Flesh out Rotation{2, 3} traits, and impl for some types

src/cgmath/matrix.rs

@@ -242,6 +242,8 @@ pub trait Matrix
     #[inline] fn add_self_m(&mut self, other: &Self) { self.each_mut(|i, c| *c = c.add_v(other.c(i))) }
     #[inline] fn sub_self_m(&mut self, other: &Self) { self.each_mut(|i, c| *c = c.sub_v(other.c(i))) }
 
+    #[inline] fn mul_self_m(&mut self, other: &Self) { *self = self.mul_m(other); }
+
     fn transpose(&self) -> Self;
     fn transpose_self(&mut self);
     fn determinant(&self) -> S;

src/cgmath/quaternion.rs

@@ -16,6 +16,7 @@
 use std::num::{zero, one, sqrt};
 
 use angle::{Angle, Rad, acos, cos, sin};
+use array::{Array, build};
 use matrix::{Mat3, ToMat3};
 use vector::{Vec3, Vector, EuclideanVector};
 use util::two;
@@ -24,6 +25,9 @@ use util::two;
 #[deriving(Clone, Eq)]
 pub struct Quat<S> { s: S, v: Vec3<S> }
 
+array!(impl<S> Quat<S> -> [S, ..4] _4)
+approx_eq!(impl<S> Quat<S>)
+
 pub trait ToQuat<S: Clone + Float> {
     fn to_quat(&self) -> Quat<S>;
 }
@@ -81,19 +85,13 @@ impl<S: Clone + Float> Quat<S> {
     /// The sum of this quaternion and `other`
     #[inline]
     pub fn add_q(&self, other: &Quat<S>) -> Quat<S> {
-        Quat::new(self.s   + other.s,
-                  self.v.x + other.v.x,
-                  self.v.y + other.v.y,
-                  self.v.z + other.v.z)
+        build(|i| self.i(i).add(other.i(i)))
     }
 
-    /// The sum of this quaternion and `other`
+    /// The difference between this quaternion and `other`
     #[inline]
     pub fn sub_q(&self, other: &Quat<S>) -> Quat<S> {
-        Quat::new(self.s   - other.s,
-                  self.v.x - other.v.x,
-                  self.v.y - other.v.y,
-                  self.v.z - other.v.z)
+        build(|i| self.i(i).add(other.i(i)))
     }
 
     /// The the result of multipliplying the quaternion by `other`
@@ -104,6 +102,31 @@ impl<S: Clone + Float> Quat<S> {
                   self.s * other.v.z + self.v.z * other.s + self.v.x * other.v.y - self.v.y * other.v.x)
     }
 
+    #[inline]
+    pub fn mul_self_s(&mut self, s: S) {
+        self.each_mut(|_, x| *x = x.mul(&s))
+    }
+
+    #[inline]
+    pub fn div_self_s(&mut self, s: S) {
+        self.each_mut(|_, x| *x = x.div(&s))
+    }
+
+    #[inline]
+    pub fn add_self_q(&mut self, other: &Quat<S>) {
+        self.each_mut(|i, x| *x = x.add(other.i(i)));
+    }
+
+    #[inline]
+    pub fn sub_self_q(&mut self, other: &Quat<S>) {
+        self.each_mut(|i, x| *x = x.sub(other.i(i)));
+    }
+
+    #[inline]
+    pub fn mul_self_q(&mut self, other: &Quat<S>) {
+        *self = self.mul_q(other);
+    }
+
     /// The dot product of the quaternion and `other`
     #[inline]
     pub fn dot(&self, other: &Quat<S>) -> S {
@@ -116,12 +139,6 @@ impl<S: Clone + Float> Quat<S> {
         Quat::from_sv(self.s.clone(), -self.v.clone())
     }
 
-    /// The multiplicative inverse of the quaternion
-    #[inline]
-    pub fn inverse(&self) -> Quat<S> {
-        self.conjugate().div_s(self.magnitude2())
-    }
-
     /// The squared magnitude of the quaternion. This is useful for
     /// magnitude comparisons where the exact magnitude does not need to be
     /// calculated.

