cgmath/src/vec.rs

// Copyright 2013 The Lmath Developers. For a full listing of the authors,
// refer to the AUTHORS file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

use std::cast::transmute;
use std::cmp::ApproxEq;
use std::num::{Zero, One};

use num::NumAssign;

/// The base generic vector trait.
///
/// # Type parameters
///
/// - `T`: The type of the components. This is intended to support boolean,
///        integer, unsigned integer, and floating point types.
pub trait BaseVec<T>: Eq {
    /// The component of the vector at the index `i`
    fn index<'a>(&'a self, i: uint) -> &'a T;

    /// Construct the vector from a single value, copying it to each component
    fn from_value(value: T) -> Self;

    /// A pointer to the first component of the vector
    fn to_ptr(&self) -> *T;

    /// Get a mutable reference to the component at `i`
    fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut T;

    /// Swap two components of the vector in place
    fn swap(&mut self, a: uint, b: uint);
}

/// A generic 2-dimensional vector
pub trait BaseVec2<T>: BaseVec<T> {
    fn new(x: T, y: T) -> Self;
}

/// A generic 3-dimensional vector
pub trait BaseVec3<T>: BaseVec<T> {
    fn new(x: T, y: T, z: T) -> Self;
}

/// A generic 4-dimensional vector
pub trait BaseVec4<T>: BaseVec<T> {
    fn new(x: T, y: T, z: T, w: T) -> Self;
}

/// A vector with numeric components
pub trait NumVec<T>: BaseVec<T> + Neg<Self> {
    /// The standard basis vector
    ///
    /// # Return value
    ///
    /// A vector with each component set to one
    fn identity() -> Self;

    /// The null vector
    ///
    /// # Return value
    ///
    /// A vector with each component set to zero
    fn zero() -> Self;

    /// True if the vector is equal to zero
    fn is_zero(&self) -> bool;

    /// The scalar multiplication of the vector and `value`
    fn mul_t(&self, value: T) -> Self;

    /// The scalar division of the vector and `value`
    fn div_t(&self, value: T) -> Self;

    /// Component-wise vector addition
    fn add_v(&self, other: &Self) -> Self;

    /// Component-wise vector subtraction
    fn sub_v(&self, other: &Self) -> Self;

    /// Component-wise vector multiplication
    fn mul_v(&self, other: &Self) -> Self;

    /// Component-wise vector division
    fn div_v(&self, other: &Self) -> Self;

    /// The dot product of the vector and `other`
    fn dot(&self, other: &Self) -> T;

    /// Negate the vector
    fn neg_self(&mut self);

    /// Multiply the vector by a scalar
    fn mul_self_t(&mut self, value: T);

    /// Divide the vector by a scalar
    fn div_self_t(&mut self, value: T);

    /// Set the vector to the component-wise vector sum
    fn add_self_v(&mut self, other: &Self);

    /// Set the vector to the component-wise vector difference
    fn sub_self_v(&mut self, other: &Self);

    /// Set the vector to the component-wise vector product
    fn mul_self_v(&mut self, other: &Self);

    /// Set the vector to the component-wise vector quotient
    fn div_self_v(&mut self, other: &Self);
}

/// A 2-dimensional vector with numeric components
pub trait NumVec2<T>: NumVec<T> {
    fn unit_x() -> Self;
    fn unit_y() -> Self;

    /// The perp dot product of the vector and `other`
    fn perp_dot(&self, other: &Self) -> T;
}

/// A 3-dimensional vector with numeric components
pub trait NumVec3<T>: NumVec<T> {
    fn unit_x() -> Self;
    fn unit_y() -> Self;
    fn unit_z() -> Self;

    /// The cross product of the vector and `other`
    fn cross(&self, other: &Self) -> Self;

    /// Set to the cross product of the vector and `other`
    fn cross_self(&mut self, other: &Self);
}

/// A 4-dimensional vector with numeric components
pub trait NumVec4<T>: NumVec<T> {
    fn unit_x() -> Self;
    fn unit_y() -> Self;
    fn unit_z() -> Self;
    fn unit_w() -> Self;
}

pub trait ToHomogeneous<H> {
    /// Convert to a homogenous coordinate
    fn to_homogeneous(&self) -> H;
}

/// A Euclidean (or Affine) vector
///
/// # Type parameters
///
/// - `T`: The type of the components. This should be a floating point type.
pub trait AffineVec<T>: NumVec<T> {
    /// The squared length of the vector. This is useful for comparisons where
    /// the exact length does not need to be calculated.
    fn length2(&self) -> T;

    /// The length of the vector
    ///
    /// # Performance notes
    ///
    /// For instances where the exact length of the vector does not need to be
    /// known, for example for quaternion-quaternion length comparisons,
    /// it is advisable to use the `length2` method instead.
    fn length(&self) -> T;

    /// The squared distance between the vector and `other`.
    fn distance2(&self, other: &Self) -> T;

    /// The distance between the vector and `other`
    fn distance(&self, other: &Self) -> T;

    /// The angle between the vector and `other` in radians
    fn angle(&self, other: &Self) -> T;

    /// The normalized vector
    fn normalize(&self) -> Self;

    /// Set the length of the vector whilst preserving the direction
    fn normalize_to(&self, length: T) -> Self;

    /// Linearly intoperlate between the vector and `other`
    ///
    /// # Return value
    ///
    /// The intoperlated vector
    fn lerp(&self, other: &Self, amount: T) -> Self;

