diff --git a/CHANGELOG.md b/CHANGELOG.md
index e29422a6..ab56eaa2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -14,6 +14,12 @@ This project adheres to [Semantic Versioning](http://semver.org/).
     - `::canonical_basis_with_dim` -> `::canonical_basis_with_dimension`
     - `::from_elem` -> `::from_element`
     - `DiagMut` -> `DiagonalMut`
+    - `UnitQuaternion::new` becomes `UnitQuaternion::from_scaled_axis` or
+      `UnitQuaternion::from_axisangle`. The new `::new` method now requires a
+      not-normalized quaternion.
+
+Methods names starting with `new_with_` now start with `from_`. This is more
+idiomatic in Rust.
 
 The `Norm` trait now uses an associated type instead of a type parameter.
 Other similar trait changes are to be expected in the future, e.g., for the
@@ -27,8 +33,8 @@ longer unsafe. Instead, their name end with `_unchecked`. In particular:
 
 ### Added
     - A `Unit<T>` type that wraps normalized values. In particular,
-      `UnitQuaternion<N>` is now replaced by `Unit<Quaternion<N>>`.
-    - `.ln()`, `.exp()` and `.powf(..)` for quaternions.
+      `UnitQuaternion<N>` is now an alias for `Unit<Quaternion<N>>`.
+    - `.ln()`, `.exp()` and `.powf(..)` for quaternions and unit quaternions.
     - `::from_parts(...)` to build a quaternion from its scalar and vector
       parts.
     - The `Norm` trait now has a `try_normalize()` that returns `None` if the
diff --git a/src/structs/isometry.rs b/src/structs/isometry.rs
index 9dda562b..7b9ceb8e 100644
--- a/src/structs/isometry.rs
+++ b/src/structs/isometry.rs
@@ -59,7 +59,7 @@ impl<N: BaseFloat> Isometry3<N> {
     #[inline]
     pub fn new_observer_frame(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Isometry3<N> {
         let new_rotation_matrix = Rotation3::new_observer_frame(&(*target - *eye), up);
-        Isometry3::new_with_rotation_matrix(eye.to_vector(), new_rotation_matrix)
+        Isometry3::from_rotation_matrix(eye.to_vector(), new_rotation_matrix)
     }
 
     /// Builds a right-handed look-at view matrix.
@@ -77,7 +77,7 @@ impl<N: BaseFloat> Isometry3<N> {
         let rotation = Rotation3::look_at_rh(&(*target - *eye), up);
         let trans    = rotation * (-*eye);
 
-        Isometry3::new_with_rotation_matrix(trans.to_vector(), rotation)
+        Isometry3::from_rotation_matrix(trans.to_vector(), rotation)
     }
 
     /// Builds a left-handed look-at view matrix.
@@ -95,7 +95,7 @@ impl<N: BaseFloat> Isometry3<N> {
         let rotation = Rotation3::look_at_lh(&(*target - *eye), up);
         let trans    = rotation * (-*eye);
 
-        Isometry3::new_with_rotation_matrix(trans.to_vector(), rotation)
+        Isometry3::from_rotation_matrix(trans.to_vector(), rotation)
     }
 }
 
diff --git a/src/structs/isometry_macros.rs b/src/structs/isometry_macros.rs
index de0aca4f..14cfb5fd 100644
--- a/src/structs/isometry_macros.rs
+++ b/src/structs/isometry_macros.rs
@@ -15,7 +15,7 @@ macro_rules! isometry_impl(
 
             /// Creates a new isometry from a rotation matrix and a vector.
             #[inline]
-            pub fn new_with_rotation_matrix(translation: $vector<N>, rotation: $rotmatrix<N>) -> $t<N> {
+            pub fn from_rotation_matrix(translation: $vector<N>, rotation: $rotmatrix<N>) -> $t<N> {
                 $t {
                     rotation:    rotation,
                     translation: translation
@@ -48,7 +48,7 @@ macro_rules! isometry_impl(
         impl<N: BaseFloat> One for $t<N> {
             #[inline]
             fn one() -> $t<N> {
-                $t::new_with_rotation_matrix(::zero(), ::one())
+                $t::from_rotation_matrix(::zero(), ::one())
             }
         }
 