src/cgmath/rotation.rs

@@ -13,14 +13,17 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-use angle::Angle;
+use std::num::{cast, one};
+
+use angle::{Angle, sin, cos, sin_cos};
 use array::Array;
+use matrix::Matrix;
 use matrix::{Mat2, ToMat2};
 use matrix::{Mat3, ToMat3};
 use point::{Point2, Point3};
-use quaternion::ToQuat;
+use quaternion::{Quat, ToQuat};
 use ray::{Ray2, Ray3};
-use vector::{Vec2, Vec3};
+use vector::{Vector, Vec2, Vec3};
 
 /// A two-dimensional rotation
 pub trait Rotation2
@@ -29,15 +32,16 @@ pub trait Rotation2
 >
 :   Eq
 +   ApproxEq<S>
-+   Neg<Self>
-+   Add<Self, Self>
-+   Sub<Self, Self>
 +   ToMat2<S>
 +   ToRot2<S>
 {
-    fn rotate_point2(&self, point: Point2<S>) -> Point2<S>;
+    fn rotate_point2(&self, point: &Point2<S>) -> Point2<S>;
     fn rotate_vec2(&self, vec: &Vec2<S>) -> Vec2<S>;
     fn rotate_ray2(&self, ray: &Ray2<S>) -> Ray2<S>;
+    fn concat(&self, other: &Self) -> Self;
+    fn concat_self(&mut self, other: &Self);
+    fn invert(&self) -> Self;
+    fn invert_self(&mut self);
 }
 
 /// A three-dimensional rotation
@@ -47,9 +51,6 @@ pub trait Rotation3
 >
 :   Eq
 +   ApproxEq<S>
-+   Neg<Self>
-+   Add<Self, Self>
-+   Sub<Self, Self>
 +   ToMat3<S>
 +   ToRot3<S>
 +   ToQuat<S>
@@ -57,6 +58,10 @@ pub trait Rotation3
     fn rotate_point3(&self, point: &Point3<S>) -> Point3<S>;
     fn rotate_vec3(&self, vec: &Vec3<S>) -> Vec3<S>;
     fn rotate_ray3(&self, ray: &Ray3<S>) -> Ray3<S>;
+    fn concat(&self, other: &Self) -> Self;
+    fn concat_self(&mut self, other: &Self);
+    fn invert(&self) -> Self;
+    fn invert_self(&mut self);
 }
 
 /// A two-dimensional rotation matrix.
@@ -70,57 +75,386 @@ pub struct Rot2<S> {
     priv mat: Mat2<S>
 }
 
-pub trait ToRot2<S: Clone + Float> {
+impl<S: Float> Rot2<S> {
+    #[inline]
+    pub fn as_mat2<'a>(&'a self) -> &'a Mat2<S> { &'a self.mat }
+}
+
+pub trait ToRot2<S: Float> {
     fn to_rot2(&self) -> Rot2<S>;
 }
 