    /// Normalize the vector
    fn normalize_self(&mut self);

    /// Set the vector to a specified length whilst preserving the direction
    fn normalize_self_to(&mut self, length: T);

    /// Linearly intoperlate the vector towards `other`
    fn lerp_self(&mut self, other: &Self, amount: T);
}

/// Component-wise vector comparison methods
///
/// The methods contained in this trait correspond to the relational functions
/// mentioned in Section 8.7 of the [GLSL 4.30.6 specification]
/// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
pub trait OrdVec<T, BoolVec>: BaseVec<T> {
    /// Component-wise compare of `self < other`
    fn less_than(&self, other: &Self) -> BoolVec;

    /// Component-wise compare of `self <= other`
    fn less_than_equal(&self, other: &Self) -> BoolVec;

    /// Component-wise compare of `self > other`
    fn greater_than(&self, other: &Self) -> BoolVec;

    /// Component-wise compare of `self >= other`
    fn greater_than_equal(&self, other: &Self) -> BoolVec;
}

/// Component-wise equality comparison methods
///
/// The methods contained in this trait correspond to the relational functions
/// mentioned in Section 8.7 of the [GLSL 4.30.6 specification]
/// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
pub trait EqVec<T, BoolVec>: BaseVec<T> {
    /// Component-wise compare of `self == other`
    fn equal(&self, other: &Self) -> BoolVec;

    /// Component-wise compare of `self != other`
    fn not_equal(&self, other: &Self) -> BoolVec;
}

/// A vector with boolean components
///
/// The methods contained in this trait correspond to the relational functions
/// mentioned in Section 8.7 of the [GLSL 4.30.6 specification]
/// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
pub trait BoolVec: BaseVec<bool> {
    /// `true` if of any component is `true`
    fn any(&self) -> bool;

    /// `true` only if all components are `true`
    fn all(&self) -> bool;

    /// the component-wise logical complement
    fn not(&self) -> Self;
}

pub trait TrigVec<T>: BaseVec<T> {
    fn radians(&self) -> Self;
    fn degrees(&self) -> Self;

    // Triganometric functions
    fn sin(&self)                      -> Self;
    fn cos(&self)                      -> Self;
    fn tan(&self)                      -> Self;

    // Inverse triganometric functions
    fn asin(&self)                     -> Self;
    fn acos(&self)                     -> Self;
    fn atan(&self)                     -> Self;
    fn atan2(&self, other: Self)       -> Self;

    // Hyperbolic triganometric functions
    fn sinh(&self)                     -> Self;
    fn cosh(&self)                     -> Self;
    fn tanh(&self)                     -> Self;
    // fn asinh()                      -> Self;
    // fn acosh()                      -> Self;
    // fn atanh()                      -> Self;
}

pub trait ExpVec<T>: BaseVec<T> {
    // Exponential functions
    fn pow_t(&self, n: Self)           -> Self;
    fn pow_v(&self, n: T)              -> Self;
    fn exp(&self)                      -> Self;
    fn exp2(&self)                     -> Self;
    fn ln(&self)                       -> Self;
    fn ln2(&self)                      -> Self;
    fn sqrt(&self)                     -> Self;
    fn inv_sqrt(&self)                 -> Self;
}

pub trait ApproxVec<T>: BaseVec<T> {
    // Whole-number approximation functions
    fn floor(&self)                    -> Self;
    fn trunc(&self)                    -> Self;
    fn round(&self)                    -> Self;
    // fn round_even(&self)            -> Self;
    fn ceil(&self)                     -> Self;
    fn fract(&self)                    -> Self;
}

pub trait SignedVec<T,BV>: BaseVec<T> {
    fn is_positive(&self)    -> BV;
    fn is_negative(&self)    -> BV;
    fn is_nonpositive(&self) -> BV;
    fn is_nonnegative(&self) -> BV;

    fn abs(&self) -> Self;
    fn sign(&self) -> Self;
    fn copysign(&self, other: Self) -> Self;
}

pub trait ExtentVec<T>: BaseVec<T> {
    fn min_v(&self, other: &Self) -> Self;
    fn max_v(&self, other: &Self) -> Self;
    fn clamp_v(&self, mn: &Self, mx: &Self) -> Self;

    fn min_t(&self, other: T) -> Self;
    fn max_t(&self, other: T) -> Self;
    fn clamp_t(&self, mn: T, mx: T) -> Self;
}

pub trait MixVec<T>: BaseVec<T> {
    // Functions for blending numbers together
    fn mix(&self, other: Self, value: Self) -> Self;
    fn smooth_step(&self, edge0: Self, edge1: Self) -> Self;
    fn step(&self, edge: Self) -> Self;
}

