## Expand description

2D geometry, with a focus on curves.

The kurbo library contains data structures and algorithms for curves and vector paths. It was designed to serve the needs of 2D graphics applications, but it is intended to be general enough to be useful for other applications.

Kurbo is designed to be used by `Piet`

, a crate for drawing 2D graphics,
and is in turn used by `Druid`

, a cross-platform GUI toolkit.

## Examples

Basic UI-style geometry:

```
use kurbo::{Insets, Point, Rect, Size, Vec2};
let pt = Point::new(10.0, 10.0);
let vector = Vec2::new(5.0, -5.0);
let pt2 = pt + vector;
assert_eq!(pt2, Point::new(15.0, 5.0));
let rect = Rect::from_points(pt, pt2);
assert_eq!(rect, Rect::from_origin_size((10.0, 5.0), (5.0, 5.0)));
let insets = Insets::uniform(1.0);
let inset_rect = rect - insets;
assert_eq!(inset_rect.size(), Size::new(3.0, 3.0));
```

Finding the closest position on a `Shape`

’s perimeter to a `Point`

:

```
use kurbo::{Circle, ParamCurve, ParamCurveNearest, Point, Shape};
const DESIRED_ACCURACY: f64 = 0.1;
/// Given a shape and a point, returns the closest position on the shape's
/// perimeter, or `None` if the shape is malformed.
fn closest_perimeter_point(shape: impl Shape, pt: Point) -> Option<Point> {
let mut best: Option<(Point, f64)> = None;
for segment in shape.path_segments(DESIRED_ACCURACY) {
let nearest = segment.nearest(pt, DESIRED_ACCURACY);
if best.map(|(_, best_d)| nearest.distance_sq < best_d).unwrap_or(true) {
best = Some((segment.eval(nearest.t), nearest.distance_sq))
}
}
best.map(|(point, _)| point)
}
let circle = Circle::new((5.0, 5.0), 5.0);
let hit_point = Point::new(5.0, -2.0);
let expectation = Point::new(5.0, 0.0);
let hit = closest_perimeter_point(circle, hit_point).unwrap();
assert!(hit.distance(expectation) <= DESIRED_ACCURACY);
```

## Features

This crate either uses the standard library or the `libm`

crate for
math functionality. The `std`

feature is enabled by default, but can be
disabled, as long as the `libm`

feature is enabled. This is useful for
`no_std`

environments. However, note that the `libm`

crate is not as
efficient as the standard library, and that this crate still uses the
`alloc`

crate regardless.

## Modules

- Common mathematical operations
- Computation of offset curves of cubic Béziers, based on a curve fitting approach.
- Simplification of a Bézier path.

## Structs

- A 2D affine transform.
- A single arc segment.
- A Bézier path.
- A circle.
- A segment of a circle.
- A trivial “curve” that is just a constant.
- A single cubic Bézier segment.
- An iterator for cubic beziers.
- A sample point of a curve for fitting.
- An ellipse.
- Insets from the edges of a rectangle.
- A single line.
- The minimum distance between two Bézier curves.
- The nearest position on a curve to some point.
- An iterator for path segments.
- A 2D point.
- A single quadratic Bézier segment.
- An iterator for quadratic beziers.
- A quadratic Bézier spline in B-spline format.
- A rectangle.
- A rectangle with equally rounded corners.
- Radii for each corner of a rounded rectangle.
- An iterator that transforms path elements to path segments.
- A 2D size.
- A single SVG arc segment.
- A transformation including scaling and translation.
- A 2D vector.

## Enums

- The element of a Bézier path.
- A segment of a Bézier path.
- An error which can be returned when parsing an SVG.

## Constants

- A default value for methods that take an ‘accuracy’ argument.
- The maximum number of extrema that can be reported in the
`ParamCurveExtrema`

trait.

## Traits

- A curve parametrized by a scalar.
- A parametrized curve that can have its arc length measured.
- A parametrized curve that can have its signed area measured.
- A parametrized curve that reports its curvature.
- A differentiable parametrized curve.
- A parametrized curve that reports its extrema.
- The source curve for curve fitting.
- A parametrized curve that reports the nearest point.
- A generic trait for open and closed shapes.

## Functions

- Convert multiple cubic Bézier curves to quadratic splines.
- Generate a Bézier path that fits the source curve.
- Generate a highly optimized Bézier path that fits the source curve.
- Fit a single cubic to a range of the source curve.
- Flatten the path, invoking the callback repeatedly.
- Transform an iterator over path elements into one over path segments.