+impl<S: Float> ToRot2<S> for Rot2<S> {
+    #[inline]
+    fn to_rot2(&self) -> Rot2<S> { self.clone() }
+}
+
+impl<S: Float> ToMat2<S> for Rot2<S> {
+    #[inline]
+    fn to_mat2(&self) -> Mat2<S> { self.mat.clone() }
+}
+
+impl<S: Float> Rotation2<S> for Rot2<S> {
+    #[inline]
+    fn rotate_point2(&self, _point: &Point2<S>) -> Point2<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn rotate_vec2(&self, vec: &Vec2<S>) -> Vec2<S> { self.mat.mul_v(vec) }
+
+    #[inline]
+    fn rotate_ray2(&self, _ray: &Ray2<S>) -> Ray2<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat(&self, other: &Rot2<S>) -> Rot2<S> { Rot2 { mat: self.mat.mul_m(&other.mat) } }
+
+    #[inline]
+    fn concat_self(&mut self, other: &Rot2<S>) { self.mat.mul_self_m(&other.mat); }
+
+    // TODO: we know the matrix is orthogonal, so this could be re-written
+    // to be faster
+    #[inline]
+    fn invert(&self) -> Rot2<S> { Rot2 { mat: self.mat.invert().unwrap() } }
+
+    // TODO: we know the matrix is orthogonal, so this could be re-written
+    // to be faster
+    #[inline]
+    fn invert_self(&mut self) { self.mat.invert_self(); }
+}
+
+impl<S: Float> ApproxEq<S> for Rot2<S> {
+    #[inline]
+    fn approx_epsilon() -> S {
+        // TODO: fix this after static methods are fixed in rustc
+        fail!(~"Doesn't work!");
+    }
+
+    #[inline]
+    fn approx_eq(&self, other: &Rot2<S>) -> bool {
+        self.mat.approx_eq(&other.mat)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &Rot2<S>, approx_epsilon: &S) -> bool {
+        self.mat.approx_eq_eps(&other.mat, approx_epsilon)
+    }
+}
+
 /// A three-dimensional rotation matrix.
 ///
 /// The matrix is guaranteed to be orthogonal, so some operations, specifically
 /// inversion, can be implemented more efficiently than the implementations for
-/// `math::Mat3`. To enforce orthogonality at the type level the operations have
+/// `math::Mat3`. To ensure orthogonality is maintained, the operations have
 /// been restricted to a subeset of those implemented on `Mat3`.
 #[deriving(Eq, Clone)]
 pub struct Rot3<S> {
     priv mat: Mat3<S>
 }
 
-pub trait ToRot3<S: Clone + Float> {
+impl<S: Float> Rot3<S> {
+    #[inline]
+    pub fn look_at(dir: &Vec3<S>, up: &Vec3<S>) -> Rot3<S> {
+        Rot3 { mat: Mat3::look_at(dir, up) }
+    }
+
+    #[inline]
+    pub fn as_mat3<'a>(&'a self) -> &'a Mat3<S> { &'a self.mat }
+}
+
+pub trait ToRot3<S: Float> {
     fn to_rot3(&self) -> Rot3<S>;
 }
 
