no

.gitignore

@@ -0,0 +1 @@
+/target

Cargo.toml

@@ -0,0 +1,8 @@
+[package]
+name = "gears"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+flo_draw = "0.3.1"
+glam = "0.30.5"

src/main.rs

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+use std::f32::consts::PI;
+
+use flo_draw::{
+	canvas::{Color::Rgba, GraphicsContext, GraphicsPrimitives},
+	create_drawing_window, with_2d_graphics,
+};
+use glam::{Mat2, Vec2, vec2};
+
+const fn rad(deg: f32) -> f32 {
+	deg * (PI / 180.0)
+}
+
+fn involute(t: f32) -> Vec2 {
+	let v = Vec2::from_angle(t);
+	v - t * v.perp()
+}
+
+fn involute_radius_to_t(r: f32) -> f32 {
+	(r * r - 1.).sqrt()
+}
+
+fn gear_shape(n: usize) -> Vec<Vec2> {
+	const A: f32 = rad(28.);
+	const Q: usize = 6;
+	let b = A.cos();
+
+	let offset = involute(involute_radius_to_t(1. / b)).to_angle();
+	let stop_angle = involute_radius_to_t((1.0 + 2.0 / n as f32) / b);
+	let halfangle = PI / n as f32;
+	let ma = Mat2::from_angle(offset - halfangle);
+	let mb = Mat2::from_diagonal(vec2(1., -1.)) * ma;
+
+	let mut ret = Vec::with_capacity(2 * n * Q);
+	for i in 0..n {
+		let m = Mat2::from_angle(i as f32 * 2. * halfangle);
+		for k in 0..=Q {
+			let t = k as f32 / Q as f32;
+			let p = b * m * ma * involute(stop_angle * t);
+			ret.push(p);
+		}
+		for k in 0..=Q {
+			let t = 1. - k as f32 / Q as f32;
+			let p = b * m * mb * involute(stop_angle * t);
+			ret.push(p);
+		}
+	}
+	ret
+}
+
+fn main() {
+	let g24 = gear_shape(24);
+	let g36 = gear_shape(36);
+
+	with_2d_graphics(|| {
+		let canvas = create_drawing_window("Canvas window");
+		canvas.draw(|gc| {
+			gc.clear_canvas(Rgba(0.1, 0.1, 0.1, 1.0));
+
+			gc.canvas_height(50.0);
+			gc.line_width(0.5);
+
+			const N1: usize = 20;
+			const N2: usize = 50;
+			const R1: f32 = 20.;
+			const R2: f32 = 50.;
+			const A: f32 = rad(28.);
+
+			let b = A.cos();
+			let b1 = b * R1;
+			let b2 = b * R2;
+			let offset = involute_radius_to_t(1. / b);
+			let offset = involute(offset).to_angle();
+
+			gc.new_path();
+			gc.stroke_color(Rgba(0.3, 0.3, 0.3, 1.0));
+			gc.circle(-R1, 0., R1);
+			gc.circle(R2, 0., R2);
+			gc.circle(-R2, 0., R2);
+			gc.stroke();
+
+			gc.new_path();
+			gc.stroke_color(Rgba(0.1, 0.1, 0.8, 1.0));
+			gc.circle(-R1, 0., b1);
+			gc.circle(R2, 0., b2);
+			gc.circle(-R2, 0., b2);
+			gc.stroke();
+
+			// let pitch_radius = R1;
+			// let base_radius = b1;
+			// let number_of_teeth = N1;
+			// let addendum = 2.0 * pitch_radius / number_of_teeth as f32;
+			// let clearance = 0.0;
+			// let dedendum = addendum + clearance;
+
+			const Q: usize = 12;
+
+			let stop_angle = involute_radius_to_t((1.0 + 2.0 / N1 as f32) / b);
+			let halfangle = PI / N1 as f32;
+			let ma = Mat2::from_angle(offset - halfangle);
+			let mb = Mat2::from_diagonal(vec2(1., -1.)) * ma;
+			gc.new_path();
+			for i in 0..N1 {
+				let m = Mat2::from_angle(i as f32 / N1 as f32 * 2. * PI);
+				for k in 0..=Q {
