Struct QuadraticBezierSegment

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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

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§from: Point<S>§ctrl: Point<S>§to: Point<S>

Implementations§

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impl<S: Scalar> QuadraticBezierSegment<S>

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pub fn cast<NewS: NumCast>(self) -> QuadraticBezierSegment<NewS>

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

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

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

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

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

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

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

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

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

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

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

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

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pub fn flip(&self) -> Self

Swap the beginning and the end of the segment.

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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.

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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.

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pub fn local_y_extremum_t(&self) -> Option<S>

Return the y inflection point or None if this curve is y-monotonic.

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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.

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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.

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pub fn local_x_extremum_t(&self) -> Option<S>

Return the x inflection point or None if this curve is x-monotonic.

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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.

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

Split this curve into two sub-curves.

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

Return the curve before the split point.

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

Return the curve after the split point.

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

Elevate this curve to a third order bézier.

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

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

Returns whether the curve can be approximated with a single point, given a tolerance threshold.

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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.

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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.

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pub fn transformed<T: Transformation<S>>(&self, transform: &T) -> Self

Applies the transform to this curve and returns the results.

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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.

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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.

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

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.

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

Returns the flattened representation of the curve as an iterator, starting after the current point.

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pub fn flattened_t(&self, tolerance: S) -> FlattenedT<S> ⓘ

Returns the flattened representation of the curve as an iterator, starting after the current point.

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

Invokes a callback for each monotonic part of the segment.

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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.

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

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

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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.

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

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

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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.

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pub fn bounding_triangle(&self) -> Triangle<S>

Returns a triangle containing this curve segment.

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

Returns a conservative rectangle that contains the curve.

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

Returns a conservative range of x that contains this curve.

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

Returns a conservative range of y that contains this curve.

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

Returns the smallest rectangle the curve is contained in

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

Returns the smallest range of x that contains this curve.

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

Returns the smallest range of y that contains this curve.

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pub fn is_x_monotonic(&self) -> bool

Returns whether this segment is monotonic on the x axis.

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pub fn is_y_monotonic(&self) -> bool

Returns whether this segment is monotonic on the y axis.

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pub fn is_monotonic(&self) -> bool

Returns whether this segment is fully monotonic.

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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.

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pub fn line_intersections(&self, line: &Line<S>) -> ArrayVec<Point<S>, 2>

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

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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.

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