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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 { + 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(); + }); + }); +}