Struct lyon_geom::QuadraticBezierSegment
source · [−]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 + 2 * t² * to
Fields
from: Point<S>
ctrl: Point<S>
to: Point<S>
Implementations
sourceimpl<S: Scalar> QuadraticBezierSegment<S>
impl<S: Scalar> QuadraticBezierSegment<S>
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>
pub fn is_linear(&self, tolerance: S) -> bool
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(Point<S>),
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
sourcepub fn for_each_flattened_t<F>(&self, tolerance: S, callback: &mut F) where
F: FnMut(S),
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
sourcepub fn for_each_flattened_with_t<F>(&self, tolerance: S, callback: &mut F) where
F: FnMut(Point<S>, S),
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
sourcepub fn flattened(&self, tolerance: S) -> Flattened<S>ⓘNotable traits for Flattened<S>impl<S: Scalar> Iterator for Flattened<S> type Item = Point<S>;
pub fn flattened(&self, tolerance: S) -> Flattened<S>ⓘNotable traits for Flattened<S>impl<S: Scalar> Iterator for Flattened<S> type Item = Point<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>ⓘNotable traits for FlattenedT<S>impl<S: Scalar> Iterator for FlattenedT<S> type Item = S;
pub fn flattened_t(&self, tolerance: S) -> FlattenedT<S>ⓘNotable traits for FlattenedT<S>impl<S: Scalar> Iterator for FlattenedT<S> type Item = S;
Returns the flattened representation of the curve as an iterator, starting after the current point.
sourcepub fn for_each_monotonic_t<F>(&self, cb: F) where
F: FnMut(S),
pub fn for_each_monotonic_t<F>(&self, cb: F) where
F: FnMut(S),
Invokes a callback between each monotonic part of the segment.
sourcepub fn for_each_monotonic_range<F>(&self, cb: F) where
F: FnMut(Range<S>),
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>>),
sourcepub fn approximate_length(&self, tolerance: S) -> S
pub fn approximate_length(&self, tolerance: S) -> S
Compute the length of the segment using a flattened approximation.
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_rect(&self) -> Rect<S>
pub fn fast_bounding_rect(&self) -> Rect<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_rect(&self) -> Rect<S>
pub fn bounding_rect(&self) -> Rect<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 assume_monotonic(&self) -> MonotonicQuadraticBezierSegment<S>
pub fn assume_monotonic(&self) -> MonotonicQuadraticBezierSegment<S>
Cast this curve into a monotonic curve without checking that the monotonicity assumption is correct.
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 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.
Trait Implementations
sourceimpl<S: Clone> Clone for QuadraticBezierSegment<S>
impl<S: Clone> Clone for QuadraticBezierSegment<S>
sourcefn clone(&self) -> QuadraticBezierSegment<S>
fn clone(&self) -> QuadraticBezierSegment<S>
Returns a copy of the value. Read more
1.0.0 · sourcefn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
Performs copy-assignment from source
. Read more
sourceimpl<S: Debug> Debug for QuadraticBezierSegment<S>
impl<S: Debug> Debug for QuadraticBezierSegment<S>
sourceimpl<S> From<QuadraticBezierSegment<S>> for BezierSegment<S>
impl<S> From<QuadraticBezierSegment<S>> for BezierSegment<S>
sourcefn from(s: QuadraticBezierSegment<S>) -> Self
fn from(s: QuadraticBezierSegment<S>) -> Self
Converts to this type from the input type.
sourceimpl<S: PartialEq> PartialEq<QuadraticBezierSegment<S>> for QuadraticBezierSegment<S>
impl<S: PartialEq> PartialEq<QuadraticBezierSegment<S>> for QuadraticBezierSegment<S>
sourcefn eq(&self, other: &QuadraticBezierSegment<S>) -> bool
fn eq(&self, other: &QuadraticBezierSegment<S>) -> bool
This method tests for self
and other
values to be equal, and is used
by ==
. Read more
sourcefn ne(&self, other: &QuadraticBezierSegment<S>) -> bool
fn ne(&self, other: &QuadraticBezierSegment<S>) -> bool
This method tests for !=
.
sourceimpl<S: Scalar> Segment for QuadraticBezierSegment<S>
impl<S: Scalar> Segment for QuadraticBezierSegment<S>
type Scalar = S
sourcefn derivative(&self, t: S) -> Vector<S>
fn derivative(&self, t: S) -> Vector<S>
Sample the derivative at t (expecting t between 0 and 1).
sourcefn before_split(&self, t: S) -> Self
fn before_split(&self, t: S) -> Self
Return the curve before the split point.
sourcefn after_split(&self, t: S) -> Self
fn after_split(&self, t: S) -> Self
Return the curve after the split point.
sourcefn split_range(&self, t_range: Range<S>) -> Self
fn split_range(&self, t_range: Range<S>) -> Self
Return the curve inside a given range of t. Read more
sourcefn approximate_length(&self, tolerance: S) -> S
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>
Auto Trait Implementations
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
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more