gear-teeth/src/main.rs

use std::{f32::consts::PI, time::Duration};

use flo_draw::{
	canvas::{Color::Rgba, GraphicsContext, GraphicsPrimitives, Transform2D},
	create_drawing_window, create_drawing_window_with_events, with_2d_graphics,
};
use glam::{Affine2, FloatExt, Vec2, vec2};

const fn rad(deg: f32) -> f32 {
	deg * (PI / 180.0)
}

const ADDENDUM: f32 = 1.00;
const DEDENDUM: f32 = 1.25;
const PRESSURE_ANGLE: f32 = rad(20.0);
const PITCH: f32 = PI;

fn draw_rack(gc: &mut impl GraphicsContext) {
	gc.move_to(-ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
	gc.line_to(DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
	gc.line_to(0.5 * PITCH - DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
	gc.line_to(0.5 * PITCH + ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
	gc.line_to(PITCH - ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
	gc.line_to(PITCH + DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
	gc.stroke();

	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.2));

	gc.move_to(-PITCH, 0.0);
	gc.line_to(PITCH, 0.0);
	gc.stroke();
}

fn cut_involute(gc: &mut impl GraphicsContext, n_teeth: u32) {
	let tooth_angle = 360.0 / n_teeth as f32;
	let r = 0.5 * n_teeth as f32;
	let n = 500;
	for k in -n..=n {
		let t = 2.0 * k as f32 / n as f32;
		gc.push_state();
		gc.transform(Transform2D::translate(0.0, -r));
		gc.transform(Transform2D::rotate_degrees(tooth_angle * t));
		gc.transform(Transform2D::translate(0.0, r));
		gc.transform(Transform2D::translate(PITCH * t, 0.0));
		gc.transform(Transform2D::translate(-2.0 * PITCH, 0.0));
		for _ in -2..2 {
			gc.move_to(-ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
			gc.line_to(DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
			gc.line_to(0.5 * PITCH - DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
			gc.line_to(0.5 * PITCH + ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
			gc.line_to(PITCH - ADDENDUM * PRESSURE_ANGLE.tan(), ADDENDUM);
			gc.line_to(PITCH + DEDENDUM * PRESSURE_ANGLE.tan(), -DEDENDUM);
			gc.stroke();
			gc.transform(Transform2D::translate(PITCH, 0.0));
		}
		gc.pop_state();
	}

	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.2));

	gc.circle(0.0, -r, r);
	gc.stroke();
}

fn show_involute(gc: &mut impl GraphicsContext, n_teeth: u32) {
	let tooth_angle = 360.0 / n_teeth as f32;
	let r = 0.5 * n_teeth as f32;
	let n = 500;
	let size = 5.0;
	for k in -n..=n {
		let t = 2.0 * k as f32 / n as f32;
		gc.push_state();
		gc.transform(Transform2D::translate(0.0, -r));
		gc.transform(Transform2D::rotate_degrees(tooth_angle * t));
		gc.transform(Transform2D::translate(0.0, r));
		gc.transform(Transform2D::translate(PITCH * t, 0.0));

		gc.move_to(-size * PRESSURE_ANGLE.tan(), size);
		gc.line_to(size * PRESSURE_ANGLE.tan(), -size);
		gc.stroke();
		gc.pop_state();
	}

	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.2));

	gc.circle(0.0, -r, r);
	gc.circle(0.0, -r, r - DEDENDUM);
	gc.circle(0.0, -r, r + ADDENDUM);
	gc.stroke();
}

fn draw_crown(gc: &mut impl GraphicsContext, n_teeth: u32) {
	let tooth_angle = rad(360.0 / n_teeth as f32);
	let r = 0.5 * n_teeth as f32;

	let mut points = Vec::new();
	let n = 500;
	for i_point in -n..=n {
		let t_point = 5.0 * i_point as f32 / n as f32;
		let x = PITCH * t_point;
		let angle = f32::atan2(x, r);
		let tooth = angle / tooth_angle;
		let vx = PITCH * tooth.fract_gl();

		let tan = PRESSURE_ANGLE.tan();
		let vy = if vx < DEDENDUM * tan {
			-vx / tan
		} else if vx <= 0.5 * PITCH - DEDENDUM * tan {
			-DEDENDUM
		} else if vx <= 0.5 * PITCH + ADDENDUM * tan {
			(vx - 0.5 * PITCH) / tan
		} else if vx <= PITCH - ADDENDUM * tan {
			ADDENDUM
		} else {
			-(vx - PITCH) / tan
		};
		points.push(vec2(x, vy));
	}
	gc.move_to(points[0].x, points[0].y);
	for pt in &points[1..] {
		gc.line_to(pt.x, pt.y);
	}
	gc.stroke();