// Utility macros

macro_rules! zip_vec2(
    ($a:ident[] $method:ident $b:ident[]) => (
        BaseVec2::new($a.index(0).$method($b.index(0)),
                      $a.index(1).$method($b.index(1)))
    );
    ($a:ident[] $method:ident $b:ident) => (
        BaseVec2::new($a.index(0).$method(&$b),
                      $a.index(1).$method(&$b))
    );
)

macro_rules! zip_vec3(
    ($a:ident[] $method:ident $b:ident[]) => (
        BaseVec3::new($a.index(0).$method($b.index(0)),
                      $a.index(1).$method($b.index(1)),
                      $a.index(2).$method($b.index(2)))
    );
    ($a:ident[] $method:ident $b:ident) => (
        BaseVec3::new($a.index(0).$method(&$b),
                      $a.index(1).$method(&$b),
                      $a.index(2).$method(&$b))
    );
)

macro_rules! zip_vec4(
    ($a:ident[] $method:ident $b:ident[]) => (
        BaseVec4::new($a.index(0).$method($b.index(0)),
                      $a.index(1).$method($b.index(1)),
                      $a.index(2).$method($b.index(2)),
                      $a.index(3).$method($b.index(3)))
    );
    ($a:ident[] $method:ident $b:ident) => (
        BaseVec4::new($a.index(0).$method(&$b),
                      $a.index(1).$method(&$b),
                      $a.index(2).$method(&$b),
                      $a.index(3).$method(&$b))
    );
)

macro_rules! zip_assign(
    ($a:ident[] $method:ident $b:ident[] ..2) => ({ $a.index_mut(0).$method($b.index(0)); $a.index_mut(1).$method($b.index(1)); });
    ($a:ident[] $method:ident $b:ident[] ..3) => ({ zip_assign!($a[] $method $b[] ..2); $a.index_mut(2).$method($b.index(2)); });
    ($a:ident[] $method:ident $b:ident[] ..4) => ({ zip_assign!($a[] $method $b[] ..3); $a.index_mut(3).$method($b.index(3)); });

    ($a:ident[] $method:ident $b:ident ..2) => ({ $a.index_mut(0).$method(&$b); $a.index_mut(1).$method(&$b); });
    ($a:ident[] $method:ident $b:ident ..3) => ({ zip_assign!($a[] $method $b ..2); $a.index_mut(2).$method(&$b); });
    ($a:ident[] $method:ident $b:ident ..4) => ({ zip_assign!($a[] $method $b ..3); $a.index_mut(3).$method(&$b); });
)

/// A 2-dimensional vector
///
/// # Type parameters
///
/// - `T`: The type of the components. This is intended to support boolean,
///        integer, unsigned integer, and floating point types.
///
/// # Fields
///
/// - `x`: the first component of the vector
/// - `y`: the second component of the vector
 #[deriving(Eq)]
pub struct Vec2<T> { x: T, y: T }

impl<T:Copy + Eq> BaseVec<T> for Vec2<T> {
    #[inline(always)]
    fn index<'a>(&'a self, i: uint) -> &'a T {
        unsafe { &'a transmute::<&'a Vec2<T>, &'a [T,..2]>(self)[i] }
    }

    #[inline(always)]
    fn from_value(value: T) -> Vec2<T> {
        BaseVec2::new(value, value)
    }

    #[inline(always)]
    fn to_ptr(&self) -> *T {
        unsafe { transmute(self) }
    }

    #[inline(always)]
    fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut T {
        unsafe { &'a mut transmute::<&'a mut Vec2<T>, &'a mut [T,..2]>(self)[i] }
    }

    #[inline(always)]
    fn swap(&mut self, a: uint, b: uint) {
        let tmp = *self.index(a);
        *self.index_mut(a) = *self.index(b);
        *self.index_mut(b) = tmp;
    }
}

impl<T> BaseVec2<T> for Vec2<T> {
    #[inline(always)]
    fn new(x: T, y: T ) -> Vec2<T> {
        Vec2 { x: x, y: y }
    }
}

impl<T:Copy + Num + NumAssign> NumVec<T> for Vec2<T> {
    #[inline(always)]
    fn identity() -> Vec2<T> {
        BaseVec2::new(One::one::<T>(),
                      One::one::<T>())
    }

    #[inline(always)]
    fn zero() -> Vec2<T> {
        BaseVec2::new(Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn is_zero(&self) -> bool {
        *self.index(0) == Zero::zero() &&
        *self.index(1) == Zero::zero()
    }

    #[inline(always)]
    fn mul_t(&self, value: T) -> Vec2<T> {
        zip_vec2!(self[] mul value)
    }

    #[inline(always)]
    fn div_t(&self, value: T) -> Vec2<T> {
        zip_vec2!(self[] div value)
    }

    #[inline(always)]
    fn add_v(&self, other: &Vec2<T>) -> Vec2<T> {
        zip_vec2!(self[] add other[])
    }

    #[inline(always)]
    fn sub_v(&self, other: &Vec2<T>) -> Vec2<T> {
        zip_vec2!(self[] sub other[])
    }

    #[inline(always)]
    fn mul_v(&self, other: &Vec2<T>) -> Vec2<T> {
        zip_vec2!(self[] mul other[])
    }

    #[inline(always)]
    fn div_v(&self, other: &Vec2<T>) -> Vec2<T> {
        zip_vec2!(self[] div other[])
    }

    #[inline(always)]
    fn dot(&self, other: &Vec2<T>) -> T {
        (*self.index(0)) * (*other.index(0)) +
        (*self.index(1)) * (*other.index(1))
    }

    #[inline(always)]
    fn neg_self(&mut self) {
        *self.index_mut(0) = -self.index(0);
        *self.index_mut(1) = -self.index(1);
    }

    #[inline(always)]
    fn mul_self_t(&mut self, value: T) {
        zip_assign!(self[] mul_assign value ..2);
    }

    #[inline(always)]
    fn div_self_t(&mut self, value: T) {
        zip_assign!(self[] div_assign value ..2);
    }

    #[inline(always)]
    fn add_self_v(&mut self, other: &Vec2<T>) {
        zip_assign!(self[] add_assign other[] ..2);
    }