+impl<S: Float> ToRot3<S> for Rot3<S> {
+    #[inline]
+    fn to_rot3(&self) -> Rot3<S> { self.clone() }
+}
+
+impl<S: Float> ToMat3<S> for Rot3<S> {
+    #[inline]
+    fn to_mat3(&self) -> Mat3<S> { self.mat.clone() }
+}
+
+impl<S: Float> ToQuat<S> for Rot3<S> {
+    #[inline]
+    fn to_quat(&self) -> Quat<S> { self.mat.to_quat() }
+}
+
+impl<S: Float> Rotation3<S> for Rot3<S> {
+    #[inline]
+    fn rotate_point3(&self, _point: &Point3<S>) -> Point3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn rotate_vec3(&self, vec: &Vec3<S>) -> Vec3<S> { self.mat.mul_v(vec) }
+
+    #[inline]
+    fn rotate_ray3(&self, _ray: &Ray3<S>) -> Ray3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat(&self, other: &Rot3<S>) -> Rot3<S> { Rot3 { mat: self.mat.mul_m(&other.mat) } }
+
+    #[inline]
+    fn concat_self(&mut self, other: &Rot3<S>) { self.mat.mul_self_m(&other.mat); }
+
+    // TODO: we know the matrix is orthogonal, so this could be re-written
+    // to be faster
+    #[inline]
+    fn invert(&self) -> Rot3<S> { Rot3 { mat: self.mat.invert().unwrap() } }
+
+    // TODO: we know the matrix is orthogonal, so this could be re-written
+    // to be faster
+    #[inline]
+    fn invert_self(&mut self) { self.mat.invert_self(); }
+}
+
+impl<S: Float> ApproxEq<S> for Rot3<S> {
+    #[inline]
+    fn approx_epsilon() -> S {
+        // TODO: fix this after static methods are fixed in rustc
+        fail!(~"Doesn't work!");
+    }
+
+    #[inline]
+    fn approx_eq(&self, other: &Rot3<S>) -> bool {
+        self.mat.approx_eq(&other.mat)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &Rot3<S>, approx_epsilon: &S) -> bool {
+        self.mat.approx_eq_eps(&other.mat, approx_epsilon)
+    }
+}
+
+// Quaternion Rotation impls
+
+impl<S: Float> ToRot3<S> for Quat<S> {
+    #[inline]
+    fn to_rot3(&self) -> Rot3<S> { Rot3 { mat: self.to_mat3() } }
+}
+
+impl<S: Float> ToQuat<S> for Quat<S> {
+    #[inline]
+    fn to_quat(&self) -> Quat<S> { self.clone() }
+}
+
+impl<S: Float> Rotation3<S> for Quat<S> {
+    #[inline]
+    fn rotate_point3(&self, _point: &Point3<S>) -> Point3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn rotate_vec3(&self, vec: &Vec3<S>) -> Vec3<S> { self.mul_v(vec) }
+
+    #[inline]
+    fn rotate_ray3(&self, _ray: &Ray3<S>) -> Ray3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat(&self, other: &Quat<S>) -> Quat<S> { self.mul_q(other) }
+
+    #[inline]
+    fn concat_self(&mut self, other: &Quat<S>) { self.mul_self_q(other); }
+
+    #[inline]
+    fn invert(&self) -> Quat<S> { self.conjugate().div_s(self.magnitude2()) }
+
+    #[inline]
+    fn invert_self(&mut self) { *self = self.invert() }
+}
+
 /// Euler angles
 ///
-/// Whilst Euler angles are easier to visualise, and more intuitive to specify,
-/// they are not reccomended for general use because they are prone to gimble
-/// lock.
-///
 /// # Fields
 ///
 /// - `x`: the angular rotation around the `x` axis (pitch)
 /// - `y`: the angular rotation around the `y` axis (yaw)
 /// - `z`: the angular rotation around the `z` axis (roll)
+///
+/// # Notes
+///
+/// Whilst Euler angles are more intuitive to specify than quaternions,
+/// they are not reccomended for general use because they are prone to gimble
+/// lock.
 #[deriving(Eq, Clone)]
 pub struct Euler<A> { x: A, y: A, z: A }
 
 array!(impl<A> Euler<A> -> [A, ..3] _3)
 
-pub trait ToEuler<A> {
-    fn to_euler(&self) -> Euler<A>;
-}
-
-impl<S: Clone + Float, A: Angle<S>> Euler<A> {
+impl<S: Float, A: Angle<S>> Euler<A> {
     #[inline]
     pub fn new(x: A, y: A, z: A) -> Euler<A> {
         Euler { x: x, y: y, z: z }
     }
 }
 
