noteuclid/refraction
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Split the metric into two functions

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numzero 2024-06-10 15:29:57 +03:00
parent 08fbff38fa
commit 4e6c3b19ae
1 changed files with 45 additions and 18 deletions
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63
src/bin/flat.rs
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@ -543,16 +543,46 @@ struct Rect {
} }
impl Rect { impl Rect {
fn γ(&self) -> f32 { self.external_halflength / self.internal_halflength } fn fx(&self) -> fns::RectX { fns::RectX { min: self.inner_radius, max: self.outer_radius } }
fn a(&self) -> f32 { -(self.γ() - 1.0) / self.internal_halflength } fn fy(&self) -> fns::RectY { fns::RectY { internal: self.internal_halflength, external: self.external_halflength } }
fn b(&self) -> f32 { 2.0 * self.γ() - 1.0 }
fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x).sqrt() } pub fn x(&self, u: f32) -> f32 { self.fy().x(u) }
fn d(&self, u: f32) -> f32 { 2.0 * self.a() * u + self.b() } pub fn u(&self, x: f32) -> f32 { self.fy().u(x) }
pub fn x(&self, u: f32) -> f32 { (self.a() * u.abs() + self.b()) * u } pub fn dx(&self, u: f32, du: f32) -> f32 { self.fy().dx(u, du) }
pub fn u(&self, x: f32) -> f32 { 0.5 * x.signum() * (-self.b() + self.root(x.abs())) / self.a() } pub fn du(&self, x: f32, dx: f32) -> f32 { self.fy().du(x, dx) }
pub fn dx(&self, u: f32, du: f32) -> f32 { du * self.d(u.abs()) } }
pub fn du(&self, x: f32, dx: f32) -> f32 { dx / self.root(x.abs()) }
mod fns {
pub struct RectX {
pub min: f32,
pub max: f32,
}
impl RectX {
pub fn value(&self, x: f32) -> f32 { ((x.abs() - self.min) / (self.max - self.min)).clamp(0.0, 1.0) }
pub fn derivative(&self, x: f32) -> f32 { if x.abs() > self.min && x.abs() < self.max { x.signum() / (self.max - self.min) } else { 0.0 } }
}
pub struct RectY {
pub internal: f32,
pub external: f32,
}
impl RectY {
fn γ(&self) -> f32 { self.external / self.internal }
fn a(&self) -> f32 { -(self.γ() - 1.0) / self.internal }
fn b(&self) -> f32 { 2.0 * self.γ() - 1.0 }
fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x).sqrt() }
fn d(&self, u: f32) -> f32 { 2.0 * self.a() * u + self.b() }
pub fn x(&self, u: f32) -> f32 { (self.a() * u.abs() + self.b()) * u }
pub fn u(&self, x: f32) -> f32 { 0.5 * x.signum() * (-self.b() + self.root(x.abs())) / self.a() }
pub fn dx(&self, u: f32, du: f32) -> f32 { du * self.d(u.abs()) }
pub fn du(&self, x: f32, dx: f32) -> f32 { dx / self.root(x.abs()) }
pub fn value(&self, x: f32) -> f32 { if x.abs() <= self.external { 1.0 / self.root(x.abs()) } else { 1.0 } }
pub fn derivative(&self, x: f32) -> f32 { if x.abs() <= self.external { -2.0 * x.signum() * self.a() * self.root(x.abs()).powi(-3) } else { 0.0 } }
}
} }
#[test] #[test]
@ -606,9 +636,8 @@ impl FloatExt2 for (f32, f32) {
impl Metric for Rect { impl Metric for Rect {
fn sqrt_at(&self, pos: Vec2) -> Decomp2 { fn sqrt_at(&self, pos: Vec2) -> Decomp2 {
let y = pos.y.abs(); let sx = self.fx().value(pos.x);
let sx = ((pos.x.abs() - self.inner_radius) / (self.outer_radius - self.inner_radius)).clamp(0.0, 1.0); let sy = self.fy().value(pos.y);
let sy = if y <= self.external_halflength { 1.0 / self.root(y) } else { 1.0 };
assert!(sx.is_finite()); assert!(sx.is_finite());
assert!(sy.is_finite()); assert!(sy.is_finite());
assert!(sy > 0.0); assert!(sy > 0.0);
@ -619,13 +648,11 @@ impl Metric for Rect {
} }
fn part_derivs_at(&self, pos: Vec2) -> Tens2 { fn part_derivs_at(&self, pos: Vec2) -> Tens2 {
let x = pos.x.abs(); let sx = self.fx().value(pos.x);
let y = pos.y.abs(); let sy = self.fy().value(pos.y);
let sx = ((x - self.inner_radius) / (self.outer_radius - self.inner_radius)).clamp(0.0, 1.0);
let sy = if y <= self.external_halflength { 1.0 / self.root(y) } else { 1.0 };
let s = (sy, 1.0).lerp(sx); let s = (sy, 1.0).lerp(sx);
let dsx_dx = if x > self.inner_radius && x < self.outer_radius { pos.x.signum() / (self.outer_radius - self.inner_radius) } else { 0.0 }; let dsx_dx = self.fx().derivative(pos.x);
let dsy_dy = if y <= self.external_halflength { -2.0 * pos.y.signum() * self.a() * sy.powi(3) } else { 0.0 }; let dsy_dy = self.fy().derivative(pos.y);
let ds2_dx = 2.0 * s * (1.0 - sy) * dsx_dx; let ds2_dx = 2.0 * s * (1.0 - sy) * dsx_dx;
let ds2_dy = 2.0 * s * (1.0 - sx) * dsy_dy; let ds2_dy = 2.0 * s * (1.0 - sx) * dsy_dy;
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