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use std::f64::consts::PI;
pub type Vector2 = nalgebra::Vector2<f64>;
const TAU: f64 = 2.0 * PI;
const RECUSION_LIMIT: u32 = 8;
const FLOAT_EPSILON: f64 = 1.19209290e-7;
const PATH_DISTANCE_EPSILON: f64 = 1.0;
const CURVE_ANGLE_TOERANCE_EPSILON: f64 = 0.01;
const M_ANGLE_TOLERANCE: f64 = 0.0;
const M_CUSP_LIMIT: f64 = 0.0;
#[inline]
fn clamp_angle(x: f64) -> f64 {
if x >= PI {
TAU - x
} else {
x
}
}
pub fn adaptive_bezier_curve(
start: Vector2,
c1: Vector2,
c2: Vector2,
end: Vector2,
scale: f64,
) -> Vec<Vector2> {
let distance_tolerance = (PATH_DISTANCE_EPSILON / scale).powi(2);
let mut sample_points = Vec::new();
sample_points.push(start);
adaptive_bezier_curve_impl(
start,
c1,
c2,
end,
&mut sample_points,
distance_tolerance,
0,
);
sample_points.push(end);
sample_points
}
pub fn adaptive_bezier_curve_impl(
p1: Vector2,
p2: Vector2,
p3: Vector2,
p4: Vector2,
points: &mut Vec<Vector2>,
distance_tolerance: f64,
level: u32,
) {
if level > RECUSION_LIMIT {
return;
}
let p12 = (p1 + p2) / 2.0;
let p23 = (p2 + p3) / 2.0;
let p34 = (p3 + p4) / 2.0;
let p123 = (p12 + p23) / 2.0;
let p234 = (p23 + p34) / 2.0;
let p1234 = (p123 + p234) / 2.0;
if level > 0 {
let d = p4 - p1;
let d2 = (p2 - p4).perp(&d).abs();
let d3 = (p3 - p4).perp(&d).abs();
if d2 > FLOAT_EPSILON && d3 > FLOAT_EPSILON {
if (d2 + d3).powi(2) <= distance_tolerance * d.norm_squared() {
if M_ANGLE_TOLERANCE < CURVE_ANGLE_TOERANCE_EPSILON {
points.push(p1234);
return;
}
let a23 = (p3.y - p2.y).atan2(p3.x - p2.x);
let da1 = clamp_angle((a23 - (p2.y - p1.y).atan2(p2.x - p1.x)).abs());
let da2 = clamp_angle(((p4.y - p3.y).atan2(p4.x - p3.x) - a23).abs());
if da1 + da2 < M_ANGLE_TOLERANCE {
points.push(p1234);
return;
}
if M_CUSP_LIMIT != 0.0 {
if da1 > M_CUSP_LIMIT {
points.push(p2);
return;
}
if da2 > M_CUSP_LIMIT {
points.push(p3);
return;
}
}
}
} else if d2 > FLOAT_EPSILON {
if d2 * d2 <= distance_tolerance * d.norm_squared() {
if M_ANGLE_TOLERANCE < CURVE_ANGLE_TOERANCE_EPSILON {
points.push(p1234);
return;
}
let da1 = clamp_angle(
((p3.y - p2.y).atan2(p3.x - p2.x) - (p2.y - p1.y).atan2(p2.x - p1.x)).abs(),
);
if da1 < M_ANGLE_TOLERANCE {
points.push(p2);
points.push(p3);
return;
}
if M_CUSP_LIMIT != 0.0 && da1 > M_CUSP_LIMIT {
points.push(p2);
return;
}
}
} else if d3 > FLOAT_EPSILON {
if d3 * d3 <= distance_tolerance * d.norm_squared() {
if M_ANGLE_TOLERANCE < CURVE_ANGLE_TOERANCE_EPSILON {
points.push(p1234);
return;
}
let da1 = clamp_angle(
((p4.y - p3.y).atan2(p4.x - p3.x) - (p3.y - p2.y).atan2(p3.x - p2.x)).abs(),
);
if da1 < M_ANGLE_TOLERANCE {
points.push(p2);
points.push(p3);
return;
}
if M_CUSP_LIMIT != 0.0 && da1 > M_CUSP_LIMIT {
points.push(p3);
return;
}
}
} else {
let d = p1234 - (p1 + p4) / 2.0;
if d.norm_squared() < distance_tolerance {
points.push(p1234);
return;
}
}
}
adaptive_bezier_curve_impl(p1, p12, p123, p1234, points, distance_tolerance, level + 1);
adaptive_bezier_curve_impl(p1234, p234, p34, p4, points, distance_tolerance, level + 1);
}
#[cfg(test)]
mod tests {
use super::{adaptive_bezier_curve, Vector2, FLOAT_EPSILON};
#[test]
fn simple() {
let answer = vec![
Vector2::new(20.0, 20.0),
Vector2::new(27.12921142578125, 32.740386962890625),
Vector2::new(39.34417724609375, 56.408416748046875),
Vector2::new(53.46435546875, 87.040771484375),
Vector2::new(63.99200439453125, 111.28897094726562),
Vector2::new(69.82025146484375, 123.60739135742188),
Vector2::new(73.9102554321289, 130.69841384887695),
Vector2::new(76.61632537841797, 134.36077499389648),
Vector2::new(79.37641143798828, 137.14487075805664),
Vector2::new(82.25093841552734, 139.02817916870117),
Vector2::new(85.30033111572266, 139.98817825317383),
Vector2::new(88.58501434326172, 140.00234603881836),
Vector2::new(92.16541290283203, 139.04816055297852),
Vector2::new(96.1019515991211, 137.10309982299805),
Vector2::new(100.4550552368164, 134.1446418762207),
Vector2::new(105.28514862060547, 130.15026473999023),
Vector2::new(113.55682373046875, 122.16708374023438),
Vector2::new(126.81915283203125, 107.68692016601562),
Vector2::new(143.07708740234375, 88.65768432617188),
Vector2::new(174.13818359375, 51.190185546875),
Vector2::new(200.0, 20.0),
];
let start = Vector2::new(20.0, 20.0);
let c1 = Vector2::new(100.0, 159.0);
let c2 = Vector2::new(50.0, 200.0);
let end = Vector2::new(200.0, 20.0);
let scale = 2.0;
let output = adaptive_bezier_curve(start, c1, c2, end, scale);
assert_eq!(output.len(), answer.len());
for i in 0..answer.len() {
assert_eq!((output[i].x - answer[i].x).abs() < FLOAT_EPSILON, true);
assert_eq!((output[i].y - answer[i].y).abs() < FLOAT_EPSILON, true);
}
}
}