    #[inline(always)]
    fn sub_self_v(&mut self, other: &Vec2<T>) {
        zip_assign!(self[] sub_assign other[] ..2);
    }

    #[inline(always)]
    fn mul_self_v(&mut self, other: &Vec2<T>) {
        zip_assign!(self[] mul_assign other[] ..2);
    }

    #[inline(always)]
    fn div_self_v(&mut self, other: &Vec2<T>) {
        zip_assign!(self[] div_assign other[] ..2);
    }
}

impl<T:Copy + Num> Neg<Vec2<T>> for Vec2<T> {
    #[inline(always)]
    fn neg(&self) -> Vec2<T> {
        BaseVec2::new(-self.index(0), -self.index(1))
    }
}

impl<T:Copy + Num> NumVec2<T> for Vec2<T> {
    #[inline(always)]
    fn unit_x() -> Vec2<T> {
        BaseVec2::new(One::one::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_y() -> Vec2<T> {
        BaseVec2::new(Zero::zero::<T>(),
                      One::one::<T>())
    }

    #[inline(always)]
    fn perp_dot(&self, other: &Vec2<T>) ->T {
        (*self.index(0) * *other.index(1)) - (*self.index(1) * *other.index(0))
    }
}

impl<T:Copy + Num> ToHomogeneous<Vec3<T>> for Vec2<T> {
    #[inline(always)]
    fn to_homogeneous(&self) -> Vec3<T> {
        BaseVec3::new(self.x, self.y, Zero::zero())
    }
}

impl<T:Copy + Real + NumAssign> AffineVec<T> for Vec2<T> {
    #[inline(always)]
    fn length2(&self) -> T {
        self.dot(self)
    }

    #[inline(always)]
    fn length(&self) -> T {
        self.length2().sqrt()
    }

    #[inline(always)]
    fn distance2(&self, other: &Vec2<T>) -> T {
        other.sub_v(self).length2()
    }

    #[inline(always)]
    fn distance(&self, other: &Vec2<T>) -> T {
        other.distance2(self).sqrt()
    }

    #[inline(always)]
    fn angle(&self, other: &Vec2<T>) -> T {
        self.perp_dot(other).atan2(self.dot(other))
    }

    #[inline(always)]
    fn normalize(&self) -> Vec2<T> {
        self.mul_t(One::one::<T>()/self.length())
    }

    #[inline(always)]
    fn normalize_to(&self, length: T) -> Vec2<T> {
        self.mul_t(length / self.length())
    }

    #[inline(always)]
    fn lerp(&self, other: &Vec2<T>, amount: T) -> Vec2<T> {
        self.add_v(&other.sub_v(self).mul_t(amount))
    }

    #[inline(always)]
    fn normalize_self(&mut self) {
        let n = One::one::<T>() / self.length();
        self.mul_self_t(n);
    }

    #[inline(always)]
    fn normalize_self_to(&mut self, length: T) {
        let n = length / self.length();
        self.mul_self_t(n);
    }

    fn lerp_self(&mut self, other: &Vec2<T>, amount: T) {
        let v = other.sub_v(self).mul_t(amount);
        self.add_self_v(&v);
    }
}

impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Vec2<T> {
    #[inline(always)]
    fn approx_epsilon() -> T {
        ApproxEq::approx_epsilon::<T,T>()
    }

    #[inline(always)]
    fn approx_eq(&self, other: &Vec2<T>) -> bool {
        self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
    }

    #[inline(always)]
    fn approx_eq_eps(&self, other: &Vec2<T>, epsilon: &T) -> bool {
        self.index(0).approx_eq_eps(other.index(0), epsilon) &&
        self.index(1).approx_eq_eps(other.index(1), epsilon)
    }
}

impl<T:Copy + Ord + Eq> OrdVec<T, Vec2<bool>> for Vec2<T> {
    #[inline(always)]
    fn less_than(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] lt other[])
    }

    #[inline(always)]
    fn less_than_equal(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] le other[])
    }

    #[inline(always)]
    fn greater_than(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] gt other[])
    }

    #[inline(always)]
    fn greater_than_equal(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] ge other[])
    }
}

impl<T:Copy + Eq> EqVec<T, Vec2<bool>> for Vec2<T> {
    #[inline(always)]
    fn equal(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] eq other[])
    }

    #[inline(always)]
    fn not_equal(&self, other: &Vec2<T>) -> Vec2<bool> {
        zip_vec2!(self[] ne other[])
    }
}

impl BoolVec for Vec2<bool> {
    #[inline(always)]
    fn any(&self) -> bool {
        *self.index(0) || *self.index(1)
    }

    #[inline(always)]
    fn all(&self) -> bool {
        *self.index(0) && *self.index(1)
    }

    #[inline(always)]
    fn not(&self) -> Vec2<bool> {
        BaseVec2::new(!*self.index(0), !*self.index(1))
    }
}

// GLSL-style type aliases, corresponding to Section 4.1.5 of the [GLSL 4.30.6 specification]
// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).

