diff --git a/src/bevel_gear.rs b/src/bevel_gear.rs
index c8173f8..d109e12 100644
--- a/src/bevel_gear.rs
+++ b/src/bevel_gear.rs
@@ -70,19 +70,30 @@ impl BevelGearShape {
 		let angle = 2.0 * PI / self.points.len() as f32;
 		for (k, pt) in self.points.iter_mut().enumerate() {
 			let dir = Vec2::from_angle(k as f32 * angle);
-			for line in cutting_line.iter().zip(&cutting_line[1..]) {
-				if line.0.dot(dir) <= 0. || line.1.dot(dir) <= 0. {
-					continue;
+			for (&a, &b) in cutting_line.iter().zip(&cutting_line[1..]) {
+				if let Some(intersect) = intersect_ray_segment(dir, (a, b))
+					&& intersect > 0.
+				{
+					*pt = pt.min(intersect);
 				}
-				if line.0.dot(dir.perp()) < 0. || line.1.dot(dir.perp()) > 0. {
-					continue;
-				}
-				*pt = pt.min(f32::min(line.0.length(), line.1.length()));
 			}
 		}
 	}
 }
 
+/// Computes the intersection point of a line (from the origin along `dir`) and a line segment (from `a` to `b`).
+/// Returns the distance from the origin, in multiples of `dir`.
+fn intersect_ray_segment(dir: Vec2, (a, b): (Vec2, Vec2)) -> Option<f32> {
+	const EPS: f32 = 1e-4;
+	let den = dir.perp_dot(b - a);
+	if den.abs() < EPS {
+		// parallel or almost parallel
+		return None;
+	}
+	let u = a.perp_dot(dir) / den; // intersection = a + u * (b - a)
+	(0.0..1.0).contains(&u).then(|| a.perp_dot(b - a) / den)
+}
+
 #[derive(Debug, Clone, Copy)]
 pub enum BevelGearCap {
 	Flat,