Add quaternions.

Fix #24.

src/lib.rs

@@ -102,7 +102,6 @@ Feel free to add your project to this list if you happen to use **nalgebra**!
 #![feature(globs)]
 #![doc(html_root_url = "http://nalgebra.org/doc")]
 
-extern crate rand;
 extern crate serialize;
 
 #[cfg(test)]
@@ -176,7 +175,8 @@ pub use structs::{
     Vec0, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6,
     Pnt0, Pnt1, Pnt2, Pnt3, Pnt4, Pnt5, Pnt6,
     Persp3, PerspMat3,
-    Ortho3, OrthoMat3
+    Ortho3, OrthoMat3,
+    Quat, UnitQuat
 };
 
 pub use linalg::{

src/structs/iso.rs

@@ -3,7 +3,7 @@
 #![allow(missing_doc)]
 
 use std::num::{Zero, One};
-use rand::{Rand, Rng};
+use std::rand::{Rand, Rng};
 use structs::mat::{Mat3, Mat4, Mat5};
 use traits::structure::{Cast, Dim, Col};
 use traits::operations::{Inv, ApproxEq};

src/structs/mod.rs

@@ -9,6 +9,7 @@ pub use self::rot::{Rot2, Rot3, Rot4};
 pub use self::iso::{Iso2, Iso3, Iso4};
 pub use self::persp::{Persp3, PerspMat3};
 pub use self::ortho::{Ortho3, OrthoMat3};
+pub use self::quat::{Quat, UnitQuat};
 
 pub use self::vec::{Vec1MulRhs, Vec2MulRhs, Vec3MulRhs, Vec4MulRhs, Vec5MulRhs, Vec6MulRhs,
                     Vec1DivRhs, Vec2DivRhs, Vec3DivRhs, Vec4DivRhs, Vec5DivRhs, Vec6DivRhs,
@@ -31,6 +32,7 @@ mod vec_macros;
 mod vec;
 mod pnt_macros;
 mod pnt;
+mod quat;
 mod mat_macros;
 mod mat;
 mod rot_macros;

src/structs/quat.rs

@@ -1,21 +1,35 @@
 //! Quaternion definition.
 
+#![allow(missing_doc)] // we allow missing to avoid having to document the dispatch trait.
+
+use std::mem;
+use std::num::{Zero, One, Bounded};
+use std::num;
+use std::rand::{Rand, Rng};
+use std::slice::{Items, MutItems};
+use structs::{Vec3, Pnt3, Rot3, Mat3, Vec3MulRhs, Pnt3MulRhs};
+use traits::operations::{ApproxEq, Inv, PartialOrd, PartialOrdering, NotComparable, PartialLess,
+                         PartialGreater, PartialEqual, Axpy};
+use traits::structure::{Cast, Indexable, Iterable, IterableMut, Dim};
+use traits::geometry::{Norm, Cross, Rotation, Rotate, Transform};
+
 /// A quaternion.
-///
+#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Rand, Zero, Show)]
-/// A single unit quaternion can represent a 3d rotation while a pair of unit quaternions can
-/// represent a 4d rotation.
 pub struct Quat<N> {
-    w: N
+    /// The scalar component of the quaternion.
-    i: N,
+    pub w: N,
-    j: N,
+    /// The first vector component of the quaternion.
-    k: N,
+    pub i: N,
+    /// The second vector component of the quaternion.
+    pub j: N,
+    /// The third vector component of the quaternion.
+    pub k: N
 }
 
-// FIXME: find a better name
-type QuatPair<N> = (Quat<N>, Quat<N>)
-
 impl<N> Quat<N> {
-    pub fn new(w: N, x: N, y: N, z: N) -> Quat<N> {
+    /// Creates a new quaternion from its components.
+    #[inline]
+    pub fn new(w: N, i: N, j: N, k: N) -> Quat<N> {
         Quat {
             w: w,
             i: i,
@@ -23,53 +37,497 @@ impl<N> Quat<N> {
             k: k
         }
     }
-}
 
