     1
     2
     3
     4
     5
     6
     7
     8
     9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95

    // Copyright 2018 Developers of the Rand project.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    #![allow(deprecated)]

    use crate::Rng;
    use crate::distributions::{Distribution, Uniform};

    /// 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<R: Rng + ?Sized>(&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 crate::distributions::Distribution;
        use super::UnitSphereSurface;

        /// 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);
        }
    }

# Help

## Keyboard Shortcuts

`?`
  Show this help dialog
`S`
  Focus the search field
`↑`
  Move up in search results
`↓`
  Move down in search results
`↹`
  Switch tab
`⏎`
  Go to active search result
`+`
  Expand all sections
`-`
  Collapse all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g., `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g., `vec -> usize` or `* -> vec`)

Search multiple things at once by splitting your query with comma (e.g., `str,u8` or `String,struct:Vec,test`)