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 // Copyright 2018 Developers of the Rand project. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. #![allow(deprecated)] #![allow(clippy::all)] use crate::distributions::{Distribution, Uniform}; use crate::Rng; /// Samples uniformly from the surface of the unit sphere in three dimensions. /// /// Implemented via a method by Marsaglia[^1]. /// /// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a /// Sphere.*](https://doi.org/10.1214/aoms/1177692644) /// Ann. Math. Statist. 43, no. 2, 645--646. #[deprecated(since = "0.7.0", note = "moved to rand_distr crate")] #[derive(Clone, Copy, Debug)] pub struct UnitSphereSurface; impl UnitSphereSurface { /// Construct a new `UnitSphereSurface` distribution. #[inline] pub fn new() -> UnitSphereSurface { UnitSphereSurface } } impl Distribution<[f64; 3]> for UnitSphereSurface { #[inline] fn sample(&self, rng: &mut R) -> [f64; 3] { let uniform = Uniform::new(-1., 1.); loop { let (x1, x2) = (uniform.sample(rng), uniform.sample(rng)); let sum = x1 * x1 + x2 * x2; if sum >= 1. { continue; } let factor = 2. * (1.0_f64 - sum).sqrt(); return [x1 * factor, x2 * factor, 1. - 2. * sum]; } } } #[cfg(test)] mod tests { use super::UnitSphereSurface; use crate::distributions::Distribution; /// Assert that two numbers are almost equal to each other. /// /// On panic, this macro will print the values of the expressions with their /// debug representations. macro_rules! assert_almost_eq { (\$a:expr, \$b:expr, \$prec:expr) => { let diff = (\$a - \$b).abs(); if diff > \$prec { panic!(format!( "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \ (left: `{}`, right: `{}`)", diff, \$prec, \$a, \$b )); } }; } #[test] fn norm() { let mut rng = crate::test::rng(1); let dist = UnitSphereSurface::new(); for _ in 0..1000 { let x = dist.sample(&mut rng); assert_almost_eq!(x[0] * x[0] + x[1] * x[1] + x[2] * x[2], 1., 1e-15); } } #[test] fn value_stability() { let mut rng = crate::test::rng(2); let expected = [ [0.03247542860231647, -0.7830477442152738, 0.6211131755296027], [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952], [0.2735582468624679, 0.9435374242279655, -0.1868234852870203], ]; let samples = [ UnitSphereSurface.sample(&mut rng), UnitSphereSurface.sample(&mut rng), UnitSphereSurface.sample(&mut rng), ]; assert_eq!(samples, expected); } }