// a two-component single-precision floating-point vector
pub type vec2  = Vec2<f32>;
// a two-component double-precision floating-point vector
pub type dvec2 = Vec2<f64>;
// a two-component Boolean vector
pub type bvec2 = Vec2<bool>;
// a two-component signed integer vector
pub type ivec2 = Vec2<i32>;
// a two-component unsigned integer vector
pub type uvec2 = Vec2<u32>;

// Rust-style type aliases
pub type Vec2f   = Vec2<float>;
pub type Vec2f32 = Vec2<f32>;
pub type Vec2f64 = Vec2<f64>;
pub type Vec2i   = Vec2<int>;
pub type Vec2i8  = Vec2<i8>;
pub type Vec2i16 = Vec2<i16>;
pub type Vec2i32 = Vec2<i32>;
pub type Vec2i64 = Vec2<i64>;
pub type Vec2u   = Vec2<uint>;
pub type Vec2u8  = Vec2<u8>;
pub type Vec2u16 = Vec2<u16>;
pub type Vec2u32 = Vec2<u32>;
pub type Vec2u64 = Vec2<u64>;
pub type Vec2b   = Vec2<bool>;

/// A 3-dimensional vector
///
/// # Type parameters
///
/// - `T`: The type of the components. This is intended to support boolean,
///         integer, unsigned integer, and floating point types.
///
/// # Fields
///
/// - `x`: the first component of the vector
/// - `y`: the second component of the vector
/// - `z`: the third component of the vector
#[deriving(Eq)]
pub struct Vec3<T> { x: T, y: T, z: T }

impl<T:Copy + Eq> BaseVec<T> for Vec3<T> {
    #[inline(always)]
    fn index<'a>(&'a self, i: uint) -> &'a T {
        unsafe { &'a transmute::<&'a Vec3<T>, &'a [T,..3]>(self)[i] }
    }

    #[inline(always)]
    fn from_value(value: T) -> Vec3<T> {
        BaseVec3::new(value, value, value)
    }

    #[inline(always)]
    fn to_ptr(&self) -> *T {
        unsafe { transmute(self) }
    }

    #[inline(always)]
    fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut T {
        unsafe { &mut transmute::<&'a mut Vec3<T>, &'a mut [T,..3]>(self)[i] }
    }

    #[inline(always)]
    fn swap(&mut self, a: uint, b: uint) {
        let tmp = *self.index(a);
        *self.index_mut(a) = *self.index(b);
        *self.index_mut(b) = tmp;
    }
}

impl<T> BaseVec3<T> for Vec3<T> {
    #[inline(always)]
    fn new(x: T, y: T, z: T) -> Vec3<T> {
        Vec3 { x: x, y: y, z: z }
    }
}

impl<T:Copy + Num + NumAssign> NumVec<T> for Vec3<T> {
    #[inline(always)]
    fn identity() -> Vec3<T> {
        BaseVec3::new(One::one::<T>(),
                      One::one::<T>(),
                      One::one::<T>())
    }

    #[inline(always)]
    fn zero() -> Vec3<T> {
        BaseVec3::new(Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn is_zero(&self) -> bool {
        *self.index(0) == Zero::zero() &&
        *self.index(1) == Zero::zero() &&
        *self.index(2) == Zero::zero()
    }

    #[inline(always)]
    fn mul_t(&self, value: T) -> Vec3<T> {
        zip_vec3!(self[] mul value)
    }

    #[inline(always)]
    fn div_t(&self, value: T) -> Vec3<T> {
        zip_vec3!(self[] div value)
    }

    #[inline(always)]
    fn add_v(&self, other: &Vec3<T>) -> Vec3<T> {
        zip_vec3!(self[] add other[])
    }

    #[inline(always)]
    fn sub_v(&self, other: &Vec3<T>) -> Vec3<T> {
        zip_vec3!(self[] sub other[])
    }

    #[inline(always)]
    fn mul_v(&self, other: &Vec3<T>) -> Vec3<T> {
        zip_vec3!(self[] mul other[])
    }

    #[inline(always)]
    fn div_v(&self, other: &Vec3<T>) -> Vec3<T> {
        zip_vec3!(self[] div other[])
    }

    #[inline(always)]
    fn dot(&self, other: &Vec3<T>) -> T {
        (*self.index(0)) * (*other.index(0)) +
        (*self.index(1)) * (*other.index(1)) +
        (*self.index(2)) * (*other.index(2))
    }

    #[inline(always)]
    fn neg_self(&mut self) {
        *self.index_mut(0) = -self.index(0);
        *self.index_mut(1) = -self.index(1);
        *self.index_mut(2) = -self.index(2);
    }

    #[inline(always)]
    fn mul_self_t(&mut self, value: T) {
        zip_assign!(self[] mul_assign value ..3);
    }

    #[inline(always)]
    fn div_self_t(&mut self, value: T) {
        zip_assign!(self[] div_assign value ..3);
    }

    #[inline(always)]
    fn add_self_v(&mut self, other: &Vec3<T>) {
        zip_assign!(self[] add_assign other[] ..3);
    }

    #[inline(always)]
    fn sub_self_v(&mut self, other: &Vec3<T>) {
        zip_assign!(self[] sub_assign other[] ..3);
    }

    #[inline(always)]
    fn mul_self_v(&mut self, other: &Vec3<T>) {
        zip_assign!(self[] mul_assign other[] ..3);
    }

    #[inline(always)]
    fn div_self_v(&mut self, other: &Vec3<T>) {
        zip_assign!(self[] div_assign other[] ..3);
    }
}

impl<T:Copy + Num> Neg<Vec3<T>> for Vec3<T> {
    #[inline(always)]
    fn neg(&self) -> Vec3<T> {
        BaseVec3::new(-self.index(0), -self.index(1), -self.index(2))
    }
}

impl<T:Copy + Num> NumVec3<T> for Vec3<T> {
    #[inline(always)]
    fn unit_x() -> Vec3<T> {
        BaseVec3::new(One::one::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_y() -> Vec3<T> {
        BaseVec3::new(Zero::zero::<T>(),
                      One::one::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_z() -> Vec3<T> {
        BaseVec3::new(Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      One::one::<T>())
    }