+					let t = k as f32 / Q as f32;
+					let p = b1 * m * ma * involute(stop_angle * t) - vec2(R1, 0.);
+					gc.line_to(p.x, p.y);
+				}
+				for k in 0..=Q {
+					let t = 1. - k as f32 / Q as f32;
+					let p = b1 * m * mb * involute(stop_angle * t) - vec2(R1, 0.);
+					gc.line_to(p.x, p.y);
+				}
+			}
+			gc.close_path();
+			gc.stroke_color(Rgba(0.1, 0.8, 0.1, 1.0));
+			gc.stroke();
+
+			let stop_angle = involute_radius_to_t((1.0 + 2.0 / N2 as f32) / b);
+			let halfangle = PI / N2 as f32;
+			let ma = Mat2::from_angle(offset - halfangle);
+			let mb = Mat2::from_diagonal(vec2(1., -1.)) * ma;
+			gc.new_path();
+			for i in 0..N2 {
+				let m = Mat2::from_angle((i as f32 - 0.5) / N2 as f32 * 2. * PI);
+				for k in 0..=Q {
+					let t = k as f32 / Q as f32;
+					let p = b2 * m * ma * involute(stop_angle * t) + vec2(R2, 0.);
+					gc.line_to(p.x, p.y);
+				}
+				for k in 0..=Q {
+					let t = 1. - k as f32 / Q as f32;
+					let p = b2 * m * mb * involute(stop_angle * t) + vec2(R2, 0.);
+					gc.line_to(p.x, p.y);
+				}
+			}
+			gc.close_path();
+			gc.stroke_color(Rgba(0.1, 0.8, 0.1, 1.0));
+			gc.stroke();
+
+			gc.new_path();
+			gc.stroke_color(Rgba(0.1, 0.4, 0.8, 1.0));
+			gc.move_to(-5., 0.);
+			gc.line_to(5., 0.);
+			gc.stroke();
+
+			return;
+
+			let m = Mat2::IDENTITY; // Mat2::from_angle(-offset);
+
+			gc.new_path();
+			for k in 0..=Q {
+				let t = k as f32 / Q as f32;
+				let p = vec2(R2, 0.) - b2 * m * involute(t);
+				gc.line_to(p.x, p.y);
+			}
+			gc.stroke_color(Rgba(0.1, 0.8, 0.1, 1.0));
+			gc.stroke();
+
+			gc.new_path();
+			for k in 0..=Q {
+				let t = k as f32 / Q as f32;
+				let m1 = Mat2::from_angle(A - t);
+				let m2 = Mat2::from_angle((A - t) * R1 / R2);
+				let p = b1 * m1 * m * involute(t) - vec2(R1, 0.);
+				let p = m2 * (p - vec2(R2, 0.)) + vec2(R2, 0.);
+				gc.line_to(p.x, p.y);
+			}
+			gc.stroke_color(Rgba(0.8, 0.8, 0.1, 1.0));
+			gc.stroke();
+
+			gc.new_path();
+			for k in 0..=Q {
+				let t = k as f32 / Q as f32;
+				let m1 = Mat2::from_angle(A - t);
+				let m2 = Mat2::from_angle((t - A) * R1 / R2);
+				let p = b1 * m1 * m * involute(t) - vec2(R1, 0.);
+				let p = m2 * (p + vec2(R2, 0.)) - vec2(R2, 0.);
+				gc.line_to(p.x, p.y);
+			}
+			gc.stroke_color(Rgba(0.8, 0.1, 0.1, 1.0));
+			gc.stroke();
+
+			gc.new_path();
+			for k in 0..=Q {
+				let t = k as f32 / Q as f32;
+				let m1 = Mat2::from_angle(A - t);
+				let m2 = Mat2::from_angle(t - A);
+				let p = b2 * m1 * m * involute(t) - vec2(R2, 0.);
+				let p = m2 * (p + vec2(R2, 0.)) - vec2(R2, 0.);
+				gc.line_to(p.x, p.y);
+			}
+			gc.stroke_color(Rgba(0.8, 0.4, 0.1, 1.0));
+			gc.stroke();
+
+			gc.new_path();
+			for k in 0..=Q {
+				let t = k as f32 / Q as f32;
+				let p = b2 * m * involute(t) - vec2(R2, 0.);
+				gc.line_to(p.x, p.y);
+			}
+			gc.stroke_color(Rgba(0.1, 0.8, 0.8, 0.5));
+			gc.stroke();
+		});
+	});
+}