-impl<N: Add<N, N>> Add<Quat<N>, Quat<N>> for Quat<N> {
+    /// The vector part `(i, j, k)` of this quaternion.
-    fn add(&self, other: &Quat<N>) -> Quat<N> {
+    #[inline]
-        Quat::new(
+    pub fn vector<'a>(&'a self) -> &'a Vec3<N> {
-            self.w + other.w,
+        // FIXME: do this require a `repr(C)` ?
-            self.i + other.i,
+        unsafe {
-            self.j + other.j,
+            mem::transmute(&self.i)
-            self.k + other.k)
         }
     }
 
-impl<N> Mul<Quat<N>, Quat<N>> for Quat<N> {
+    /// The scalar part `w` of this quaternion.
-    fn mul(&self, other: &Quat<N>) -> Quat<N> {
+    #[inline]
+    pub fn scalar<'a>(&'a self) -> &'a N {
+        &self.w
+    }
+}
+
+impl<N: Neg<N>> Quat<N> {
+    /// Replaces this quaternion by its conjugate.
+    #[inline]
+    pub fn conjugate(&mut self) {
+        self.i = -self.i;
+        self.j = -self.j;
+        self.k = -self.k;
+    }
+}
+
+impl<N: Float + ApproxEq<N> + Clone> Inv for Quat<N> {
+    #[inline]
+    fn inv_cpy(m: &Quat<N>) -> Option<Quat<N>> {
+        let mut res = m.clone();
+
+        if res.inv() {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    #[inline]
+    fn inv(&mut self) -> bool {
+        let sqnorm = Norm::sqnorm(self);
+
+        if ApproxEq::approx_eq(&sqnorm, &Zero::zero()) {
+            false
+        }
+        else {
+            self.conjugate();
+            self.w = self.w / sqnorm;
+            self.i = self.i / sqnorm;
+            self.j = self.j / sqnorm;
+            self.k = self.k / sqnorm;
+
+            true
+        }
+    }
+}
+
+impl<N: Float> Norm<N> for Quat<N> {
+    #[inline]
+    fn sqnorm(q: &Quat<N>) -> N {
+        q.w * q.w + q.i * q.i + q.j * q.j + q.k * q.k
+    }
+
+    #[inline]
+    fn normalize_cpy(v: &Quat<N>) -> Quat<N> {
+        let n = Norm::norm(v);
+        Quat::new(v.w / n, v.i / n, v.j / n, v.k / n)
+    }
+
+    #[inline]
+    fn normalize(&mut self) -> N {
+        let n = Norm::norm(self);
+
+        self.w = self.w / n;
+        self.i = self.i / n;
+        self.j = self.j / n;
+        self.k = self.k / n;
+
+        n
+    }
+}
+
+impl<N: Mul<N, N> + Sub<N, N> + Add<N, N>> QuatMulRhs<N, Quat<N>> for Quat<N> {
+    #[inline]
+    fn binop(left: &Quat<N>, right: &Quat<N>) -> Quat<N> {
         Quat::new(
-            self.w * other.w - self.x * other.x - self.y * other.y - self.z * other.z,
+            left.w * right.w - left.i * right.i - left.j * right.j - left.k * right.k,
-            self.a * other.b - self.b * other.a - self.c * other.d - self.d * other.c,
+            left.w * right.i + left.i * right.w + left.j * right.k - left.k * right.j,
-            self.a * other.c - self.b * other.d - self.c * other.a - self.d * other.b,
+            left.w * right.j - left.i * right.k + left.j * right.w + left.k * right.i,
-            self.w * other.w - self.x * other.x - self.y * other.y - self.z * other.z,
+            left.w * right.k + left.i * right.j - left.j * right.i + left.k * right.w)
+    }
+}
+
+impl<N: ApproxEq<N> + Float + Clone> QuatDivRhs<N, Quat<N>> for Quat<N> {
+    #[inline]
+    fn binop(left: &Quat<N>, right: &Quat<N>) -> Quat<N> {
+        left * Inv::inv_cpy(right).expect("Unable to invert the denominator.")
+    }
+}
+
+/// A unit quaternion that can represent a 3D rotation.
+#[deriving(Eq, PartialEq, Encodable, Decodable, Clone, Hash, Show)]
+pub struct UnitQuat<N> {
+    q: Quat<N>
+}
+
+impl<N: FloatMath> UnitQuat<N> {
+    /// Creates a new unit quaternion from the axis-angle representation of a rotation.
+    #[inline]
+    pub fn new(axisangle: Vec3<N>) -> UnitQuat<N> {
+        let sqang = Norm::sqnorm(&axisangle);
+
+        if sqang.is_zero() {
+            One::one()
+        }
+        else {
+            let ang    = sqang.sqrt();
+            let (s, c) = (ang / num::cast(2.0f64).unwrap()).sin_cos();
+
+            let s_ang = s / ang;
+
+            unsafe {
+                UnitQuat::new_with_unit_quat(
+                    Quat::new(
+                        c,
+                        axisangle.x * s_ang,
+                        axisangle.y * s_ang,
+                        axisangle.z * s_ang)
+                )
+            }
+        }
+    }
+
+    /// Creates a new unit quaternion from a quaternion.
+    ///
+    /// The input quaternion will be normalized.
+    #[inline]
+    pub fn new_with_quat(q: Quat<N>) -> UnitQuat<N> {
+        let mut q = q;
+        let _ = q.normalize();
+
+        UnitQuat {
+            q: q
+        }
+    }
+
+    /// Creates a new unit quaternion from Euler angles.
+    ///
+    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
+    #[inline]
+    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> UnitQuat<N> {
+        let _0_5: N  = num::cast(0.5f64).unwrap();
+        let (sr, cr) = (roll * _0_5).sin_cos();
+        let (sp, cp) = (pitch * _0_5).sin_cos();
+        let (sy, cy) = (yaw * _0_5).sin_cos();
+
+        unsafe {
+            UnitQuat::new_with_unit_quat(
+                Quat::new(
+                    cr * cp * cy + sr * sp * sy,
+                    sr * cp * cy - cr * sp * sy,
+                    cr * sp * cy + sr * cp * sy,
+                    cr * cp * sy - sr * sp * cy)
             )
         }
     }
 