    #[inline(always)]
    fn cross(&self, other: &Vec3<T>) -> Vec3<T> {
        BaseVec3::new((*self.index(1) * *other.index(2)) - (*self.index(2) * *other.index(1)),
                      (*self.index(2) * *other.index(0)) - (*self.index(0) * *other.index(2)),
                      (*self.index(0) * *other.index(1)) - (*self.index(1) * *other.index(0)))
    }

    #[inline(always)]
    fn cross_self(&mut self, other: &Vec3<T>) {
        *self = self.cross(other);
    }
}

impl<T:Copy + Num> ToHomogeneous<Vec4<T>> for Vec3<T> {
    #[inline(always)]
    fn to_homogeneous(&self) -> Vec4<T> {
        BaseVec4::new(self.x, self.y, self.z, Zero::zero())
    }
}

impl<T:Copy + Real + NumAssign> AffineVec<T> for Vec3<T> {
    #[inline(always)]
    fn length2(&self) -> T {
        self.dot(self)
    }

    #[inline(always)]
    fn length(&self) -> T {
        self.length2().sqrt()
    }

    #[inline(always)]
    fn distance2(&self, other: &Vec3<T>) -> T {
        other.sub_v(self).length2()
    }

    #[inline(always)]
    fn distance(&self, other: &Vec3<T>) -> T {
        other.distance2(self).sqrt()
    }

    #[inline(always)]
    fn angle(&self, other: &Vec3<T>) -> T {
        self.cross(other).length().atan2(self.dot(other))
    }

    #[inline(always)]
    fn normalize(&self) -> Vec3<T> {
        self.mul_t(One::one::<T>()/self.length())
    }

    #[inline(always)]
    fn normalize_to(&self, length: T) -> Vec3<T> {
        self.mul_t(length / self.length())
    }

    #[inline(always)]
    fn lerp(&self, other: &Vec3<T>, amount: T) -> Vec3<T> {
        self.add_v(&other.sub_v(self).mul_t(amount))
    }

    #[inline(always)]
    fn normalize_self(&mut self) {
        let n = One::one::<T>() / self.length();
        self.mul_self_t(n);
    }

    #[inline(always)]
    fn normalize_self_to(&mut self, length: T) {
        let n = length / self.length();
        self.mul_self_t(n);
    }

    fn lerp_self(&mut self, other: &Vec3<T>, amount: T) {
        let v = other.sub_v(self).mul_t(amount);
        self.add_self_v(&v);
    }
}

impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Vec3<T> {
    #[inline(always)]
    fn approx_epsilon() -> T {
        ApproxEq::approx_epsilon::<T,T>()
    }

    #[inline(always)]
    fn approx_eq(&self, other: &Vec3<T>) -> bool {
        self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
    }

    #[inline(always)]
    fn approx_eq_eps(&self, other: &Vec3<T>, epsilon: &T) -> bool {
        self.index(0).approx_eq_eps(other.index(0), epsilon) &&
        self.index(1).approx_eq_eps(other.index(1), epsilon) &&
        self.index(2).approx_eq_eps(other.index(2), epsilon)
    }
}

impl<T:Copy + Ord + Eq> OrdVec<T, Vec3<bool>> for Vec3<T> {
    #[inline(always)]
    fn less_than(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] lt other[])
    }

    #[inline(always)]
    fn less_than_equal(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] le other[])
    }

    #[inline(always)]
    fn greater_than(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] gt other[])
    }

    #[inline(always)]
    fn greater_than_equal(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] ge other[])
    }
}

impl<T:Copy + Eq> EqVec<T, Vec3<bool>> for Vec3<T> {
    #[inline(always)]
    fn equal(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] eq other[])
    }

    #[inline(always)]
    fn not_equal(&self, other: &Vec3<T>) -> Vec3<bool> {
        zip_vec3!(self[] ne other[])
    }
}

impl BoolVec for Vec3<bool> {
    #[inline(always)]
    fn any(&self) -> bool {
        *self.index(0) || *self.index(1) || *self.index(2)
    }

    #[inline(always)]
    fn all(&self) -> bool {
        *self.index(0) && *self.index(1) && *self.index(2)
    }

    #[inline(always)]
    fn not(&self) -> Vec3<bool> {
        BaseVec3::new(!*self.index(0), !*self.index(1), !*self.index(2))
    }
}

// GLSL-style type aliases, corresponding to Section 4.1.5 of the [GLSL 4.30.6 specification]
// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).

