add gear profile

src/lib.rs

@@ -3,6 +3,7 @@ use std::error::Error;
 use glam::{Mat4, UVec2, Vec3, Vec4, vec3, vec4};
 
 mod camera;
+mod profile;
 mod render;
 
 const BACKGROUND: Vec4 = vec4(0.00, 0.39, 0.52, 1.00);

src/profile.rs

@@ -0,0 +1,98 @@
+use std::f32::consts::PI;
+
+use glam::FloatExt;
+
+#[derive(Debug, Clone, Copy)]
+pub struct Profile {
+	pub addendum: f32,
+	pub dedendum: f32,
+	pub pressure_angle: f32,
+}
+
+impl Default for Profile {
+	fn default() -> Self {
+		Profile {
+			addendum: 1.0,
+			dedendum: 1.25,
+			pressure_angle: const { 20.0f32.to_radians() },
+		}
+	}
+}
+
+impl Profile {
+	pub(crate) const PITCH: f32 = PI;
+
+	pub fn y_from_x(&self, x: f32) -> f32 {
+		self.y_from_tooth(x / Self::PITCH)
+	}
+
+	pub fn y_from_tooth(&self, t: f32) -> f32 {
+		debug_assert!(self.addendum > 0.0);
+		debug_assert!(self.dedendum > 0.0);
+		debug_assert!(self.pressure_angle > 0.0);
+		let t = t.fract_gl();
+		let slope = PI * self.slope();
+		let a = self.addendum / slope;
+		let d = self.dedendum / slope;
+		debug_assert!(2.0 * a + 2.0 * d < 1.0, "pressure angle is too high");
+		if t < a {
+			slope * t
+		} else if t < 0.5 - a {
+			self.addendum
+		} else if t < 0.5 + d {
+			-(t - 0.5) * slope
+		} else if t < 1.0 - d {
+			-self.dedendum
+		} else {
+			(t - 1.0) * slope
+		}
+	}
+
+	pub fn slope(&self) -> f32 {
+		1.0 / self.pressure_angle.tan()
+	}
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+
+	#[test]
+	fn test_profile() {
+		let profile = Profile::default();
+		let eps = 0.01;
+		for (t, y) in [
+			(0.0, 0.0),
+			(0.25, profile.addendum),
+			(0.5, 0.0),
+			(0.75, -profile.dedendum),
+			(1.0, 0.0),
+			(1.25, profile.addendum),
+		] {
+			let x = Profile::PITCH * t;
+			let comp_y = profile.y_from_x(x);
+			assert!(
+				(comp_y - y).abs() < eps,
+				"At t={t} (x={x}), expected y={y}, got y={comp_y}"
+			);
+		}
+		for (t, slope) in [
+			(0.0, 1.0),
+			(eps, 1.0),
+			(0.25, 0.0),
+			(0.5, -1.0),
+			(0.75, 0.0),
+			(1.0 - eps, 1.0),
+			(1.0, 1.0),
+			(1.0 + eps, 1.0),
+		] {
+			let x = Profile::PITCH * t;
+			let comp_slope = (profile.y_from_x(x + eps) - profile.y_from_x(x - eps)) / (2.0 * eps);
+			let exp_slope = profile.slope() * slope;
+			assert!(
+				(comp_slope - exp_slope).abs() < eps,
+				"At t={t} (x={x}), expected slope={exp_slope}, got slope={comp_slope}"
+			);
+		}
+	}
+}