Start implementation of quaternions.

src/structs/quat.rs

@@ -0,0 +1,75 @@
+//! Quaternion definition.
+
+/// A quaternion.
+///
+/// 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
+    i: N,
+    j: N,
+    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> {
+        Quat {
+            w: w,
+            i: i,
+            j: j,
+            k: k
+        }
+    }
+}
+
+impl<N: Add<N, N>> Add<Quat<N>, Quat<N>> for Quat<N> {
+    fn add(&self, other: &Quat<N>) -> Quat<N> {
+        Quat::new(
+            self.w + other.w,
+            self.i + other.i,
+            self.j + other.j,
+            self.k + other.k)
+    }
+}
+
+impl<N> Mul<Quat<N>, Quat<N>> for Quat<N> {
+    fn mul(&self, other: &Quat<N>) -> Quat<N> {
+        Quat::new(
+            self.w * other.w - self.x * other.x - self.y * other.y - self.z * other.z,
+            self.a * other.b - self.b * other.a - self.c * other.d - self.d * other.c,
+            self.a * other.c - self.b * other.d - self.c * other.a - self.d * other.b,
+            self.w * other.w - self.x * other.x - self.y * other.y - self.z * other.z,
+            )
+    }
+}
+
+impl<N: Zero> Rotate<Vec3<N>> for Quat<N> {
+    #[inline]
+    fn rotate(&self, v: &Vec3<N>) -> Vec3<N> {
+        *self * *v_quat * self.inv()
+    }
+
+    #[inline]
+    fn inv_rotate(&self, v: &Vec3<N>) -> Vec3<N> {
+        -self * *v
+    }
+}
+
+impl Rotate<Vec4<N>> for (QuatPair<N>, QuatPair<N>) {
+    #[inline]
+    fn rotate(&self, v: &Vec4<N>) -> Vec4<N> {
+        let (ref l, ref r) = *self;
+
+        *l * *v * *r
+    }
+
+    #[inline]
+    fn inv_rotate(&self, v: &Vec4<N>) -> Vec4<N> {
+        let (ref l, ref r) = *self;
+
+        (-r) * **v * (-l)
+    }
+}