Struct CubicBezierSegment

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pub struct CubicBezierSegment<S> {
    pub from: Point<S>,
    pub ctrl1: Point<S>,
    pub ctrl2: Point<S>,
    pub to: Point<S>,
}

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: Point<S>§ctrl1: Point<S>§ctrl2: Point<S>§to: Point<S>

Implementations§

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impl<S: Scalar> CubicBezierSegment<S>

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

Return the parameter values corresponding to a given x coordinate.

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

Return the parameter values corresponding to a given y coordinate.

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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 split_range(&self, t_range: Range<S>) -> Self

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

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

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

Split this curve into two sub-curves.

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

Return the curve before the split point.

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

Return the curve after the split point.

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

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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 flip(&self) -> Self

Swap the beginning and the end of the segment.

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

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.

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pub fn to_quadratic_error(&self) -> S

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

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

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.

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

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

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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 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(&CubicBezierSegment<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(&CubicBezierSegment<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(&CubicBezierSegment<S>),

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

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

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

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

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

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

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

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.

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

Compute the length of the segment using a flattened approximation.

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

Invokes a callback at each inflection point if any.

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

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

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

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

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

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

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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 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 x-least position in the curve.

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

Returns a conservative rectangle the curve is contained in.

This method is faster than bounding_box but more conservative.

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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 a conservative rectangle that contains the curve.

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

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.

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

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

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

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.

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

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

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

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.

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

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

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

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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