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use crate::{PathEl, Point, Rect, Shape, Vec2};
use std::{
f64::consts::{FRAC_PI_2, PI},
iter,
};
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
pub struct Arc {
pub center: Point,
pub radii: Vec2,
pub start_angle: f64,
pub sweep_angle: f64,
pub x_rotation: f64,
}
impl Arc {
pub fn append_iter(&self, tolerance: f64) -> ArcAppendIter {
let sign = self.sweep_angle.signum();
let scaled_err = self.radii.x.max(self.radii.y) / tolerance;
let n_err = (1.1163 * scaled_err).powf(1.0 / 6.0).max(3.999_999);
let n = (n_err * self.sweep_angle.abs() * (1.0 / (2.0 * PI))).ceil();
let angle_step = self.sweep_angle / n;
let n = n as usize;
let arm_len = (4.0 / 3.0) * (0.25 * angle_step).abs().tan() * sign;
let angle0 = self.start_angle;
let p0 = sample_ellipse(self.radii, self.x_rotation, angle0);
ArcAppendIter {
idx: 0,
center: self.center,
radii: self.radii,
x_rotation: self.x_rotation,
n,
arm_len,
angle_step,
p0,
angle0,
}
}
pub fn to_cubic_beziers<P>(self, tolerance: f64, mut p: P)
where
P: FnMut(Point, Point, Point),
{
let mut path = self.append_iter(tolerance);
while let Some(PathEl::CurveTo(p1, p2, p3)) = path.next() {
p(p1, p2, p3);
}
}
}
#[doc(hidden)]
pub struct ArcAppendIter {
idx: usize,
center: Point,
radii: Vec2,
x_rotation: f64,
n: usize,
arm_len: f64,
angle_step: f64,
p0: Vec2,
angle0: f64,
}
impl Iterator for ArcAppendIter {
type Item = PathEl;
fn next(&mut self) -> Option<Self::Item> {
if self.idx >= self.n {
return None;
}
let angle1 = self.angle0 + self.angle_step;
let p0 = self.p0;
let p1 = p0
+ self.arm_len * sample_ellipse(self.radii, self.x_rotation, self.angle0 + FRAC_PI_2);
let p3 = sample_ellipse(self.radii, self.x_rotation, angle1);
let p2 =
p3 - self.arm_len * sample_ellipse(self.radii, self.x_rotation, angle1 + FRAC_PI_2);
self.angle0 = angle1;
self.p0 = p3;
self.idx += 1;
Some(PathEl::CurveTo(
self.center + p1,
self.center + p2,
self.center + p3,
))
}
}
fn sample_ellipse(radii: Vec2, x_rotation: f64, angle: f64) -> Vec2 {
let u = radii.x * angle.cos();
let v = radii.y * angle.sin();
rotate_pt(Vec2::new(u, v), x_rotation)
}
fn rotate_pt(pt: Vec2, angle: f64) -> Vec2 {
Vec2::new(
pt.x * angle.cos() - pt.y * angle.sin(),
pt.x * angle.sin() + pt.y * angle.cos(),
)
}
impl Shape for Arc {
type BezPathIter = iter::Chain<iter::Once<PathEl>, ArcAppendIter>;
fn to_bez_path(&self, tolerance: f64) -> Self::BezPathIter {
let p0 = sample_ellipse(self.radii, self.x_rotation, self.start_angle);
iter::once(PathEl::MoveTo(self.center + p0)).chain(self.append_iter(tolerance))
}
#[inline]
fn area(&self) -> f64 {
let Vec2 { x, y } = self.radii;
PI * x * y
}
#[inline]
fn perimeter(&self, accuracy: f64) -> f64 {
self.clone()
.into_bez_path(0.1)
.elements()
.perimeter(accuracy)
}
#[inline]
fn winding(&self, pt: Point) -> i32 {
self.clone().into_bez_path(0.1).elements().winding(pt)
}
#[inline]
fn bounding_box(&self) -> Rect {
self.clone().into_bez_path(0.1).elements().bounding_box()
}
}