@@ -63,7 +63,7 @@ macro_rules! isometry_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self.translation + self.rotation * right.translation,
                     self.rotation * right.rotation)
             }
@@ -88,7 +88,7 @@ macro_rules! isometry_impl(
 
             #[inline]
             fn mul(self, right: $rotmatrix<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(self.translation, self.rotation * right)
+                $t::from_rotation_matrix(self.translation, self.rotation * right)
             }
         }
 
@@ -97,7 +97,7 @@ macro_rules! isometry_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self * right.translation,
                     self * right.rotation)
             }
@@ -164,7 +164,7 @@ macro_rules! isometry_impl(
 
             #[inline]
             fn append_translation(&self, t: &$vector<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(*t + self.translation, self.rotation)
+                $t::from_rotation_matrix(*t + self.translation, self.rotation)
             }
 
             #[inline]
@@ -174,7 +174,7 @@ macro_rules! isometry_impl(
 
             #[inline]
             fn prepend_translation(&self, t: &$vector<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(self.translation + self.rotation * *t, self.rotation)
+                $t::from_rotation_matrix(self.translation + self.rotation * *t, self.rotation)
             }
 
             #[inline]
@@ -230,7 +230,7 @@ macro_rules! isometry_impl(
             fn append_rotation(&self, rotation: &$rotvector<N>) -> $t<N> {
                 let delta = $rotmatrix::new(*rotation);
 
-                $t::new_with_rotation_matrix(delta * self.translation, delta * self.rotation)
+                $t::from_rotation_matrix(delta * self.translation, delta * self.rotation)
             }
 
             #[inline]
@@ -244,7 +244,7 @@ macro_rules! isometry_impl(
             fn prepend_rotation(&self, rotation: &$rotvector<N>) -> $t<N> {
                 let delta = $rotmatrix::new(*rotation);
 
-                $t::new_with_rotation_matrix(self.translation, self.rotation * delta)
+                $t::from_rotation_matrix(self.translation, self.rotation * delta)
             }
 
             #[inline]
@@ -435,7 +435,7 @@ macro_rules! isometry_impl(
         #[cfg(feature="arbitrary")]
         impl<N: Arbitrary + BaseFloat> Arbitrary for $t<N> {
             fn arbitrary<G: Gen>(g: &mut G) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     Arbitrary::arbitrary(g),
                     Arbitrary::arbitrary(g)
                 )
diff --git a/src/structs/orthographic.rs b/src/structs/orthographic.rs
index 9564fcfb..7e355279 100644
--- a/src/structs/orthographic.rs
+++ b/src/structs/orthographic.rs
@@ -183,7 +183,7 @@ impl<N: BaseFloat> OrthographicMatrix3<N> {
     }
 
     /// Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.
-    pub fn new_with_fov(aspect: N, vfov: N, znear: N, zfar: N) -> OrthographicMatrix3<N> {
+    pub fn from_fov(aspect: N, vfov: N, znear: N, zfar: N) -> OrthographicMatrix3<N> {
         assert!(znear < zfar, "The far plane must be farther than the near plane.");
         assert!(!::is_zero(&aspect));
 
@@ -196,7 +196,7 @@ impl<N: BaseFloat> OrthographicMatrix3<N> {
 
     /// Creates a new orthographic matrix from a 4D matrix.
     #[inline]
-    pub fn new_with_matrix_unchecked(matrix: Matrix4<N>) -> OrthographicMatrix3<N> {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> OrthographicMatrix3<N> {
         OrthographicMatrix3 {
             matrix: matrix
         }
diff --git a/src/structs/perspective.rs b/src/structs/perspective.rs
index 0a03c604..4788e279 100644
--- a/src/structs/perspective.rs
+++ b/src/structs/perspective.rs
@@ -155,7 +155,7 @@ impl<N: BaseFloat> PerspectiveMatrix3<N> {
 