-impl<N: Zero> Rotate<Vec3<N>> for Quat<N> {
+    /// Builds a rotation matrix from this quaternion.
+    pub fn to_rot(&self) -> Rot3<N> {
+        let _2: N = num::cast(2.0f64).unwrap();
+        let ww = self.q.w * self.q.w;
+        let ii = self.q.i * self.q.i;
+        let jj = self.q.j * self.q.j;
+        let kk = self.q.k * self.q.k;
+        let ij = _2 * self.q.i * self.q.j;
+        let wk = _2 * self.q.w * self.q.k;
+        let wj = _2 * self.q.w * self.q.j;
+        let ik = _2 * self.q.i * self.q.k;
+        let jk = _2 * self.q.j * self.q.k;
+        let wi = _2 * self.q.w * self.q.i;
+
+        unsafe {
+            Rot3::new_with_mat(
+                Mat3::new(
+                    ww + ii - jj - kk, ij - wk,           wj + ik,
+                    wk + ij,           ww - ii + jj - kk, jk - wi,
+                    ik - wj,           wi + jk,           ww - ii - jj + kk
+                )
+            )
+        }
+    }
+}
+
+impl<N> UnitQuat<N> {
+    /// Creates a new unit quaternion from a quaternion.
+    ///
+    /// This is unsafe because the input quaternion will not be normalized.
+    #[inline]
+    pub unsafe fn new_with_unit_quat(q: Quat<N>) -> UnitQuat<N> {
+        UnitQuat {
+            q: q
+        }
+    }
+
+    /// The `Quat` representation of this unit quaternion.
+    #[inline]
+    pub fn quat<'a>(&'a self) -> &'a Quat<N> {
+        &self.q
+    }
+}
+
+impl<N: Num + Clone> One for UnitQuat<N> {
+    #[inline]
+    fn one() -> UnitQuat<N> {
+        unsafe {
+            UnitQuat::new_with_unit_quat(Quat::new(One::one(), Zero::zero(), Zero::zero(), Zero::zero()))
+        }
+    }
+}
+
+impl<N: Clone + Neg<N>> Inv for UnitQuat<N> {
+    #[inline]
+    fn inv_cpy(m: &UnitQuat<N>) -> Option<UnitQuat<N>> {
+        let mut cpy = m.clone();
+
+        cpy.inv();
+        Some(cpy)
+    }
+
+    #[inline]
+    fn inv(&mut self) -> bool {
+        self.q.conjugate();
+
+        true
+    }
+}
+
+impl<N: Clone + Rand + FloatMath> Rand for UnitQuat<N> {
+    #[inline]
+    fn rand<R: Rng>(rng: &mut R) -> UnitQuat<N> {
+        UnitQuat::new(rng.gen())
+    }
+}
+
+impl<N: ApproxEq<N>> ApproxEq<N> for UnitQuat<N> {
+    #[inline]
+    fn approx_epsilon(_: Option<UnitQuat<N>>) -> N {
+        ApproxEq::approx_epsilon(None::<N>)
+    }
+
+    #[inline]
+    fn approx_eq(a: &UnitQuat<N>, b: &UnitQuat<N>) -> bool {
+        ApproxEq::approx_eq(&a.q, &b.q)
+    }
+
+    #[inline]
+    fn approx_eq_eps(a: &UnitQuat<N>, b: &UnitQuat<N>, eps: &N) -> bool {
+        ApproxEq::approx_eq_eps(&a.q, &b.q, eps)
+    }
+}
+
+impl<N: Float + ApproxEq<N> + Clone> Div<UnitQuat<N>, UnitQuat<N>> for UnitQuat<N> {
+    #[inline]
+    fn div(&self, other: &UnitQuat<N>) -> UnitQuat<N> {
