Transcendentals2

src/geometry/quaternion.rs

@@ -21,6 +21,27 @@ use base::{Matrix3, MatrixN, MatrixSlice, MatrixSliceMut, Unit, Vector3, Vector4
 
 use geometry::Rotation;
 
+/// Calculates the cardinal sine function
+#[inline]
+fn sinc<N: Real>(v: N) -> N {
+    if v == N::zero() {
+        N::zero()
+    }
+    else {
+        v.sin() / v
+    }
+}
+
+#[inline]
+fn sinhc<N: Real>(v: N) -> N {
+    if v == N::zero() {
+        N::zero()
+    }
+    else {
+        v.sinh() / v
+    }
+}
+
 /// A quaternion. See the type alias `UnitQuaternion = Unit<Quaternion>` for a quaternion
 /// that may be used as a rotation.
 #[repr(C)]
@@ -124,6 +145,12 @@ impl<N: Real> Quaternion<N> {
         Self::from(self.coords.normalize())
     }
 
+    /// The imaginary part of this quaternion.
+    #[inline]
+    pub fn imag(&self) -> Vector3<N> {
+        self.coords.xyz()
+    }
+
     /// The conjugate of this quaternion.
     ///
     /// # Example
@@ -135,13 +162,7 @@ impl<N: Real> Quaternion<N> {
     /// ```
     #[inline]
     pub fn conjugate(&self) -> Self {
-        let v = Vector4::new(
-            -self.coords[0],
-            -self.coords[1],
-            -self.coords[2],
-            self.coords[3],
-        );
-        Self::from(v)
+        Self::from_parts(self.w, -self.imag())
     }
 
     /// Inverts this quaternion if it is not zero.
@@ -506,6 +527,22 @@ impl<N: Real> Quaternion<N> {
     pub fn normalize_mut(&mut self) -> N {
         self.coords.normalize_mut()
     }
+
+    /// Calculates quaternionic sin
+    #[inline]
+    pub fn cos(&self) -> Self {
+        let z = self.imag().magnitude();
+        let w = -self.w.sin() * sinhc(z);
+        Self::from_parts(self.w.cos() * z.cosh(), self.imag() * w)
+    }
+
+    /// Calculates quaternionic sin
+    #[inline]
+    pub fn sin(&self) -> Self {
+        let z = self.imag().magnitude();
+        let w = self.w.cos() * sinhc(z);
+        Self::from_parts(self.w.sin() * z.cosh(), self.imag() * w)
+    }
 }
 
 impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {