✨ Add function inv_rotation

The function `inv_rotation` can be used to return the inverse
rotation depending on the type of the argument (DCM or Quaternion).

Author: ronisbr

src/ReferenceFrameRotations.jl

@@ -77,6 +77,7 @@ include("compose_rotations.jl")
 include("DCM.jl")
 include("euler_angle_axis.jl")
 include("euler_angles.jl")
+include("inv_rotations.jl")
 include("quaternion.jl")
 
 end # module

src/inv_rotations.jl

@@ -0,0 +1,35 @@
+export inv_rotation
+
+################################################################################
+#                              Inverse Rotations
+################################################################################
+
+"""
+### @inline function inv_rotation(R)
+
+Compute the inverse rotation of `R`, which can be a Direction Cosine Matrix or
+Quaternion.
+
+The output will have the same type as `R` (DCM or quaternion).
+
+##### Args
+
+* R: Rotation that will be inversed.
+
+##### Returns
+
+The inverse rotation.
+
+##### Remarks
+
+If `R` is a DCM, than its transpose is computed instead of its inverse to reduce
+the computational burden. The both are equal if the DCM has unit norm. This must
+be verified by the used.
+
+If `R` is a quaternion, than its conjugate is computed instead of its inverse to
+reduce the computational burden. The both are equal if the quaternion has unit
+norm. This must be verified by the used.
+
+"""
+@inline inv_rotation(D::DCM) = D'
+@inline inv_rotation(q::Quaternion) = conj(q)

test/test_dcm.jl

@@ -80,5 +80,5 @@ for k = 1:samples
     dcm3 = dcm2*dcm1
 
     # Check if they are orthonormal.
-    @test norm(dcm3'-inv(dcm1)*inv(dcm2)) < 1e-10
+    @test norm(inv_rotation(dcm3)-inv(dcm1)*inv(dcm2)) < 5e-10
 end

test/test_quaternions.jl

@@ -19,7 +19,7 @@ for i = 1:samples
     v = [0;randn();randn()]
 
     # Rotate the reference using the quaternion.
-    v_r = vect(inv(q)*v*q)
+    v_r = vect(inv_rotation(q)*v*q)
 
     # Get the sine of the angle between the representations.
     sin_ang = (cross(v_r, v)/norm(v)^2)[1]
@@ -49,7 +49,7 @@ for i = 1:samples
     v = [randn();0;randn()]
 
     # Rotate the reference using the quaternion.
-    v_r = vect(inv(q)*v*q)
+    v_r = vect(inv_rotation(q)*v*q)
 
     # Get the sine of the angle between the representations.
     sin_ang = (cross(v_r, v)/norm(v)^2)[2]
@@ -80,7 +80,7 @@ for i = 1:samples
     v = [randn();randn();0]
 
     # Rotate the reference using the quaternion.
-    v_r = vect(inv(q)*v*q)
+    v_r = vect(inv_rotation(q)*v*q)
 
     # Get the sine of the angle between the representations.
     sin_ang = (cross(v_r, v)/norm(v)^2)[3]
@@ -173,3 +173,7 @@ qc = conj(q)
 @test qc.q1 == -6
 @test qc.q2 == -9
 @test qc.q3 == -12
+
+q = Quaternion(1.0,1.0,1.0,1.0)
+@test inv_rotation(q) != inv(q)
+@test (q*inv(q))[:] ≈ [1;0;0;0]