	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.2));

	gc.move_to(-20.0, 0.0);
	gc.line_to(20.0, 0.0);
	gc.stroke();

	let n = 4;
	for k in -n..=n {
		let angle = tooth_angle * k as f32;
		let x = r * angle.tan();
		gc.move_to(x, -1.0);
		gc.line_to(x, 1.0);
		gc.stroke();
	}
}

fn cut_crown(gc: &mut impl GraphicsContext, n_teeth_crown: u32, n_teeth_gear: u32) {
	let tooth_angle_crown = rad(360.0 / n_teeth_crown as f32);
	let r_crown = 0.5 * n_teeth_crown as f32;

	let tooth_angle_gear = rad(360.0 / n_teeth_gear as f32);
	let r_gear = 0.5 * n_teeth_gear as f32;

	let n_subcuts = 200;
	for i_subcut in -n_subcuts..=n_subcuts {
		let t_cut = 2.0 * i_subcut as f32 / n_subcuts as f32;

		let rot_gear = t_cut * tooth_angle_gear;
		let rot_crown = t_cut * tooth_angle_crown;

		let tfm_gear = Affine2::from_translation(vec2(0.0, -r_gear))
			* Affine2::from_angle_translation(-rot_gear, Vec2::ZERO)
			* Affine2::from_translation(vec2(0.0, r_gear));

		let mut points = Vec::new();
		let n_points = 300;
		for i_point in -n_points..=n_points {
			let t_point = 2.0 * i_point as f32 / n_points as f32;
			let x = PITCH * t_point;
			let angle = f32::atan2(x, r_crown) + rot_crown;
			let tooth = angle / tooth_angle_crown;
			let vx = PITCH * tooth.fract_gl();

			let tan = PRESSURE_ANGLE.tan();
			let vy = if vx < DEDENDUM * tan {
				-vx / tan
			} else if vx <= 0.5 * PITCH - DEDENDUM * tan {
				-DEDENDUM
			} else if vx <= 0.5 * PITCH + ADDENDUM * tan {
				(vx - 0.5 * PITCH) / tan
			} else if vx <= PITCH - ADDENDUM * tan {
				ADDENDUM
			} else {
				-(vx - PITCH) / tan
			};
			points.push(tfm_gear.transform_point2(vec2(x, vy)));
		}
		gc.move_to(points[0].x, points[0].y);
		for pt in &points[1..] {
			gc.line_to(pt.x, pt.y);
		}
		gc.stroke();
	}

	gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.2));

	gc.move_to(-20.0, 0.0);
	gc.line_to(20.0, 0.0);
	gc.stroke();

	let n = 4;
	for k in -n..=n {
		let angle = tooth_angle_crown * k as f32;
		let x = r_crown * angle.tan();
		gc.move_to(x, -1.0);
		gc.line_to(x, 1.0);
		gc.stroke();
	}

	gc.circle(0.0, -r_gear, r_gear);
	gc.circle(0.0, -r_gear, r_gear - DEDENDUM);
	gc.circle(0.0, -r_gear, r_gear + ADDENDUM);
	gc.stroke();

	let n = 4;
	for k in -n..=n {
		let angle = tooth_angle_gear * k as f32;
		let (x, y) = angle.sin_cos();
		gc.move_to(0.0, -r_gear);
		gc.line_to(x * r_gear, (y - 1.0) * r_gear);
		gc.stroke();
	}
}

fn cutter_y_at_x(x: f32) -> f32 {
	let x = (x / PITCH).fract_gl() * PITCH;
	let a = DEDENDUM * vec2(PRESSURE_ANGLE.tan(), 1.0);
	let d = ADDENDUM * vec2(PRESSURE_ANGLE.tan(), -1.0);
	let slope = 1.0 / PRESSURE_ANGLE.tan();
	if x < d.x {
		return -x * slope;
	}
	if x <= 0.5 * PITCH - d.x {
		return d.y;
	}
	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";
		use futures::StreamExt;
		use std::task::{Context, Poll, Waker};

		let (canvas, mut events) = create_drawing_window_with_events(title);
		let mut t = 0.0;

		let n_rack_teeth = 10;

		let n_teeth = 36;
		let n_teeth_sample = n_teeth;
		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 };
			}
			canvas.draw(|gc| {
				gc.clear_canvas(Rgba(0.1, 0.1, 0.1, 1.0));

				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);
	}
}