| use crate::path_segment::PathSegment; |
|
|
| const EPS: f64 = 1e-12; |
|
|
| pub fn path_cubic_segment_self_intersection(seg: &PathSegment) -> Option<[f64; 2]> { |
| |
|
|
| if let PathSegment::Cubic(p1, p2, p3, p4) = seg { |
| let ax = -p1.x + 3. * p2.x - 3. * p3.x + p4.x; |
| let ay = -p1.y + 3. * p2.y - 3. * p3.y + p4.y; |
| let bx = 3. * p1.x - 6. * p2.x + 3. * p3.x; |
| let by = 3. * p1.y - 6. * p2.y + 3. * p3.y; |
| let cx = -3. * p1.x + 3. * p2.x; |
| let cy = -3. * p1.y + 3. * p2.y; |
|
|
| let m = ay * bx - ax * by; |
| let n = ax * cy - ay * cx; |
|
|
| let k = (-3. * ax * ax * cy * cy + 6. * ax * ay * cx * cy + 4. * ax * bx * by * cy - 4. * ax * by * by * cx - 3. * ay * ay * cx * cx - 4. * ay * bx * bx * cy + 4. * ay * bx * by * cx) |
| / (ax * ax * by * by - 2. * ax * ay * bx * by + ay * ay * bx * bx); |
|
|
| if k < 0. { |
| return None; |
| } |
|
|
| let t1 = (n / m + k.sqrt()) / 2.; |
| let t2 = (n / m - k.sqrt()) / 2.; |
|
|
| if (EPS..=1. - EPS).contains(&t1) && (EPS..=1. - EPS).contains(&t2) { |
| let mut result = [t1, t2]; |
| result.sort_by(|a, b| a.partial_cmp(b).unwrap()); |
| Some(result) |
| } else { |
| None |
| } |
| } else { |
| None |
| } |
| } |
|
|
