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use std::f32::consts::{FRAC_PI_2, PI};
use crate::utils::{Scale, Size};
const TOL: f32 = 1e-6;
pub fn arc_to_bezier(r: Size, xar: f32, laf: bool, sf: bool, d: Size) -> Vec<(Size, Size, Size)> {
if d.abs() < TOL {
return vec![];
}
// Ensure our radii are large enough
// If either radius is 0 we just return a straight line
let r = Size::new(r.w.abs(), r.h.abs());
if r.w < TOL || r.h < TOL {
return vec![(d / 3., d * (2. / 3.), d)];
}
// Rotate the point by -xar. We calculate the result as if xar==0 and then re-rotate the result
// It's a lot easier this way, I swear
let (sin, cos) = (-xar).sin_cos();
let d = Size {
w: d.w * cos - d.h * sin,
h: d.w * sin + d.h * cos,
};
// Scale the radii up if they can't meet the distance, maintaining their ratio
let lambda = (d / (r * 2.)).abs().max(1.);
let r = r * lambda;
let c = get_center(r, laf, sf, d);
let phi0 = (-c / r).arg();
let dphi = ((d - c) / r).arg() - phi0;
// Add and subtract 2pi (360 deg) to make sure dphi is the correct angle to sweep
let dphi = match (laf, sf) {
(true, true) if dphi < PI => dphi + 2. * PI,
(true, false) if dphi > -PI => dphi - 2. * PI,
(false, true) if dphi < 0. => dphi + 2. * PI,
(false, false) if dphi > 0. => dphi - 2. * PI,
_ => dphi,
};
// Double checks the quadrant of dphi
// TODO remove these? They shouldn't ever fail I think aside from the odd tolerance issue
// match (laf, sf) {
// (false, false) => assert!((-PI..=0.).contains(&dphi)),
// (false, true) => assert!((0. ..=PI).contains(&dphi)),
// (true, false) => assert!((-(2. * PI)..=-PI).contains(&dphi)),
// (true, true) => assert!((PI..=(2. * PI)).contains(&dphi)),
// }
// Subtract TOL so 90.0001 deg doesn't become 2 segs
let segments = ((dphi / FRAC_PI_2).abs() - TOL).ceil();
#[allow(clippy::cast_possible_truncation, clippy::cast_sign_loss)]
let i_segments = segments as u8; // u8 is fine since segments <= 4
let dphi = dphi / segments;
(0..i_segments)
.map(|i| phi0 + f32::from(i) * dphi) // Starting angle for segment
.map(|phi0| create_arc(r, phi0, dphi)) // Create seggment arc
.map(|(ctrl1, ctrl2, point)| {
// Re-rotate by xar
let (sin, cos) = xar.sin_cos();
let [ctrl1, ctrl2, point] = [ctrl1, ctrl2, point].map(|p| Size {
w: p.w * cos - p.h * sin,
h: p.w * sin + p.h * cos,
});
(ctrl1, ctrl2, point)
})
.collect()
}
fn get_center(r: Size, laf: bool, sf: bool, d: Size) -> Size {
// Since we only use half d in this calculation, pre-halve it
let d_2 = d / 2.;
let sign = if laf == sf { 1. } else { -1. };
let expr = (r.w * d_2.h).powi(2) + (r.h * d_2.w).powi(2);
let v = ((r.w * r.h).powi(2) - expr) / expr;
let co = if v.abs() < TOL { 0. } else { sign * v.sqrt() };
let c = Size {
w: r.w * d_2.h / r.h,
h: -r.h * d_2.w / r.w,
};
c * co + d_2
}
fn create_arc(r: Size, phi0: f32, dphi: f32) -> (Size, Size, Size) {
let a = (4. / 3.) * (dphi / 4.).tan();
let swap = |(a, b)| (b, a);
let d1: Size = swap(phi0.sin_cos()).into();
let d4: Size = swap((phi0 + dphi).sin_cos()).into();
let d2 = Size {
w: d1.w - d1.h * a,
h: d1.h + d1.w * a,
};
let d3 = Size {
w: d4.w + d4.h * a,
h: d4.h - d4.w * a,
};
let r_scale = Scale { x: r.w, y: r.h };
(
(d2 - d1) * r_scale,
(d3 - d1) * r_scale,
(d4 - d1) * r_scale,
)
}
#[cfg(test)]
mod tests {
use super::*;
use std::f32::consts::{FRAC_PI_2, PI, SQRT_2};
use assert_approx_eq::assert_approx_eq;
use crate::utils::Size;
#[test]
fn test_arc_to_bezier() {
struct Params {
r: Size,
xar: f32,
laf: bool,
sf: bool,
d: Size,
exp: Vec<Size>,
}
let params = vec![
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: false,
sf: false,
d: Size::new(1., 1.),
exp: vec![Size::new(1., 1.)],
},
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: true,
sf: false,
d: Size::new(1., 1.),
exp: vec![Size::new(-1., 1.), Size::new(1., 1.), Size::new(1., -1.)],
},
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: true,
sf: true,
d: Size::new(1., 1.),