+pub trait ToEuler<A> {
+    fn to_euler(&self) -> Euler<A>;
+}
+
+impl<S: Float, A: Angle<S>> ToMat3<S> for Euler<A> {
+    fn to_mat3(&self) -> Mat3<S> {
+        // http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
+        let (sx, cx) = sin_cos(self.x.clone());
+        let (sy, cy) = sin_cos(self.y.clone());
+        let (sz, cz) = sin_cos(self.z.clone());
+
+        Mat3::new(cy * cz, cy * sz, -sy,
+                  -cx * sz + sx * sy * cz, cx * cz + sx * sy * sz, sx * cy,
+                  sx * sz + cx * sy * cz, -sx * cz + cx * sy * sz, cx * cy)
+    }
+}
+
+impl<S: Float, A: Angle<S>> ToRot3<S> for Euler<A> {
+    #[inline]
+    fn to_rot3(&self) -> Rot3<S> {
+        Rot3 { mat: self.to_mat3() }
+    }
+}
+
+impl<S: Float, A: Angle<S>> ToQuat<S> for Euler<A> {
+    fn to_quat(&self) -> Quat<S> {
+        // http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles#Conversion
+        let (sx2, cx2) = sin_cos(self.x.div_s(cast(2)));
+        let (sy2, cy2) = sin_cos(self.y.div_s(cast(2)));
+        let (sz2, cz2) = sin_cos(self.z.div_s(cast(2)));
+
+        Quat::new(cz2 * cx2 * cy2 + sz2 * sx2 * sy2,
+                  sz2 * cx2 * cy2 - cz2 * sx2 * sy2,
+                  cz2 * sx2 * cy2 + sz2 * cx2 * sy2,
+                  cz2 * cx2 * sy2 - sz2 * sx2 * cy2)
+    }
+}
+
+impl<S: Float, A: Angle<S>> Rotation3<S> for Euler<A> {
+    #[inline]
+    fn rotate_point3(&self, _point: &Point3<S>) -> Point3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn rotate_vec3(&self, _vec: &Vec3<S>) -> Vec3<S> { fail!("Not yet implemented"); }
+
+    #[inline]
+    fn rotate_ray3(&self, _ray: &Ray3<S>) -> Ray3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat(&self, _other: &Euler<A>) -> Euler<A> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat_self(&mut self, _other: &Euler<A>) { fail!("Not yet implemented"); }
+
+    #[inline]
+    fn invert(&self) -> Euler<A> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn invert_self(&mut self) { fail!("Not yet implemented"); }
+}
+
+impl<S: Float, A: Angle<S>> ApproxEq<S> for Euler<A> {
+    #[inline]
+    fn approx_epsilon() -> S {
+        // TODO: fix this after static methods are fixed in rustc
+        fail!(~"Doesn't work!");
+    }
+
+    #[inline]
+    fn approx_eq(&self, other: &Euler<A>) -> bool {
+        self.x.approx_eq(&other.x) &&
+        self.y.approx_eq(&other.y) &&
+        self.z.approx_eq(&other.z)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &Euler<A>, approx_epsilon: &S) -> bool {
+        self.x.approx_eq_eps(&other.x, approx_epsilon) &&
+        self.y.approx_eq_eps(&other.y, approx_epsilon) &&
+        self.z.approx_eq_eps(&other.z, approx_epsilon)
+    }
+}
+
 /// A rotation about an arbitrary axis
 #[deriving(Eq, Clone)]
-pub struct AxisAngle<S, A> {
-    axis: Vec3<S>,
-    angle: A,
+pub struct AxisAngle<S, A> { v: Vec3<S>, a: A }
+
+impl<S: Float, A: Angle<S>> AxisAngle<S, A> {
+    #[inline]
+    pub fn new(v: Vec3<S>, a: A) -> AxisAngle<S, A> {
+        AxisAngle { v: v, a: a }
+    }
+}
+
+impl<S: Float, A: Angle<S>> ToMat3<S> for AxisAngle<S, A> {
+    fn to_mat3(&self) -> Mat3<S> {
+        let (s, c) = sin_cos(self.a.clone());
+        let _1subc = one::<S>() - c;
+
+        Mat3::new(_1subc * self.v.x * self.v.x + c,
+                  _1subc * self.v.x * self.v.y + s * self.v.z,
+                  _1subc * self.v.x * self.v.z - s * self.v.y,
+
+                  _1subc * self.v.x * self.v.y - s * self.v.z,
+                  _1subc * self.v.y * self.v.y + c,
+                  _1subc * self.v.y * self.v.z + s * self.v.x,
+
+                  _1subc * self.v.x * self.v.z + s * self.v.y,
+                  _1subc * self.v.y * self.v.z - s * self.v.x,
+                  _1subc * self.v.z * self.v.z + c)
+    }
+}
+
+impl<S: Float, A: Angle<S>> ToRot3<S> for AxisAngle<S, A> {
+    #[inline]
+    fn to_rot3(&self) -> Rot3<S> {
+        Rot3 { mat: self.to_mat3() }
+    }
+}
+
+impl<S: Float, A: Angle<S>> ToQuat<S> for AxisAngle<S, A> {
+    fn to_quat(&self) -> Quat<S> {
+        let half = self.a.div_s(cast(2));
+        Quat::from_sv(
+            cos(half.clone()),
+            self.v.mul_s(sin(half.clone()))
+        )
+    }
+}
+
+impl<S: Float, A: Angle<S>> Rotation3<S> for AxisAngle<S, A> {
+    #[inline]
+    fn rotate_point3(&self, _point: &Point3<S>) -> Point3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn rotate_vec3(&self, _vec: &Vec3<S>) -> Vec3<S> { fail!("Not yet implemented"); }
+
+    #[inline]
+    fn rotate_ray3(&self, _ray: &Ray3<S>) -> Ray3<S> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat(&self, _other: &AxisAngle<S, A>) -> AxisAngle<S, A> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn concat_self(&mut self, _other: &AxisAngle<S, A>) { fail!("Not yet implemented"); }
+
+    #[inline]
+    fn invert(&self) -> AxisAngle<S, A> { fail!("Not yet implemented") }
+
+    #[inline]
+    fn invert_self(&mut self) { fail!("Not yet implemented"); }
+}
+
+impl<S: Float, A: Angle<S>> ApproxEq<S> for AxisAngle<S, A> {
+    #[inline]
+    fn approx_epsilon() -> S {
+        // TODO: fix this after static methods are fixed in rustc
+        fail!(~"Doesn't work!");
+    }
+
+    #[inline]
+    fn approx_eq(&self, other: &AxisAngle<S, A>) -> bool {
+        self.v.approx_eq(&other.v) &&
+        self.a.approx_eq(&other.a)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &AxisAngle<S, A>, approx_epsilon: &S) -> bool {
+        self.v.approx_eq_eps(&other.v, approx_epsilon) &&
+        self.a.approx_eq_eps(&other.a, approx_epsilon)
+    }
 }
 