+        UnitQuat { q: self.q / other.q }
+    }
+}
+
+impl<N: Num + Clone> UnitQuatMulRhs<N, UnitQuat<N>> for UnitQuat<N> {
+    #[inline]
+    fn binop(left: &UnitQuat<N>, right: &UnitQuat<N>) -> UnitQuat<N> {
+        UnitQuat { q: left.q * right.q }
+    }
+}
+
+impl<N: Num + Clone> UnitQuatMulRhs<N, Vec3<N>> for Vec3<N> {
+    #[inline]
+    fn binop(left: &UnitQuat<N>, right: &Vec3<N>) -> Vec3<N> {
+        let _2: N = num::one::<N>() + num::one();
+        let mut t = Cross::cross(left.q.vector(), right);
+        t.x = t.x * _2;
+        t.y = t.y * _2;
+        t.z = t.z * _2;
+
+        Vec3::new(t.x * left.q.w, t.y * left.q.w, t.z * left.q.w) +
+        Cross::cross(left.q.vector(), &t) +
+        *right
+    }
+}
+
+impl<N: Num + Clone> UnitQuatMulRhs<N, Pnt3<N>> for Pnt3<N> {
+    #[inline]
+    fn binop(left: &UnitQuat<N>, right: &Pnt3<N>) -> Pnt3<N> {
+        (left * *right.as_vec()).to_pnt()
+    }
+}
+
+impl<N: Num + Clone> Vec3MulRhs<N, Vec3<N>> for UnitQuat<N> {
+    #[inline]
+    fn binop(left: &Vec3<N>, right: &UnitQuat<N>) -> Vec3<N> {
+        let mut inv_quat = right.clone();
+        inv_quat.inv();
+
+        inv_quat * *left
+    }
+}
+
+impl<N: Num + Clone> Pnt3MulRhs<N, Pnt3<N>> for UnitQuat<N> {
+    #[inline]
+    fn binop(left: &Pnt3<N>, right: &UnitQuat<N>) -> Pnt3<N> {
+        (left.as_vec() * *right).to_pnt()
+    }
+}
+
+impl<N: FloatMath + Clone> Rotation<Vec3<N>> for UnitQuat<N> {
+    #[inline]
+    fn rotation(&self) -> Vec3<N> {
+        let _2 = num::one::<N>() + num::one();
+        let mut v = self.q.vector().clone();
+        let ang = _2 * v.normalize().atan2(self.q.w);
+
+        if ang.is_zero() {
+            num::zero()
+        }
+        else {
+            Vec3::new(v.x * ang, v.y * ang, v.z * ang)
+        }
+    }
+
+    #[inline]
+    fn inv_rotation(&self) -> Vec3<N> {
+        -self.rotation()
+    }
+
+    #[inline]
+    fn append_rotation(&mut self, amount: &Vec3<N>) {
+        *self = Rotation::append_rotation_cpy(self, amount)
+    }
+
+    #[inline]
+    fn append_rotation_cpy(t: &UnitQuat<N>, amount: &Vec3<N>) -> UnitQuat<N> {
+        *t * UnitQuat::new(amount.clone())
+    }
+
+    #[inline]
+    fn prepend_rotation(&mut self, amount: &Vec3<N>) {
+        *self = Rotation::prepend_rotation_cpy(self, amount)
+    }
+
+    #[inline]
+    fn prepend_rotation_cpy(t: &UnitQuat<N>, amount: &Vec3<N>) -> UnitQuat<N> {
+        UnitQuat::new(amount.clone()) * *t
+    }
+
+    #[inline]
+    fn set_rotation(&mut self, v: Vec3<N>) {
+        *self = UnitQuat::new(v)
+    }
+}
+
+impl<N: Num + Clone> Rotate<Vec3<N>> for UnitQuat<N> {
     #[inline]
     fn rotate(&self, v: &Vec3<N>) -> Vec3<N> {
-        *self * *v_quat * self.inv()
+        *self * *v
     }
 