     /// Creates a new perspective projection matrix from a 4D matrix.
     #[inline]
-    pub fn new_with_matrix_unchecked(matrix: Matrix4<N>) -> PerspectiveMatrix3<N> {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> PerspectiveMatrix3<N> {
         PerspectiveMatrix3 {
             matrix: matrix
         }
diff --git a/src/structs/quaternion.rs b/src/structs/quaternion.rs
index 0752a0ac..2c0128ad 100644
--- a/src/structs/quaternion.rs
+++ b/src/structs/quaternion.rs
@@ -337,7 +337,7 @@ impl<N: BaseFloat> UnitQuaternion<N> {
         let jk = self.as_ref().j * self.as_ref().k * ::cast(2.0);
         let wi = self.as_ref().w * self.as_ref().i * ::cast(2.0);
 
-        Rotation3::new_with_matrix_unchecked(
+        Rotation3::from_matrix_unchecked(
             Matrix3::new(
                 ww + ii - jj - kk, ij - wk,           wj + ik,
                 wk + ij,           ww - ii + jj - kk, jk - wi,
diff --git a/src/structs/rotation.rs b/src/structs/rotation.rs
index 4c8f63a8..c8be3a11 100644
--- a/src/structs/rotation.rs
+++ b/src/structs/rotation.rs
@@ -157,7 +157,7 @@ impl<N: BaseFloat> Rotation3<N> {
     }
 
     /// Builds a rotation matrix from an orthogonal matrix.
-    pub fn new_with_matrix_unchecked(matrix: Matrix3<N>) -> Rotation3<N> {
+    pub fn from_matrix_unchecked(matrix: Matrix3<N>) -> Rotation3<N> {
         Rotation3 {
             submatrix: matrix
         }
@@ -166,12 +166,12 @@ impl<N: BaseFloat> Rotation3<N> {
     /// 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) -> Rotation3<N> {
+    pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Rotation3<N> {
         let (sr, cr) = roll.sin_cos();
         let (sp, cp) = pitch.sin_cos();
         let (sy, cy) = yaw.sin_cos();
 
-        Rotation3::new_with_matrix_unchecked(
+        Rotation3::from_matrix_unchecked(
             Matrix3::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,
@@ -198,7 +198,7 @@ impl<N: BaseFloat> Rotation3<N> {
         let xaxis = Norm::normalize(&Cross::cross(up, &zaxis));
         let yaxis = Norm::normalize(&Cross::cross(&zaxis, &xaxis));
 
-        Rotation3::new_with_matrix_unchecked(Matrix3::new(
+        Rotation3::from_matrix_unchecked(Matrix3::new(
                 xaxis.x, yaxis.x, zaxis.x,
                 xaxis.y, yaxis.y, zaxis.y,
                 xaxis.z, yaxis.z, zaxis.z))
diff --git a/src/structs/similarity_macros.rs b/src/structs/similarity_macros.rs
index 845e3d6e..73e8aaf7 100644
--- a/src/structs/similarity_macros.rs
+++ b/src/structs/similarity_macros.rs
@@ -29,12 +29,12 @@ macro_rules! similarity_impl(
             ///
             /// The scale factor may be negative but not zero.
             #[inline]
-            pub fn new_with_rotation_matrix(translation: $vector<N>, rotation: $rotation_matrix<N>, scale: N) -> $t<N> {
+            pub fn from_rotation_matrix(translation: $vector<N>, rotation: $rotation_matrix<N>, scale: N) -> $t<N> {
                 assert!(!scale.is_zero(), "A similarity transformation scale factor cannot be zero.");
 