 /// An angle around the X axis (pitch).
@@ -134,14 +468,3 @@ pub struct AngleY<A>(A);
 /// An angle around the Z axis (roll).
 #[deriving(Eq, Ord, Clone)]
 pub struct AngleZ<A>(A);
-
-impl<S: Clone + Float, A: Angle<S>> Neg<AngleX<A>> for AngleX<A> { #[inline] fn neg(&self) -> AngleX<A> { AngleX(-**self) } }
-impl<S: Clone + Float, A: Angle<S>> Neg<AngleY<A>> for AngleY<A> { #[inline] fn neg(&self) -> AngleY<A> { AngleY(-**self) } }
-impl<S: Clone + Float, A: Angle<S>> Neg<AngleZ<A>> for AngleZ<A> { #[inline] fn neg(&self) -> AngleZ<A> { AngleZ(-**self) } }
-
-impl<S: Clone + Float, A: Angle<S>> Add<AngleX<A>, AngleX<A>> for AngleX<A> { #[inline] fn add(&self, other: &AngleX<A>) -> AngleX<A> { AngleX((**self).add_a(*other.clone())) } }
-impl<S: Clone + Float, A: Angle<S>> Add<AngleY<A>, AngleY<A>> for AngleY<A> { #[inline] fn add(&self, other: &AngleY<A>) -> AngleY<A> { AngleY((**self).add_a(*other.clone())) } }
-impl<S: Clone + Float, A: Angle<S>> Add<AngleZ<A>, AngleZ<A>> for AngleZ<A> { #[inline] fn add(&self, other: &AngleZ<A>) -> AngleZ<A> { AngleZ((**self).add_a(*other.clone())) } }
-impl<S: Clone + Float, A: Angle<S>> Sub<AngleX<A>, AngleX<A>> for AngleX<A> { #[inline] fn sub(&self, other: &AngleX<A>) -> AngleX<A> { AngleX((**self).sub_a(*other.clone())) } }
-impl<S: Clone + Float, A: Angle<S>> Sub<AngleY<A>, AngleY<A>> for AngleY<A> { #[inline] fn sub(&self, other: &AngleY<A>) -> AngleY<A> { AngleY((**self).sub_a(*other.clone())) } }
-impl<S: Clone + Float, A: Angle<S>> Sub<AngleZ<A>, AngleZ<A>> for AngleZ<A> { #[inline] fn sub(&self, other: &AngleZ<A>) -> AngleZ<A> { AngleZ((**self).sub_a(*other.clone())) } }