ncollide_math 0.6.0

2 and 3-dimensional collision detection library in Rust: module describing the algebraic entities used by ncollide.
Documentation 
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use std::fmt::Display;
use num::Bounded;
use approx::ApproxEq;

use alga::general::{Lattice, Real};
use alga::linear::{InnerSpace, FiniteDimInnerSpace};
use na::{self, ColumnVector};
use na::dimension::{U1, U2, U3};
use na::storage::OwnedStorage;
use na::allocator::{Allocator, OwnedAllocator};

/// Trait implemented by vector types usable by ncollide.
pub trait Vector: Copy + Send + Sync + 'static +
                  Display +
                  Lattice +
                  Bounded +
                  ApproxEq<Epsilon = <Self as InnerSpace>::Real> +
                  FiniteDimInnerSpace {
    /// Iterate through the samples.
    fn sample_sphere<F: FnMut(Self)>(F);
}

impl<N, S> Vector for ColumnVector<N, U2, S>
    where N: Real + Display,
          S: Send + Sync + Copy + 'static + OwnedStorage<N, U2, U1>,
          S::Alloc: OwnedAllocator<N, U2, U1, S> +
                    Allocator<usize, U2, U1> {

    #[inline(always)]
    fn sample_sphere<F: FnMut(Self)>(mut f: F) {
        for e in SAMPLES_2_F64.iter() {
            let mut s = unsafe { Self::new_uninitialized() };
            s[0] = na::convert(e[0]);
            s[1] = na::convert(e[1]);
            f(s)
        }
    }
}

impl<N, S> Vector for ColumnVector<N, U3, S>
    where N: Real + Display,
          S: Send + Sync + Copy + 'static + OwnedStorage<N, U3, U1>,
          S::Alloc: OwnedAllocator<N, U3, U1, S> +
                    Allocator<usize, U3, U1> {

    #[inline(always)]
    fn sample_sphere<F: FnMut(Self)>(mut f: F) {
        for e in SAMPLES_3_F64.iter() {
            let mut s = unsafe { Self::new_uninitialized() };
            s[0] = na::convert(e[0]);
            s[1] = na::convert(e[1]);
            s[2] = na::convert(e[2]);
            f(s)
        }
    }
}

// FIXME: this is bad: this fixes definitely the number of samples…
static SAMPLES_2_F64: [[ f64; 2 ]; 21] = [
    [ 1.0,         0.0         ],
    [ 0.95557281,  0.29475517  ],
    [ 0.82623877,  0.56332006  ],
    [ 0.6234898,   0.78183148  ],
    [ 0.36534102,  0.93087375  ],
    [ 0.07473009,  0.9972038   ],
    [ -0.22252093, 0.97492791  ],
    [ -0.5,        0.8660254   ],
    [ -0.73305187, 0.68017274  ],
    [ -0.90096887, 0.43388374  ],
    [ -0.98883083, 0.14904227  ],
    [ -0.98883083, -0.14904227 ],
    [ -0.90096887, -0.43388374 ],
    [ -0.73305187, -0.68017274 ],
    [ -0.5,        -0.8660254  ],
    [ -0.22252093, -0.97492791 ],
    [ 0.07473009,  -0.9972038  ],
    [ 0.36534102,  -0.93087375 ],
    [ 0.6234898,   -0.78183148 ],
    [ 0.82623877,  -0.56332006 ],
    [ 0.95557281,  -0.29475517 ],
];


// Those vectors come from bullet 3d
static SAMPLES_3_F64: [[ f64; 3 ]; 42] = [
    [ 0.000000 , -0.000000, -1.000000 ],
    [ 0.723608 , -0.525725, -0.447219 ],
    [ -0.276388, -0.850649, -0.447219 ],
    [ -0.894426, -0.000000, -0.447216 ],
    [ -0.276388, 0.850649 , -0.447220 ],
    [ 0.723608 , 0.525725 , -0.447219 ],
    [ 0.276388 , -0.850649, 0.447220  ],
    [ -0.723608, -0.525725, 0.447219  ],
    [ -0.723608, 0.525725 , 0.447219  ],
    [ 0.276388 , 0.850649 , 0.447219  ],
    [ 0.894426 , 0.000000 , 0.447216  ],
    [ -0.000000, 0.000000 , 1.000000  ],
    [ 0.425323 , -0.309011, -0.850654 ],
    [ -0.162456, -0.499995, -0.850654 ],
    [ 0.262869 , -0.809012, -0.525738 ],
    [ 0.425323 , 0.309011 , -0.850654 ],
    [ 0.850648 , -0.000000, -0.525736 ],
    [ -0.525730, -0.000000, -0.850652 ],
    [ -0.688190, -0.499997, -0.525736 ],
    [ -0.162456, 0.499995 , -0.850654 ],
    [ -0.688190, 0.499997 , -0.525736 ],
    [ 0.262869 , 0.809012 , -0.525738 ],
    [ 0.951058 , 0.309013 , 0.000000  ],
    [ 0.951058 , -0.309013, 0.000000  ],
    [ 0.587786 , -0.809017, 0.000000  ],
    [ 0.000000 , -1.000000, 0.000000  ],
    [ -0.587786, -0.809017, 0.000000  ],
    [ -0.951058, -0.309013, -0.000000 ],
    [ -0.951058, 0.309013 , -0.000000 ],
    [ -0.587786, 0.809017 , -0.000000 ],
    [ -0.000000, 1.000000 , -0.000000 ],
    [ 0.587786 , 0.809017 , -0.000000 ],
    [ 0.688190 , -0.499997, 0.525736  ],
    [ -0.262869, -0.809012, 0.525738  ],
    [ -0.850648, 0.000000 , 0.525736  ],
    [ -0.262869, 0.809012 , 0.525738  ],
    [ 0.688190 , 0.499997 , 0.525736  ],
    [ 0.525730 , 0.000000 , 0.850652  ],
    [ 0.162456 , -0.499995, 0.850654  ],
    [ -0.425323, -0.309011, 0.850654  ],
    [ -0.425323, 0.309011 , 0.850654  ],
    [ 0.162456 , 0.499995 , 0.850654  ]
];