                 $t {
                     scale:    scale,
-                    isometry: $isometry::new_with_rotation_matrix(translation, rotation)
+                    isometry: $isometry::from_rotation_matrix(translation, rotation)
                 }
             }
 
@@ -42,7 +42,7 @@ macro_rules! similarity_impl(
             ///
             /// The scale factor may be negative but not zero.
             #[inline]
-            pub fn new_with_isometry(isometry: $isometry<N>, scale: N) -> $t<N> {
+            pub fn from_isometry(isometry: $isometry<N>, scale: N) -> $t<N> {
                 assert!(!scale.is_zero(), "A similarity transformation scale factor cannot be zero.");
 
                 $t {
@@ -80,7 +80,7 @@ macro_rules! similarity_impl(
             #[inline]
             pub fn append_scale(&self, s: &N) -> $t<N> {
                 assert!(!s.is_zero(), "Cannot append a zero scale to a similarity transformation.");
-                $t::new_with_rotation_matrix(self.isometry.translation * *s, self.isometry.rotation, self.scale * *s)
+                $t::from_rotation_matrix(self.isometry.translation * *s, self.isometry.rotation, self.scale * *s)
             }
 
             /// Prepends in-place a scale to this similarity transformation.
@@ -94,7 +94,7 @@ macro_rules! similarity_impl(
             #[inline]
             pub fn prepend_scale(&self, s: &N) -> $t<N> {
                 assert!(!s.is_zero(), "A similarity transformation scale must not be zero.");
-                $t::new_with_isometry(self.isometry, self.scale * *s)
+                $t::from_isometry(self.isometry, self.scale * *s)
             }
 
             /// Sets the scale of this similarity transformation.
@@ -113,7 +113,7 @@ macro_rules! similarity_impl(
         impl<N: BaseFloat> One for $t<N> {
             #[inline]
             fn one() -> $t<N> {
-                $t::new_with_isometry(::one(), ::one())
+                $t::from_isometry(::one(), ::one())
             }
         }
 
@@ -164,7 +164,7 @@ macro_rules! similarity_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self.isometry.translation + self.isometry.rotation * (right.isometry.translation * self.scale),
                     self.isometry.rotation * right.isometry.rotation,
                     self.scale * right.scale)
@@ -191,7 +191,7 @@ macro_rules! similarity_impl(
 
             #[inline]
             fn mul(self, right: $isometry<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self.isometry.translation + self.isometry.rotation * (right.translation * self.scale),
                     self.isometry.rotation * right.rotation,
                     self.scale)
@@ -211,7 +211,7 @@ macro_rules! similarity_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self.translation + self.rotation * right.isometry.translation,
                     self.rotation * right.isometry.rotation,
                     right.scale)
@@ -228,7 +228,7 @@ macro_rules! similarity_impl(
 
             #[inline]
             fn mul(self, right: $rotation_matrix<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self.isometry.translation,
                     self.isometry.rotation * right,
                     self.scale)
@@ -247,7 +247,7 @@ macro_rules! similarity_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotation_matrix(
+                $t::from_rotation_matrix(
                     self * right.isometry.translation,
                     self * right.isometry.rotation,
                     right.scale)
@@ -389,7 +389,7 @@ macro_rules! similarity_impl(
                     scale = rng.gen();
                 }
 
-                $t::new_with_isometry(rng.gen(), scale)
+                $t::from_isometry(rng.gen(), scale)
             }
         }
 
