cut involute gear teeth

src/main.rs

@@ -1,4 +1,4 @@
-use std::f32::consts::PI;
+use std::{f32::consts::PI, time::Duration};
 
 use flo_draw::{
 	canvas::{Color::Rgba, GraphicsContext, GraphicsPrimitives, Transform2D},
@@ -216,38 +216,147 @@ fn cut_crown(gc: &mut impl GraphicsContext, n_teeth_crown: u32, n_teeth_gear: u3
 	}
 }
 
-fn draw(gc: &mut impl GraphicsContext) {
+fn cutter_y_at_x(x: f32) -> f32 {
-	gc.clear_canvas(Rgba(0.1, 0.1, 0.1, 1.0));
+	let x = (x / PITCH).fract_gl() * PITCH;
-
+	let a = DEDENDUM * vec2(PRESSURE_ANGLE.tan(), 1.0);
-	gc.canvas_height(20.0);
+	let d = ADDENDUM * vec2(PRESSURE_ANGLE.tan(), -1.0);
-	gc.line_width(0.05);
+	let slope = 1.0 / PRESSURE_ANGLE.tan();
-
+	if x < d.x {
-	gc.stroke_color(Rgba(1.0, 0.1, 0.1, 0.1));
+		return -x * slope;
-	// cut_involute(gc, 24);
+	}
-
+	if x <= 0.5 * PITCH - d.x {
-	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.1));
+		return d.y;
-	cut_crown(gc, 36, 24);
+	}
+	if x <= 0.5 * PITCH + a.x {
+		return (x - 0.5 * PITCH) * slope;
+	}
+	if x <= PITCH - a.x {
+		return a.y;
+	}
+	return (PITCH - x) * slope;
 }
 
+const FPS: f32 = 60.0;
+const TPS: f32 = 1.0;
+
 fn main() {
 	with_2d_graphics(|| {
 		let title = "Gear shape test";
-		if cfg!(events) {
+		use futures::StreamExt;
-			use futures::StreamExt;
+		use std::task::{Context, Poll, Waker};
-			use std::task::{Context, Poll, Waker};
 
-			let (canvas, mut events) = create_drawing_window_with_events(title);
+		let (canvas, mut events) = create_drawing_window_with_events(title);
-			'main: loop {
+		let mut t = 0.0;
-				while let Poll::Ready(event) =
+
-					events.poll_next_unpin(&mut Context::from_waker(Waker::noop()))
+		let n_rack_teeth = 10;
-				{
+
-					let Some(_event) = event else { break 'main };
+		let n_teeth = 36;
-				}
+		let n_teeth_sample = n_teeth;
-				canvas.draw(draw);
+		let r_pitch = 0.5 * n_teeth as f32;
+		let n_points_per_tooth = 100;
+		let n_points = n_points_per_tooth * n_teeth_sample;
+		let mut shape = vec![r_pitch + ADDENDUM; n_points];
+		'main: loop {
+			while let Poll::Ready(event) =
+				events.poll_next_unpin(&mut Context::from_waker(Waker::noop()))
+			{
+				let Some(_event) = event else { break 'main };
 			}
-		} else {
+			canvas.draw(|gc| {
-			let canvas = create_drawing_window(title);
+				gc.clear_canvas(Rgba(0.1, 0.1, 0.1, 1.0));
-			canvas.draw(draw);
+
+				gc.canvas_height(20.0);
+				gc.line_width(0.05);
+
+				gc.stroke_color(Rgba(1.0, 1.0, 1.0, 0.1));
+				gc.move_to(-20.0, 0.0);
+				gc.line_to(20.0, 0.0);
+				gc.move_to(0.0, -20.0);
+				gc.line_to(0.0, 20.0);
+				gc.stroke();
+
+				let gear_offset = t * TPS - (n_teeth_sample as f32 + 5.0);
+				let rack_offset = (t * TPS).fract_gl();
+
+				let kr_to_xy = |k, r: f32| {
+					let u = k as f32 / n_points_per_tooth as f32;
+					let angle = 2.0 * PI * (gear_offset + u) / n_teeth as f32;
+					let (s, c) = angle.sin_cos();
+					vec2(s * r, r_pitch - c * r)
+				};
+
+				for (k, r) in shape.iter_mut().enumerate() {
+					loop {
+						let xy = kr_to_xy(k, *r);
+						let cut_y = cutter_y_at_x(xy.x - rack_offset * PITCH);
+						if cut_y < xy.y {
+							break;
+						}
+						*r -= 0.01;
+					}
+				}
+
+				#[cfg(false)]
+				{
+					line(
+						gc,
+						shape.iter().enumerate().map(|(k, r)| {
+							let xy = kr_to_xy(k, *r);
+							let cut_y = cutter_y_at_x(xy.x - rack_offset * PITCH);
+							vec2(xy.x, cut_y)
+						}),
+					);
+					gc.stroke_color(Rgba(1.0, 1.0, 0.1, 0.4));
+					gc.stroke();
+				}
+
+				line(gc, shape.iter().enumerate().map(|(k, r)| kr_to_xy(k, *r)));
+				gc.close_path();
+				gc.stroke_color(Rgba(0.1, 0.6, 1.0, 0.4));
+				gc.stroke();
+
+				let mut pts = Vec::new();
+				for tooth in -n_rack_teeth..=n_rack_teeth {
+					let x = (tooth as f32 + rack_offset) * PITCH;
+					let a = DEDENDUM * vec2(PRESSURE_ANGLE.tan(), 1.0);
+					let d = ADDENDUM * vec2(PRESSURE_ANGLE.tan(), -1.0);
+					pts.push(vec2(x - 0.5 * PITCH - d.x, d.y));
+					pts.push(vec2(x - 0.5 * PITCH + a.x, a.y));
+					pts.push(vec2(x - a.x, a.y));
+					pts.push(vec2(x + d.x, d.y));
+				}
+				line(gc, pts);
+				gc.stroke_color(Rgba(1.0, 0.1, 0.1, 0.4));
+				gc.stroke();
+
+				let mut pts = Vec::new();
+				for tooth in -n_rack_teeth..=n_rack_teeth {
+					let x = (tooth as f32 + rack_offset) * PITCH;
+					let a = ADDENDUM * vec2(PRESSURE_ANGLE.tan(), 1.0);
+					let d = DEDENDUM * vec2(PRESSURE_ANGLE.tan(), -1.0);
+					pts.push(vec2(x - 0.5 * PITCH - d.x, d.y));
+					pts.push(vec2(x - 0.5 * PITCH + a.x, a.y));
+					pts.push(vec2(x - a.x, a.y));
+					pts.push(vec2(x + d.x, d.y));
+				}
+				line(gc, pts);
+				gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.4));
+				gc.stroke();
+			});
+
+			std::thread::sleep(Duration::from_secs_f32(1.0 / FPS));
+			t += 1.0 / FPS;
 		}
 	});
 }
+
+fn line(gc: &mut impl GraphicsContext, pts: impl IntoIterator<Item = Vec2>) {
+	let mut pts = pts.into_iter();
+	let Some(pt) = pts.next() else {
+		return;
+	};
+	gc.move_to(pt.x, pt.y);
+	for pt in pts {
+		gc.line_to(pt.x, pt.y);
+	}
+}