     #[inline]
     fn inv_rotate(&self, v: &Vec3<N>) -> Vec3<N> {
-        -self * *v
+        *v * *self
     }
 }
 
-impl Rotate<Vec4<N>> for (QuatPair<N>, QuatPair<N>) {
+impl<N: Num + Clone> Rotate<Pnt3<N>> for UnitQuat<N> {
     #[inline]
-    fn rotate(&self, v: &Vec4<N>) -> Vec4<N> {
+    fn rotate(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        let (ref l, ref r) = *self;
+        *self * *p
-
-        *l * *v * *r
     }
 
     #[inline]
-    fn inv_rotate(&self, v: &Vec4<N>) -> Vec4<N> {
+    fn inv_rotate(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        let (ref l, ref r) = *self;
+        *p * *self
+    }
+}
 
-        (-r) * **v * (-l)
+impl<N: Num + Clone> Transform<Vec3<N>> for UnitQuat<N> {
+    #[inline]
+    fn transform(&self, v: &Vec3<N>) -> Vec3<N> {
+        *self * *v
+    }
+
+    #[inline]
+    fn inv_transform(&self, v: &Vec3<N>) -> Vec3<N> {
+        *v * *self
     }
 }
+
+impl<N: Num + Clone> Transform<Pnt3<N>> for UnitQuat<N> {
+    #[inline]
+    fn transform(&self, p: &Pnt3<N>) -> Pnt3<N> {
+        *self * *p
+    }
+
+    #[inline]
+    fn inv_transform(&self, p: &Pnt3<N>) -> Pnt3<N> {
+        *p * *self
+    }
+}
+
+double_dispatch_binop_decl_trait!(Quat, QuatMulRhs)
+double_dispatch_binop_decl_trait!(Quat, QuatDivRhs)
+double_dispatch_binop_decl_trait!(Quat, QuatAddRhs)
+double_dispatch_binop_decl_trait!(Quat, QuatSubRhs)
+double_dispatch_cast_decl_trait!(Quat, QuatCast)
+mul_redispatch_impl!(Quat, QuatMulRhs)
+div_redispatch_impl!(Quat, QuatDivRhs)
+add_redispatch_impl!(Quat, QuatAddRhs)
+sub_redispatch_impl!(Quat, QuatSubRhs)
+cast_redispatch_impl!(Quat, QuatCast)
+ord_impl!(Quat, w, i, j, k)
+vec_axis_impl!(Quat, w, i, j, k)
+vec_cast_impl!(Quat, QuatCast, w, i, j, k)
+as_slice_impl!(Quat, 4)
+index_impl!(Quat)
+indexable_impl!(Quat, 4)
+at_fast_impl!(Quat, 4)
+new_repeat_impl!(Quat, val, w, i, j, k)
+dim_impl!(Quat, 3)
+container_impl!(Quat)
+add_impl!(Quat, QuatAddRhs, w, i, j, k)
+sub_impl!(Quat, QuatSubRhs, w, i, j, k)
+neg_impl!(Quat, w, i, j, k)
+vec_mul_scalar_impl!(Quat, f64, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, f32, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, u64, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, u32, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, u16, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, u8, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, i64, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, i32, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, i16, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, i8, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, uint, QuatMulRhs, w, i, j, k)
+vec_mul_scalar_impl!(Quat, int, QuatMulRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, f64, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, f32, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, u64, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, u32, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, u16, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, u8, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, i64, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, i32, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, i16, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, i8, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, uint, QuatDivRhs, w, i, j, k)