// a three-component single-precision floating-point vector
pub type vec3  = Vec3<f32>;
// a three-component double-precision floating-point vector
pub type dvec3 = Vec3<f64>;
// a three-component Boolean vector
pub type bvec3 = Vec3<bool>;
// a three-component signed integer vector
pub type ivec3 = Vec3<i32>;
// a three-component unsigned integer vector
pub type uvec3 = Vec3<u32>;

// Rust-style type aliases
pub type Vec3f   = Vec3<float>;
pub type Vec3f32 = Vec3<f32>;
pub type Vec3f64 = Vec3<f64>;
pub type Vec3i   = Vec3<int>;
pub type Vec3i8  = Vec3<i8>;
pub type Vec3i16 = Vec3<i16>;
pub type Vec3i32 = Vec3<i32>;
pub type Vec3i64 = Vec3<i64>;
pub type Vec3u   = Vec3<uint>;
pub type Vec3u8  = Vec3<u8>;
pub type Vec3u16 = Vec3<u16>;
pub type Vec3u32 = Vec3<u32>;
pub type Vec3u64 = Vec3<u64>;
pub type Vec3b   = Vec3<bool>;

/// A 4-dimensional vector
///
/// # Type parameters
///
/// - `T`: The type of the components. This is intended to support boolean,
///         integer, unsigned integer, and floating point types.
///
/// # Fields
///
/// - `x`: the first component of the vector
/// - `y`: the second component of the vector
/// - `z`: the third component of the vector
/// - `w`: the fourth component of the vector
#[deriving(Eq)]
pub struct Vec4<T> { x: T, y: T, z: T, w: T }

impl<T:Copy + Eq> BaseVec<T> for Vec4<T> {
    #[inline(always)]
    fn index<'a>(&'a self, i: uint) -> &'a T {
        unsafe { &'a transmute::<&'a Vec4<T>, &'a [T,..4]>(self)[i] }
    }

    #[inline(always)]
    fn from_value(value: T) -> Vec4<T> {
        BaseVec4::new(value, value, value, value)
    }

    #[inline(always)]
    fn to_ptr(&self) -> *T {
        unsafe { transmute(self) }
    }

    #[inline(always)]
    fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut T {
        unsafe { &'a mut transmute::< &'a mut Vec4<T>, &'a mut [T,..4]>(self)[i] }
    }

    #[inline(always)]
    fn swap(&mut self, a: uint, b: uint) {
        let tmp = *self.index(a);
        *self.index_mut(a) = *self.index(b);
        *self.index_mut(b) = tmp;
    }
}

impl<T> BaseVec4<T> for Vec4<T> {
    #[inline(always)]
    fn new(x: T, y: T, z: T, w: T) -> Vec4<T> {
        Vec4 { x: x, y: y, z: z, w: w }
    }
}

impl<T:Copy + Num + NumAssign> NumVec<T> for Vec4<T> {
    #[inline(always)]
    fn identity() -> Vec4<T> {
        BaseVec4::new(One::one::<T>(),
                      One::one::<T>(),
                      One::one::<T>(),
                      One::one::<T>())
    }

    #[inline(always)]
    fn zero() -> Vec4<T> {
        BaseVec4::new(Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn is_zero(&self) -> bool {
        *self.index(0) == Zero::zero() &&
        *self.index(1) == Zero::zero() &&
        *self.index(2) == Zero::zero() &&
        *self.index(3) == Zero::zero()
    }

    #[inline(always)]
    fn mul_t(&self, value: T) -> Vec4<T> {
        zip_vec4!(self[] mul value)
    }

    #[inline(always)]
    fn div_t(&self, value: T) -> Vec4<T> {
        zip_vec4!(self[] div value)
    }

    #[inline(always)]
    fn add_v(&self, other: &Vec4<T>) -> Vec4<T> {
        zip_vec4!(self[] add other[])
    }

    #[inline(always)]
    fn sub_v(&self, other: &Vec4<T>) -> Vec4<T> {
        zip_vec4!(self[] sub other[])
    }

    #[inline(always)]
    fn mul_v(&self, other: &Vec4<T>) -> Vec4<T> {
        zip_vec4!(self[] mul other[])
    }

    #[inline(always)]
    fn div_v(&self, other: &Vec4<T>) -> Vec4<T> {
        zip_vec4!(self[] div other[])
    }

    #[inline(always)]
    fn dot(&self, other: &Vec4<T>) -> T {
        (*self.index(0)) * (*other.index(0)) +
        (*self.index(1)) * (*other.index(1)) +
        (*self.index(2)) * (*other.index(2)) +
        (*self.index(3)) * (*other.index(3))
    }

    #[inline(always)]
    fn neg_self(&mut self) {
        *self.index_mut(0) = -self.index(0);
        *self.index_mut(1) = -self.index(1);
        *self.index_mut(2) = -self.index(2);
        *self.index_mut(3) = -self.index(3);
    }

    #[inline(always)]
    fn mul_self_t(&mut self, value: T) {
        zip_assign!(self[] mul_assign value ..4);
    }

    #[inline(always)]
    fn div_self_t(&mut self, value: T) {
        zip_assign!(self[] div_assign value ..4);
    }

    #[inline(always)]
    fn add_self_v(&mut self, other: &Vec4<T>) {
        zip_assign!(self[] add_assign other[] ..4);
    }

    #[inline(always)]
    fn sub_self_v(&mut self, other: &Vec4<T>) {
        zip_assign!(self[] sub_assign other[] ..4);
    }

    #[inline(always)]
    fn mul_self_v(&mut self, other: &Vec4<T>) {
        zip_assign!(self[] mul_assign other[] ..4);
    }

    #[inline(always)]
    fn div_self_v(&mut self, other: &Vec4<T>) {
        zip_assign!(self[] div_assign other[] ..4);
    }
}

impl<T:Copy + Num> Neg<Vec4<T>> for Vec4<T> {
    #[inline(always)]
    fn neg(&self) -> Vec4<T> {
        BaseVec4::new(-self.index(0), -self.index(1), -self.index(2), -self.index(3))
    }
}

impl<T:Copy + Num> NumVec4<T> for Vec4<T> {
    #[inline(always)]
    fn unit_x() -> Vec4<T> {
        BaseVec4::new(One::one::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_y() -> Vec4<T> {
        BaseVec4::new(Zero::zero::<T>(),
                      One::one::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_z() -> Vec4<T> {
        BaseVec4::new(Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      One::one::<T>(),
                      Zero::zero::<T>())
    }

