noteuclid/gear-teeth
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unify shaping code

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This commit is contained in:
numzero 2026-10-08 20:03:53 +03:00
parent 07be8faadc
commit 52baff44c3
1 changed files with 44 additions and 46 deletions
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90
src/main.rs
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@ -13,26 +13,32 @@ const fn rad(deg: f32) -> f32 {
const ADDENDUM: f32 = 1.00;
const DEDENDUM: f32 = 1.25;
const PRESSURE_ANGLE: f32 = rad(20.0);
const PITCH: f32 = PI;
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();
#[derive(Debug, Clone, Copy)]
struct Profile {
addemdum: f32,
dedendum: f32,
pressure_angle: f32,
}
fn rack_shape(x: f32, profile: &Profile) -> f32 {
let x = (x / PI).fract_gl() * PI;
let a = profile.addemdum * vec2(profile.pressure_angle.tan(), 1.0);
let d = profile.dedendum * vec2(profile.pressure_angle.tan(), -1.0);
let slope = 1.0 / profile.pressure_angle.tan();
if x < d.x {
return -x * slope;
}
if x <= 0.5 * PITCH - d.x {
if x <= 0.5 * PI - d.x {
return d.y;
}
if x <= 0.5 * PITCH + a.x {
return (x - 0.5 * PITCH) * slope;
if x <= 0.5 * PI + a.x {
return (x - 0.5 * PI) * slope;
}
if x <= PITCH - a.x {
if x <= PI - a.x {
return a.y;
}
return (PITCH - x) * slope;
return (PI - x) * slope;
}
const FPS: f32 = 60.0;
@ -52,6 +58,18 @@ fn main() {
let n_teeth = 36;
let n_teeth_sample = n_teeth;
let r_pitch = 0.5 * n_teeth as f32;
let gear_profile = Profile {
addemdum: ADDENDUM,
dedendum: DEDENDUM,
pressure_angle: PRESSURE_ANGLE,
};
let cutter_profile = Profile {
addemdum: gear_profile.dedendum,
dedendum: gear_profile.addemdum,
pressure_angle: gear_profile.pressure_angle,
};
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];
@ -77,6 +95,9 @@ fn main() {
let gear_offset = t * TPS - (n_teeth_sample as f32 + 5.0);
let rack_offset = (t * TPS).fract_gl();
let rack_y_at_x = |x, profile| rack_shape(x - rack_offset * PI, profile);
let cutter_y_at_x = |x| rack_y_at_x(x, &cutter_profile);
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;
@ -87,7 +108,7 @@ fn main() {
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);
let cut_y = cutter_y_at_x(xy.x);
if cut_y < xy.y {
break;
}
@ -95,50 +116,27 @@ fn main() {
}
}
#[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();
let mut pts_rack = Vec::new();
let mut pts_cutter = 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));
for k in 0..n_points_per_tooth {
let x = (tooth as f32 + k as f32 / n_points_per_tooth as f32 + rack_offset)
* PI;
pts_rack.push(vec2(x, rack_y_at_x(x, &gear_profile)));
pts_cutter.push(vec2(x, cutter_y_at_x(x)));
}
}
line(gc, pts);
line(gc, pts_cutter);
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);
line(gc, pts_rack);
gc.stroke_color(Rgba(0.1, 1.0, 0.1, 0.4));
gc.stroke();
});