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
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137

use na::{DefaultAllocator, RealField};

use crate::aliases::TVec;
use crate::traits::{Alloc, Dimension};

/// The squared distance between two points.
///
/// # See also:
///
/// * [`distance`](fn.distance.html)
pub fn distance2<N: RealField, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    (p1 - p0).norm_squared()
}

/// The l1-norm of `x - y`.
///
/// # See also:
///
/// * [`l1_norm`](fn.l1_norm.html)
/// * [`l2_distance`](fn.l2_distance.html)
/// * [`l2_norm`](fn.l2_norm.html)
pub fn l1_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    l1_norm(&(y - x))
}

/// The l1-norm of `v`.
///
/// This is also known as the "Manhattan distance" or "taxicab distance" and
/// corresponds to the sum of the absolute values of the components of `v`.
///
/// # See also:
///
/// * [`l1_distance`](fn.l1_distance.html)
/// * [`l2_distance`](fn.l2_distance.html)
/// * [`l2_norm`](fn.l2_norm.html)
pub fn l1_norm<N: RealField, D: Dimension>(v: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    crate::comp_add(&v.abs())
}

/// The l2-norm of `x - y`.
///
/// This is the same value as returned by [`length2`](fn.length2.html) and
/// [`magnitude2`](fn.magnitude2.html).
///
/// # See also:
///
/// * [`l1_distance`](fn.l1_distance.html)
/// * [`l1_norm`](fn.l1_norm.html)
/// * [`l2_norm`](fn.l2_norm.html)
/// * [`length`](fn.length.html)
/// * [`length2`](fn.length2.html)
/// * [`magnitude`](fn.magnitude.html)
/// * [`magnitude2`](fn.magnitude2.html)
pub fn l2_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    l2_norm(&(y - x))
}

/// The l2-norm of `v`.
///
/// This is also known as the Euclidean norm.
///
/// This is the same value as returned by [`length`](fn.length.html) and
/// [`magnitude`](fn.magnitude.html).
///
/// # See also:
///
/// * [`l1_distance`](fn.l1_distance.html)
/// * [`l1_norm`](fn.l1_norm.html)
/// * [`l2_distance`](fn.l2_distance.html)
/// * [`length`](fn.length.html)
/// * [`length2`](fn.length2.html)
/// * [`magnitude`](fn.magnitude.html)
/// * [`magnitude2`](fn.magnitude2.html)
pub fn l2_norm<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    x.norm()
}

/// The squared magnitude of `x`.
///
/// A synonym for [`magnitude2`](fn.magnitude2.html).
///
/// # See also:
///
/// * [`distance`](fn.distance.html)
/// * [`distance2`](fn.distance2.html)
/// * [`length`](fn.length.html)
/// * [`magnitude`](fn.magnitude.html)
/// * [`magnitude2`](fn.magnitude2.html)
pub fn length2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    x.norm_squared()
}

/// The squared magnitude of `x`.
///
/// A wrapper around [`nalgebra::norm_squared`](../nalgebra/fn.norm_squared.html).
///
/// # See also:
///
/// * [`distance`](fn.distance.html)
/// * [`distance2`](fn.distance2.html)
/// * [`length2`](fn.length2.html)
/// * [`magnitude`](fn.magnitude.html)
/// * [`nalgebra::norm_squared`](../nalgebra/fn.norm_squared.html)
pub fn magnitude2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
where
    DefaultAllocator: Alloc<N, D>,
{
    x.norm_squared()
}

//pub fn lxNorm<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, unsigned int Depth) -> N
//    where DefaultAllocator: Alloc<N, D> {
//    unimplemented!()
//}
//
//pub fn lxNorm<N: RealField, D: Dimension>(x: &TVec<N, D>, unsigned int Depth) -> N
//    where DefaultAllocator: Alloc<N, D> {
//    unimplemented!()
//}