    #[inline(always)]
    fn unit_w() -> Vec4<T> {
        BaseVec4::new(Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      Zero::zero::<T>(),
                      One::one::<T>())
    }
}

impl<T:Copy + Real + NumAssign> AffineVec<T> for Vec4<T> {
    #[inline(always)]
    fn length2(&self) -> T {
        self.dot(self)
    }

    #[inline(always)]
    fn length(&self) -> T {
        self.length2().sqrt()
    }

    #[inline(always)]
    fn distance2(&self, other: &Vec4<T>) -> T {
        other.sub_v(self).length2()
    }

    #[inline(always)]
    fn distance(&self, other: &Vec4<T>) -> T {
        other.distance2(self).sqrt()
    }

    #[inline(always)]
    fn angle(&self, other: &Vec4<T>) -> T {
        (self.dot(other) / (self.length() * other.length())).acos()
    }

    #[inline(always)]
    fn normalize(&self) -> Vec4<T> {
        self.mul_t(One::one::<T>()/self.length())
    }

    #[inline(always)]
    fn normalize_to(&self, length: T) -> Vec4<T> {
        self.mul_t(length / self.length())
    }

    #[inline(always)]
    fn lerp(&self, other: &Vec4<T>, amount: T) -> Vec4<T> {
        self.add_v(&other.sub_v(self).mul_t(amount))
    }

    #[inline(always)]
    fn normalize_self(&mut self) {
        let n = One::one::<T>() / self.length();
        self.mul_self_t(n);
    }

    #[inline(always)]
    fn normalize_self_to(&mut self, length: T) {
        let n = length / self.length();
        self.mul_self_t(n);
    }

    fn lerp_self(&mut self, other: &Vec4<T>, amount: T) {
        let v = other.sub_v(self).mul_t(amount);
        self.add_self_v(&v);
    }
}

impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Vec4<T> {
    #[inline(always)]
    fn approx_epsilon() -> T {
        ApproxEq::approx_epsilon::<T,T>()
    }

    #[inline(always)]
    fn approx_eq(&self, other: &Vec4<T>) -> bool {
        self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
    }

    #[inline(always)]
    fn approx_eq_eps(&self, other: &Vec4<T>, epsilon: &T) -> bool {
        self.index(0).approx_eq_eps(other.index(0), epsilon) &&
        self.index(1).approx_eq_eps(other.index(1), epsilon) &&
        self.index(2).approx_eq_eps(other.index(2), epsilon) &&
        self.index(3).approx_eq_eps(other.index(3), epsilon)
    }
}

impl<T:Copy + Ord + Eq> OrdVec<T, Vec4<bool>> for Vec4<T> {
    #[inline(always)]
    fn less_than(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] lt other[])
    }

    #[inline(always)]
    fn less_than_equal(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] le other[])
    }

    #[inline(always)]
    fn greater_than(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] gt other[])
    }

    #[inline(always)]
    fn greater_than_equal(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] ge other[])
    }
}

impl<T:Copy + Eq> EqVec<T, Vec4<bool>> for Vec4<T> {
    #[inline(always)]
    fn equal(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] eq other[])
    }

    #[inline(always)]
    fn not_equal(&self, other: &Vec4<T>) -> Vec4<bool> {
        zip_vec4!(self[] ne other[])
    }
}

impl BoolVec for Vec4<bool> {
    #[inline(always)]
    fn any(&self) -> bool {
        *self.index(0) || *self.index(1) || *self.index(2) || *self.index(3)
    }

    #[inline(always)]
    fn all(&self) -> bool {
        *self.index(0) && *self.index(1) && *self.index(2) && *self.index(3)
    }

    #[inline(always)]
    fn not(&self) -> Vec4<bool> {
        BaseVec4::new(!*self.index(0), !*self.index(1), !*self.index(2), !*self.index(3))
    }
}

// GLSL-style type aliases, corresponding to Section 4.1.5 of the [GLSL 4.30.6 specification]
// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).

// a four-component single-precision floating-point vector
pub type vec4  = Vec4<f32>;
// a four-component double-precision floating-point vector
pub type dvec4 = Vec4<f64>;
// a four-component Boolean vector
pub type bvec4 = Vec4<bool>;
// a four-component signed integer vector
pub type ivec4 = Vec4<i32>;
// a four-component unsigned integer vector
pub type uvec4 = Vec4<u32>;

// Rust-style type aliases
pub type Vec4f   = Vec4<float>;
pub type Vec4f32 = Vec4<f32>;
pub type Vec4f64 = Vec4<f64>;
pub type Vec4i   = Vec4<int>;
pub type Vec4i8  = Vec4<i8>;
pub type Vec4i16 = Vec4<i16>;
pub type Vec4i32 = Vec4<i32>;
pub type Vec4i64 = Vec4<i64>;
pub type Vec4u   = Vec4<uint>;
pub type Vec4u8  = Vec4<u8>;
pub type Vec4u16 = Vec4<u16>;
pub type Vec4u32 = Vec4<u32>;
pub type Vec4u64 = Vec4<u64>;
pub type Vec4b   = Vec4<bool>;