Struct lyon_geom::QuadraticBezierSegment
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pub struct QuadraticBezierSegment<S> { pub from: Point<S>, pub ctrl: Point<S>, pub to: Point<S>, }
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>
Methods
impl<S: Scalar> QuadraticBezierSegment<S>
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fn sample(&self, t: S) -> Point<S>
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Sample the curve at t (expecting t between 0 and 1).
fn x(&self, t: S) -> S
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Sample the x coordinate of the curve at t (expecting t between 0 and 1).
fn y(&self, t: S) -> S
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Sample the y coordinate of the curve at t (expecting t between 0 and 1).
fn derivative(&self, t: S) -> Vector<S>
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Sample the curve's derivative at t (expecting t between 0 and 1).
fn dx(&self, t: S) -> S
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Sample the x coordinate of the curve's derivative at t (expecting t between 0 and 1).
fn dy(&self, t: S) -> S
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Sample the y coordinate of the curve's derivative at t (expecting t between 0 and 1).
fn flip(&self) -> Self
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Swap the beginning and the end of the segment.
fn y_maximum_t(&self) -> S
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Find the advancement of the y-most position in the curve.
This returns the advancement along the curve, not the actual y position.
fn y_minimum_t(&self) -> S
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Find the advancement of the y-least position in the curve.
This returns the advancement along the curve, not the actual y position.
fn local_y_extremum_t(&self) -> Option<S>
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Return the y inflection point or None if this curve is y-monotonic.
fn x_maximum_t(&self) -> S
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Find the advancement of the x-most position in the curve.
This returns the advancement along the curve, not the actual x position.
fn x_minimum_t(&self) -> S
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Find the advancement of the x-least position in the curve.
This returns the advancement along the curve, not the actual x position.
fn local_x_extremum_t(&self) -> Option<S>
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Return the x inflection point or None if this curve is x-monotonic.
fn split_range(&self, t_range: Range<S>) -> Self
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Return the sub-curve inside a given range of t.
This is equivalent splitting at the range's end points.
fn split(&self, t: S) -> (QuadraticBezierSegment<S>, QuadraticBezierSegment<S>)
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Split this curve into two sub-curves.
fn before_split(&self, t: S) -> QuadraticBezierSegment<S>
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Return the curve before the split point.
fn after_split(&self, t: S) -> QuadraticBezierSegment<S>
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Return the curve after the split point.
fn to_cubic(&self) -> CubicBezierSegment<S>
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Elevate this curve to a third order bézier.
fn baseline(&self) -> LineSegment<S>
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fn is_linear(&self, tolerance: S) -> bool
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fn fat_line(&self) -> (LineEquation<S>, LineEquation<S>)
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Computes a "fat line" of this segment.
A fat line is two convervative lines between which the segment is fully contained.
fn transform(&self, transform: &Transform2D<S>) -> Self
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Applies the transform to this curve and returns the results.
fn flattening_step(&self, tolerance: S) -> S
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Find the interval of the begining of the curve that can be approximated with a line segment.
fn for_each_flattened<F: FnMut(Point<S>)>(
&self,
tolerance: S,
call_back: &mut F
)
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&self,
tolerance: S,
call_back: &mut F
)
Iterates through the curve invoking a callback at each point.
fn flattened(&self, tolerance: S) -> Flattened<S>
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Returns the flattened representation of the curve as an iterator, starting after the current point.
fn approximate_length(&self, tolerance: S) -> S
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Compute the length of the segment using a flattened approximation.
fn bounding_triangle(&self) -> Triangle<S>
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Returns a triangle containing this curve segment.
fn fast_bounding_rect(&self) -> Rect<S>
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Returns a conservative rectangle that contains the curve.
fn fast_bounding_range_x(&self) -> (S, S)
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Returns a conservative range of x this curve is contained in.
fn fast_bounding_range_y(&self) -> (S, S)
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Returns a conservative range of y this curve is contained in.