+vec_div_scalar_impl!(Quat, int, QuatDivRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, f64, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, f32, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, u64, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, u32, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, u16, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, u8, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, i64, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, i32, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, i16, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, i8, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, uint, QuatAddRhs, w, i, j, k)
+vec_add_scalar_impl!(Quat, int, QuatAddRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, f64, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, f32, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, u64, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, u32, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, u16, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, u8, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, i64, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, i32, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, i16, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, i8, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, uint, QuatSubRhs, w, i, j, k)
+vec_sub_scalar_impl!(Quat, int, QuatSubRhs, w, i, j, k)
+approx_eq_impl!(Quat, w, i, j, k)
+from_iterator_impl!(Quat, iterator, iterator, iterator, iterator)
+bounded_impl!(Quat, w, i, j, k)
+axpy_impl!(Quat, w, i, j, k)
+iterable_impl!(Quat, 4)
+iterable_mut_impl!(Quat, 4)
+
+double_dispatch_binop_decl_trait!(UnitQuat, UnitQuatMulRhs)
+mul_redispatch_impl!(UnitQuat, UnitQuatMulRhs)
+dim_impl!(UnitQuat, 3)
+as_slice_impl!(UnitQuat, 4)
+index_impl!(UnitQuat)
+indexable_impl!(UnitQuat, 5)

src/structs/rot.rs

@@ -3,7 +3,7 @@
 #![allow(missing_doc)]
 
 use std::num::{Zero, One};
-use rand::{Rand, Rng};
+use std::rand::{Rand, Rng};
 use traits::geometry::{Rotate, Rotation, AbsoluteRotate, RotationMatrix, Transform, ToHomogeneous,
                        Norm, Cross};
 use traits::structure::{Cast, Dim, Row, Col};
@@ -136,6 +136,34 @@ impl<N: Clone + FloatMath> Rot3<N> {
             }
         }
     }
+
+    /// Builds a rotation matrix from an orthogonal matrix.
+    ///
+    /// This is unsafe because the orthogonality of `mat` is not checked.
+    pub unsafe fn new_with_mat(mat: Mat3<N>) -> Rot3<N> {
+        Rot3 {
+            submat: mat
+        }
+    }
+
+    /// Creates a new rotation from Euler angles.
+    ///
+    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
+    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> Rot3<N> {
+        let (sr, cr) = roll.sin_cos();
+        let (sp, cp) = pitch.sin_cos();
+        let (sy, cy) = yaw.sin_cos();
+
+        unsafe {
+            Rot3::new_with_mat(
+                Mat3::new(
+                    cy * cp, cy * sp * sr - sy * cr, cy * sp * cr + sy * sr,
+                    sy * cp, sy * sp * sr + cy * cr, sy * sp * cr - cy * sr,
+                    -sp,     cp * sr,                cp * cr
+                )
+            )
+        }
+    }
 }
 
 impl<N: Clone + Float> Rot3<N> {

src/structs/vec.rs

@@ -1,6 +1,6 @@
 //! Vectors with dimensions known at compile-time.
 