exp: vec![Size::new(1., -1.), Size::new(1., 1.), Size::new(-1., 1.)],
},
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: true,
sf: true,
d: Size::new(1., -1.),
exp: vec![Size::new(-1., -1.), Size::new(1., -1.), Size::new(1., 1.)],
},
Params {
r: Size::new(1., 2.),
xar: 0.,
laf: false,
sf: false,
d: Size::new(1., 2.),
exp: vec![Size::new(1., 2.)],
},
Params {
r: Size::new(1., 2.),
xar: FRAC_PI_2,
laf: false,
sf: false,
d: Size::new(2., -1.),
exp: vec![Size::new(2., -1.)],
},
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: false,
sf: false,
d: Size::new(0., 0.),
exp: vec![],
},
Params {
r: Size::new(SQRT_2, SQRT_2),
xar: 0.,
laf: false,
sf: true,
d: Size::new(0., -2.),
exp: vec![Size::new(0., -2.)],
},
Params {
r: Size::new(SQRT_2, SQRT_2),
xar: 0.,
laf: false,
sf: false,
d: Size::new(0., 2.),
exp: vec![Size::new(0., 2.)],
},
Params {
r: Size::new(1., 1.),
xar: 0.,
laf: false,
sf: false,
d: Size::new(4., 0.),
exp: vec![Size::new(2., 2.), Size::new(2., -2.)],
},
Params {
r: Size::new(0., 0.),
xar: 0.,
laf: false,
sf: false,
d: Size::new(1., 0.),
exp: vec![Size::new(1., 0.)],
},
];
for Params {
r,
xar,
laf,
sf,
d,
exp,
} in params
{
let points = arc_to_bezier(r, xar, laf, sf, d);
let points = points.into_iter().map(|i| i.2);
assert_eq!(points.len(), exp.len());
for (pnt, res) in points.zip(exp) {
assert_approx_eq!(pnt.w, res.w);
assert_approx_eq!(pnt.h, res.h);
}
}
}
#[test]
fn test_get_center() {
struct Params {
r: Size,
laf: bool,
sf: bool,
d: Size,
exp: Size,
}
let params = vec![
Params {
r: Size::new(1., 1.),
laf: false,
sf: false,
d: Size::new(1., 1.),
exp: Size::new(1., 0.),
},
Params {
r: Size::new(1., 1.),
laf: true,
sf: false,
d: Size::new(1., 1.),
exp: Size::new(0., 1.),
},
Params {
r: Size::new(1., 1.),
laf: false,
sf: true,
d: Size::new(1., 1.),
exp: Size::new(0., 1.),
},
Params {
r: Size::new(1., 1.),
laf: true,
sf: true,
d: Size::new(1., 1.),
exp: Size::new(1., 0.),
},
Params {
r: Size::new(1., 1.),
laf: false,
sf: false,
d: Size::new(2., 0.),
exp: Size::new(1., 0.),
},
];
for Params { r, laf, sf, d, exp } in params {
let point = get_center(r, laf, sf, d);
assert_approx_eq!(point.w, exp.w);
assert_approx_eq!(point.h, exp.h);
}
}
#[test]
fn test_create_arc() {
const A: f32 = (4. / 3.) * (SQRT_2 - 1.); // (4 / 3) * tan(90deg / 4)
struct Params {
r: Size,
phi0: f32,
dphi: f32,
p: (Size, Size, Size),
}
let params = vec![
Params {
r: Size::new(1., 1.),
phi0: 0.,
dphi: FRAC_PI_2,
p: (Size::new(0., A), Size::new(A - 1., 1.), Size::new(-1., 1.)),
},
Params {
r: Size::new(1., 1.),
phi0: FRAC_PI_2,
dphi: FRAC_PI_2,
p: (
Size::new(-A, 0.),
Size::new(-1., A - 1.),
Size::new(-1., -1.),
),
},
Params {
r: Size::new(1., 1.),
phi0: PI,
dphi: FRAC_PI_2,
p: (
Size::new(0., -A),
Size::new(1. - A, -1.),
Size::new(1., -1.),
),
},
Params {
r: Size::new(1., 1.),
phi0: -FRAC_PI_2,
dphi: FRAC_PI_2,
p: (Size::new(A, 0.), Size::new(1., 1. - A), Size::new(1., 1.)),
},
Params {
r: Size::new(1., 1.),
phi0: 0.,
dphi: -FRAC_PI_2,
p: (
Size::new(0., -A),
Size::new(A - 1., -1.),
Size::new(-1., -1.),
),
},
Params {
r: Size::new(1., 1.),
phi0: FRAC_PI_2,
dphi: -FRAC_PI_2,
p: (Size::new(A, 0.), Size::new(1., A - 1.), Size::new(1., -1.)),
},
Params {
r: Size::new(1., 1.),
phi0: PI,
dphi: -FRAC_PI_2,
p: (Size::new(0., A), Size::new(1. - A, 1.), Size::new(1., 1.)),
},
Params {
r: Size::new(1., 1.),
phi0: -FRAC_PI_2,
dphi: -FRAC_PI_2,
p: (
Size::new(-A, 0.),
Size::new(-1., 1. - A),
Size::new(-1., 1.),
),
},
Params {
r: Size::new(2., 1.),
phi0: 0.,
dphi: FRAC_PI_2,
p: (
Size::new(0., A),
Size::new(2. * (A - 1.), 1.),
Size::new(-2., 1.),
),
},
];
for Params { r, phi0, dphi, p } in params {
let points = create_arc(r, phi0, dphi);
assert_approx_eq!(p.0.w, points.0.w);
assert_approx_eq!(p.0.h, points.0.h);
assert_approx_eq!(p.1.w, points.1.w);
assert_approx_eq!(p.1.h, points.1.h);
assert_approx_eq!(p.2.w, points.2.w);
assert_approx_eq!(p.2.h, points.2.h);
}
}
}