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

//!Contains primitive objects and traits for performing vector geometry

pub mod cartesian1;
pub mod cartesian2;
pub mod cartesian3;
pub mod space;
pub use self::cartesian1::*;
pub use self::cartesian2::*;
pub use self::cartesian3::*;
pub use self::space::*;

extern crate num;
extern crate nalgebra as na;
use self::num::{Float, Zero, FromPrimitive};
use std::ops::{Add, Sub, Neg, Mul, Div};
use std::f64::consts::PI;

///Trait that implements all the functions necessary for any n-dimensional vector
pub trait Vector<D>: Sized + Clone + Copy + Zero + Add<Self, Output=Self> + Sub<Self, Output=Self> + Neg<Output=Self> +
    Mul<D, Output=Self> + Div<D, Output=Self>
    where D: Float
{
    ///Returns the space contained by an n-sphere with edge displacement d in the dimensional system of this vector
    fn space_ball(d: D) -> D;

    ///Returns the result of the cos of the angle between two vectors multiplied by their magnitudes
    fn dot(&lhs: &Self, rhs: &Self) -> D;

    ///Returns the space contained by the vector relative to the origin forming a box
    fn space_box(&self) -> D;

    ///Returns the length of a vector
    fn displacement(&self) -> D;

    ///Returns the squared length of a vector; this is more efficient than displacement() for cartesian vectors
    fn displacement_squared(&self) -> D {
        self.displacement().powi(2)
    }

    ///Returns a vector in the same direction as this one, but with length 1
    fn normalized(&self) -> Self {
        *self / self.displacement()
    }

    ///Make this vector normalized().
    fn normalize(&mut self) {
        *self = self.normalized();
    }
}

#[test]
fn dot_vector() {
    let a = Cartesian2::new(0.3, 0.5);
    let _b = Cartesian2::dot(&a, &Cartesian2::new(1.0, 0.5));
}

///CrossVector is a Vector that has dimensions such that the cross product can be computed.
pub trait CrossVector {
    fn cross(lhs: &Self, rhs: &Self) -> Self;
}

#[test]
fn cross_vector() {
    let a = Cartesian3::new(0.3, 0.5, 1.0);
    let _b = Cartesian3::cross(&a, &Cartesian3::new(1.0, 0.5, -2.0));
}

impl<D> Vector<D> for na::Vec1<D>
    where D: Float + FromPrimitive
{
    fn space_ball(d: D) -> D {
        D::from_u32(2u32).unwrap() * d
    }
    fn dot(&lhs: &Self, rhs: &Self) -> D {
        lhs.x * rhs.x
    }
    fn space_box(&self) -> D {
        self.x
    }
    fn displacement(&self) -> D {
        self.x
    }
}

impl<D> Vector<D> for na::Vec2<D>
    where D: Float + FromPrimitive
{
    fn space_ball(d: D) -> D {
        D::from_f64(PI).unwrap() * d * d
    }
    fn dot(&lhs: &Self, rhs: &Self) -> D {
        lhs.x * rhs.x + lhs.y * rhs.y
    }
    fn space_box(&self) -> D {
        self.x * self.y
    }
    fn displacement(&self) -> D {
        self.displacement_squared().sqrt()
    }
    fn displacement_squared(&self) -> D {
        self.x * self.x + self.y * self.y
    }
}

impl<D> Vector<D> for na::Vec3<D>
    where D: Float + FromPrimitive
{
    fn space_ball(d: D) -> D {
        d * d * d * D::from_f64(4.0 / 3.0 * PI).unwrap()
    }
    fn dot(&lhs: &Self, rhs: &Self) -> D {
        lhs.x * rhs.x + lhs.y * rhs.y + lhs.z * rhs.z
    }
    fn space_box(&self) -> D {
        self.x * self.y * self.z
    }
    fn displacement(&self) -> D {
        self.displacement_squared().sqrt()
    }
    fn displacement_squared(&self) -> D {
        self.x * self.x + self.y * self.y + self.z * self.z
    }
}

impl<D> CrossVector for na::Vec3<D>
    where D: Float
{
    fn cross(lhs: &Self, rhs: &Self) -> Self {
        na::Vec3{
            x: lhs.y * rhs.z - lhs.z * rhs.y,
            y: lhs.z * rhs.x - lhs.x * rhs.z,
            z: lhs.x * rhs.y - lhs.y * rhs.x,
        }
    }
}