@@ -402,7 +402,7 @@ macro_rules! similarity_impl(
         #[cfg(feature="arbitrary")]
         impl<N: Arbitrary + BaseFloat> Arbitrary for $t<N> {
             fn arbitrary<G: Gen>(g: &mut G) -> $t<N> {
-                $t::new_with_isometry(
+                $t::from_isometry(
                     Arbitrary::arbitrary(g),
                     Arbitrary::arbitrary(g)
                 )
diff --git a/src/traits/operations.rs b/src/traits/operations.rs
index 5934293f..7059e30e 100644
--- a/src/traits/operations.rs
+++ b/src/traits/operations.rs
@@ -173,7 +173,7 @@ pub trait ApproxEq<Eps>: Sized {
 impl ApproxEq<f32> for f32 {
     #[inline]
     fn approx_epsilon(_: Option<f32>) -> f32 {
-        f32::EPSILON * 10.0
+        1.0e-6
     }
 
     #[inline]
@@ -204,7 +204,7 @@ impl ApproxEq<f32> for f32 {
 impl ApproxEq<f64> for f64 {
     #[inline]
     fn approx_epsilon(_: Option<f64>) -> f64 {
-        f64::EPSILON * 10.0
+        1.0e-6
     }
 
     #[inline]
diff --git a/tests/quat.rs b/tests/quat.rs
index 1b0185eb..868f0092 100644
--- a/tests/quat.rs
+++ b/tests/quat.rs
@@ -9,7 +9,7 @@ fn test_quaternion_as_matrix() {
     for _ in 0usize .. 10000 {
         let axis_angle: Vector3<f64> = random();
 
-        assert!(na::approx_eq(&UnitQuaternion::new(axis_angle).to_rotation_matrix(), &Rotation3::new(axis_angle)))
+        assert!(na::approx_eq(&UnitQuaternion::from_scaled_axis(axis_angle).to_rotation_matrix(), &Rotation3::new(axis_angle)))
     }
 }
 
@@ -21,7 +21,7 @@ fn test_quaternion_mul_vec_or_point_as_matrix() {
         let point: Point3<f64> = random();
 
         let matrix  = Rotation3::new(axis_angle);
-        let quaternion = UnitQuaternion::new(axis_angle);
+        let quaternion = UnitQuaternion::from_scaled_axis(axis_angle);
 
         assert!(na::approx_eq(&(matrix * vector), &(quaternion * vector)));
         assert!(na::approx_eq(&(matrix * point), &(quaternion * point)));
@@ -39,8 +39,8 @@ fn test_quaternion_div_quaternion() {
         let r1 = Rotation3::new(axis_angle1);
         let r2 = na::inverse(&Rotation3::new(axis_angle2)).unwrap();
 
-        let q1 = UnitQuaternion::new(axis_angle1);
-        let q2 = UnitQuaternion::new(axis_angle2);
+        let q1 = UnitQuaternion::from_scaled_axis(axis_angle1);
+        let q2 = UnitQuaternion::from_scaled_axis(axis_angle2);
 
         assert!(na::approx_eq(&(q1 / q2).to_rotation_matrix(), &(r1 * r2)))
     }
@@ -51,7 +51,7 @@ fn test_quaternion_to_axis_angle() {
     for _ in 0usize .. 10000 {
         let axis_angle: Vector3<f64> = random();
 
-        let q = UnitQuaternion::new(axis_angle);
+        let q = UnitQuaternion::from_scaled_axis(axis_angle);
 
         println!("{:?} {:?}", q.rotation(), axis_angle);
         assert!(na::approx_eq(&q.rotation(), &axis_angle))
@@ -63,8 +63,8 @@ fn test_quaternion_euler_angles() {
     for _ in 0usize .. 10000 {
         let angles: Vector3<f64> = random();
 
-        let q = UnitQuaternion::new_with_euler_angles(angles.x, angles.y, angles.z);
-        let m = Rotation3::new_with_euler_angles(angles.x, angles.y, angles.z);
+        let q = UnitQuaternion::from_euler_angles(angles.x, angles.y, angles.z);
+        let m = Rotation3::from_euler_angles(angles.x, angles.y, angles.z);
 
         assert!(na::approx_eq(&q.to_rotation_matrix(), &m))
     }