fn bounding_rect(&self) -> Rect<S>
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Returns the smallest rectangle the curve is contained in
fn bounding_range_x(&self) -> (S, S)
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Returns the smallest range of x this curve is contained in.
fn bounding_range_y(&self) -> (S, S)
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Returns the smallest range of y this curve is contained in.
fn assume_monotonic(&self) -> MonotonicQuadraticBezierSegment<S>
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Cast this curve into a monotonic curve without checking that the monotonicity assumption is correct.
fn is_x_monotonic(&self) -> bool
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Returns whether this segment is monotonic on the x axis.
fn is_y_monotonic(&self) -> bool
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Returns whether this segment is monotonic on the y axis.
fn is_monotonic(&self) -> bool
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Returns whether this segment is fully monotonic.
fn line_intersections_t(&self, line: &Line<S>) -> ArrayVec<[S; 2]>
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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.
fn line_intersections(&self, line: &Line<S>) -> ArrayVec<[Point<S>; 2]>
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Computes the intersection points (if any) between this segment a line.
fn line_segment_intersections_t(
&self,
segment: &LineSegment<S>
) -> ArrayVec<[(S, S); 2]>
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&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.
fn from(&self) -> Point<S>
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fn to(&self) -> Point<S>
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fn line_segment_intersections(
&self,
segment: &LineSegment<S>
) -> ArrayVec<[Point<S>; 2]>
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&self,
segment: &LineSegment<S>
) -> ArrayVec<[Point<S>; 2]>
Computes the intersection points (if any) between this segment a line segment.
Trait Implementations
impl<S: Copy> Copy for QuadraticBezierSegment<S>
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impl<S: Clone> Clone for QuadraticBezierSegment<S>
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fn clone(&self) -> QuadraticBezierSegment<S>
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Returns a copy of the value. Read more
fn clone_from(&mut self, source: &Self)
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Performs copy-assignment from source
. Read more
impl<S: Debug> Debug for QuadraticBezierSegment<S>
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impl<S: PartialEq> PartialEq for QuadraticBezierSegment<S>
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fn eq(&self, __arg_0: &QuadraticBezierSegment<S>) -> bool
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This method tests for self
and other
values to be equal, and is used by ==
. Read more
fn ne(&self, __arg_0: &QuadraticBezierSegment<S>) -> bool
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This method tests for !=
.
impl<S: Scalar> Segment for QuadraticBezierSegment<S>
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type Scalar = S
fn from(&self) -> Point<S>
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Start of the curve.
fn to(&self) -> Point<S>
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End of the curve.
fn sample(&self, t: S) -> Point<S>
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Sample the curve at t (expecting t between 0 and 1).
fn x(&self, t: S) -> S
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Sample x at t (expecting t between 0 and 1).
fn y(&self, t: S) -> S
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Sample y at t (expecting t between 0 and 1).
fn derivative(&self, t: S) -> Vector<S>
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Sample the derivative at t (expecting t between 0 and 1).
fn dx(&self, t: S) -> S
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Sample x derivative at t (expecting t between 0 and 1).
fn dy(&self, t: S) -> S
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Sample y derivative at t (expecting t between 0 and 1).
fn split(&self, t: S) -> (Self, Self)
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Split this curve into two sub-curves.
fn before_split(&self, t: S) -> Self
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Return the curve before the split point.
fn after_split(&self, t: S) -> Self
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Return the curve after the split point.
fn split_range(&self, t_range: Range<S>) -> Self
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Return the curve inside a given range of t. Read more
fn flip(&self) -> Self
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Swap the direction of the segment.
fn approximate_length(&self, tolerance: S) -> S
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Compute the length of the segment using a flattened approximation.
impl<S: Scalar> FlatteningStep for QuadraticBezierSegment<S>
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fn flattening_step(&self, tolerance: S) -> S
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Find the interval of the begining of the curve that can be approximated with a line segment. Read more
fn flattened(self, tolerance: Self::Scalar) -> Flattened<Self::Scalar, Self>
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Returns the flattened representation of the curve as an iterator, starting after the current point. Read more