-#![allow(missing_doc)] // we allow missing to avoid having to document the vector components.
+#![allow(missing_doc)] // we allow missing to avoid having to document the dispatch traits.
 
 use std::mem;
 use std::num::{Zero, One, Float, Bounded};

src/traits/geometry.rs

@@ -215,15 +215,12 @@ pub trait Norm<N: Float> {
     /// Computes the squared norm of `self`.
     ///
     /// This is usually faster than computing the norm itself.
-    #[inline]
     fn sqnorm(&Self) -> N;
 
     /// Gets the normalized version of a copy of `v`.
-    #[inline]
     fn normalize_cpy(v: &Self) -> Self;
 
     /// Normalizes `self`.
-    #[inline]
     fn normalize(&mut self) -> N;
 }
 

tests/quat.rs

@@ -0,0 +1,73 @@
+#![feature(macro_rules)]
+
+extern crate debug;
+extern crate "nalgebra" as na;
+
+use na::{Pnt3, Vec3, Rot3, UnitQuat, Rotation};
+use std::rand::random;
+
+#[test]
+fn test_quat_as_mat() {
+    for _ in range(0u, 10000) {
+        let axis_angle: Vec3<f64> = random();
+
+        assert!(na::approx_eq(&UnitQuat::new(axis_angle).to_rot(), &Rot3::new(axis_angle)))
+    }
+}
+
+#[test]
+fn test_quat_mul_vec_or_pnt_as_mat() {
+    for _ in range(0u, 10000) {
+        let axis_angle: Vec3<f64> = random();
+        let vec: Vec3<f64> = random();
+        let pnt: Pnt3<f64> = random();
+
+        let mat  = Rot3::new(axis_angle);
+        let quat = UnitQuat::new(axis_angle);
+
+        assert!(na::approx_eq(&(mat * vec), &(quat * vec)));
+        assert!(na::approx_eq(&(mat * pnt), &(quat * pnt)));
+        assert!(na::approx_eq(&(vec * mat), &(vec * quat)));
+        assert!(na::approx_eq(&(pnt * mat), &(pnt * quat)));
+    }
+}
+
+#[test]
+fn test_quat_div_quat() {
+    for _ in range(0u, 10000) {
+        let axis_angle1: Vec3<f64> = random();
+        let axis_angle2: Vec3<f64> = random();
+
+        let r1 = Rot3::new(axis_angle1);
+        let r2 = na::inv(&Rot3::new(axis_angle2)).unwrap();
+
+        let q1 = UnitQuat::new(axis_angle1);
+        let q2 = UnitQuat::new(axis_angle2);
+
+        assert!(na::approx_eq(&(q1 / q2).to_rot(), &(r1 * r2)))
+    }
+}
+
+#[test]
+fn test_quat_to_axis_angle() {
+    for _ in range(0u, 10000) {
+        let axis_angle: Vec3<f64> = random();
+
+        let q = UnitQuat::new(axis_angle);
+
+        println!("{} {}", q.rotation(), axis_angle);
+        assert!(na::approx_eq(&q.rotation(), &axis_angle))
+    }
+}
+
+#[test]
+fn test_quat_euler_angles() {
+    for _ in range(0u, 10000) {
+        let angles: Vec3<f64> = random();
+
+        let q = UnitQuat::new_with_euler_angles(angles.x, angles.y, angles.z);
+        let m = Rot3::new_with_euler_angles(angles.x, angles.y, angles.z);
+
+        assert!(na::approx_eq(&q.to_rot(), &m))
+    }
+}