canvas only.

Returns a conservative rectangle the curve is contained in.

This method is faster than bounding_box but more conservative.

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

Available on crate feature canvas only.

Returns a conservative range of x that contains this curve.

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

Available on crate feature canvas only.

Returns a conservative range of y that contains this curve.

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

Available on crate feature canvas only.

Returns a conservative rectangle that contains the curve.

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

Available on crate feature canvas only.

Returns the smallest range of x that contains this curve.

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

Available on crate feature canvas only.

Returns the smallest range of y that contains this curve.

pub fn is_x_monotonic(&self) -> bool

Available on crate feature canvas only.

Returns whether this segment is monotonic on the x axis.

pub fn is_y_monotonic(&self) -> bool

Available on crate feature canvas only.

Returns whether this segment is monotonic on the y axis.

pub fn is_monotonic(&self) -> bool

Available on crate feature canvas only.

Returns whether this segment is fully monotonic.

pub fn cubic_intersections_t( &self, curve: &CubicBezierSegment<S>, ) -> ArrayVec<(S, S), 9>

Available on crate feature canvas only.

Computes the intersections (if any) between this segment and another one.

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

Returns endpoint intersections where an endpoint intersects the interior of the other curve, but not endpoint/endpoint intersections.

Returns no intersections if either curve is a point.

pub fn cubic_intersections( &self, curve: &CubicBezierSegment<S>, ) -> ArrayVec<Point2D<S, UnknownUnit>, 9>

Available on crate feature canvas only.

Computes the intersection points (if any) between this segment and another one.

pub fn quadratic_intersections_t( &self, curve: &QuadraticBezierSegment<S>, ) -> ArrayVec<(S, S), 9>

Available on crate feature canvas only.

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

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

Returns endpoint intersections where an endpoint intersects the interior of the other curve, but not endpoint/endpoint intersections.

Returns no intersections if either curve is a point.

pub fn quadratic_intersections( &self, curve: &QuadraticBezierSegment<S>, ) -> ArrayVec<Point2D<S, UnknownUnit>, 9>

Available on crate feature canvas only.

Computes the intersection points (if any) between this segment and a quadratic bézier segment.

pub fn line_intersections_t(&self, line: &Line<S>) -> ArrayVec<S, 3>

Available on crate feature canvas only.

Computes the intersections (if any) between this segment and 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>, 3>

Available on crate feature canvas only.

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

pub fn line_segment_intersections_t( &self, segment: &LineSegment<S>, ) -> ArrayVec<(S, S), 3>

Available on crate feature canvas only.

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>

Available on crate feature canvas only.

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

Available on crate feature canvas only.

pub fn line_segment_intersections( &self, segment: &LineSegment<S>, ) -> ArrayVec<Point2D<S, UnknownUnit>, 3>

Available on crate feature canvas only.

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

Available on crate feature canvas only.

pub fn drag_with_weight( &self, t: S, new_position: Point2D<S, UnknownUnit>, weight: S, ) -> CubicBezierSegment<S>

Available on crate feature canvas only.

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

Available on crate feature canvas only.

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

Available on crate feature canvas only.

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

Available on crate feature canvas only.

Trait Implementations§

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impl<S> Clone for CubicBezierSegment<S>
where S: Clone,

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

Returns a duplicate of the value. Read more
1.0.0 · Source§

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

Performs copy-assignment from source. Read more
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impl<S> Debug for CubicBezierSegment<S>
where S: Debug,

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

Formats the value using the given formatter. Read more
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impl<S> PartialEq for CubicBezierSegment<S>
where S: PartialEq,

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

Tests for self and other values to be equal, and is used by ==.
1.0.0 · Source§

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<S> Segment for CubicBezierSegment<S>
where S: Scalar,

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type Scalar = S

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

Start of the curve.
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fn to(&self) -> Point2D<S, UnknownUnit>

End of the curve.
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fn sample(&self, t: S) -> Point2D<S, UnknownUnit>

Sample the curve at t (expecting t between 0 and 1).
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fn x(&self, t: S) -> S

Sample x at t (expecting t between 0 and 1).
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fn y(&self, t: S) -> S

Sample y at t (expecting t between 0 and 1).
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fn derivative(&self, t: S) -> Vector2D<S, UnknownUnit>

Sample the derivative at t (expecting t between 0 and 1).
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fn dx(&self, t: S) -> S

Sample x derivative at t (expecting t between 0 and 1).
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fn dy(&self, t: S) -> S

Sample y derivative at t (expecting t between 0 and 1).
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fn split(&self, t: S) -> (CubicBezierSegment<S>, CubicBezierSegment<S>)

Split this curve into two sub-curves.
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fn before_split(&self, t: S) -> CubicBezierSegment<S>

Return the curve before the split point.
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fn after_split(&self, t: S) -> CubicBezierSegment<S>

Return the curve after the split point.
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fn split_range(&self, t_range: Range<S>) -> CubicBezierSegment<S>

Return the curve inside a given range of t. Read more
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fn flip(&self) -> CubicBezierSegment<S>

Swap the direction of the segment.
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fn approximate_length(&self, tolerance: S) -> S

Compute the length of the segment using a flattened approximation.
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fn for_each_flattened_with_t( &self, tolerance: <CubicBezierSegment<S> as Segment>::Scalar, callback: &mut dyn FnMut(&LineSegment<S>, Range<S>), )

Approximates the curve with sequence of line segments. Read more
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impl<S> Copy for CubicBezierSegment<S>
where S: Copy,

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impl<S> StructuralPartialEq for CubicBezierSegment<S>

Auto Trait Implementations§

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impl<S> Freeze for CubicBezierSegment<S>
where S: Freeze,

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impl<S> RefUnwindSafe for CubicBezierSegment<S>
where S: RefUnwindSafe,

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impl<S> Send for CubicBezierSegment<S>
where S: Send,

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impl<S> Sync for CubicBezierSegment<S>
where S: Sync,

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impl<S> Unpin for CubicBezierSegment<S>
where S: Unpin,

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impl<S> UnsafeUnpin for CubicBezierSegment<S>
where S: UnsafeUnpin,

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impl<S> UnwindSafe for CubicBezierSegment<S>
where S: UnwindSafe,

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Convert the source color to the destination color using the bradford method by default.
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fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self> ⓘ
where S: Into<Dispatch>,

Attaches the provided Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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fn with_current_subscriber(self) -> WithDispatch<Self> ⓘ

Attaches the current default Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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impl<ST, DT> CastableFrom<ST, Initialized, Initialized> for DT
where ST: ?Sized, DT: ?Sized,

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impl<ST, DT> CastableFrom<ST, Uninit, Uninit> for DT
where ST: ?Sized, DT: ?Sized,

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impl<T> MaybeClone for T

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impl<T> MaybeDebug for T

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impl<T> MaybeSend for T
where T: Send,

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impl<T> MaybeSend for T
where T: Send,

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impl<T> MaybeSync for T
where T: Sync,

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impl<T> MaybeSync for T
where T: Sync,

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impl<T> Read<Exclusive, BecauseExclusive> for T
where T: ?Sized,