ENH: use intermediate constants for sin/cos in coordinate rotations

- makes an easier overview of the rotation matrix coefficients
  (issue #863).

  Provided as a distinct commit for easier examination of the lines changed.

src/meshTools/coordinate/rotation/EulerCoordinateRotation.C

@@ -65,20 +65,21 @@ Foam::tensor Foam::EulerCoordinateRotation::rotation
         psi   *= degToRad();
     }
 
+    const scalar c1 = cos(phi);   const scalar s1 = sin(phi);
+    const scalar c2 = cos(theta); const scalar s2 = sin(theta);
+    const scalar c3 = cos(psi);   const scalar s3 = sin(psi);
+
+    // Compare
+    // https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
+    //
+    // Z1-X2-Z3 rotation
+
     return
         tensor
         (
-            cos(phi)*cos(psi) - sin(phi)*sin(psi)*cos(theta),
+            c1*c3 - c2*s1*s3, -c1*s3 - c2*c3*s1,  s1*s2,
-            -sin(phi)*cos(psi)*cos(theta) - cos(phi)*sin(psi),
+            c3*s1 + c1*c2*s3,  c1*c2*c3 - s1*s3, -c1*s2,
-            sin(phi)*sin(theta),
+            s2*s3,             c3*s2,             c2
-
-            cos(phi)*sin(psi)*cos(theta) + sin(phi)*cos(psi),
-            cos(phi)*cos(psi)*cos(theta) - sin(phi)*sin(psi),
-            -cos(phi)*sin(theta),
-
-            sin(psi)*sin(theta),
-            cos(psi)*sin(theta),
-            cos(theta)
         );
 }
 

src/meshTools/coordinate/rotation/EulerCoordinateRotation.H

@@ -32,14 +32,9 @@ Description
     The order of the parameter arguments matches this rotation order.
 
     For reference and illustration, see
-    http://mathworld.wolfram.com/EulerAngles.html
+    https://en.wikipedia.org/wiki/Euler_angles
-    and
-    https://en.wikipedia.org/wiki/Euler_angles#Conventions
 
-    Note, however, that it is the reverse transformation
+    The rotation angles are in degrees, unless otherwise explicitly specified:
-    (local->global) that is defined here.
-
-    - the rotation angles are in degrees, unless otherwise explicitly specified:
 
     \verbatim
     coordinateRotation

src/meshTools/coordinate/rotation/STARCDCoordinateRotation.C

@@ -166,20 +166,17 @@ Foam::tensor Foam::STARCDCoordinateRotation::rotation
         z *= degToRad();
     }
 
+    const scalar cx = cos(x);  const scalar sx = sin(x);
+    const scalar cy = cos(y);  const scalar sy = sin(y);
+    const scalar cz = cos(z);  const scalar sz = sin(z);
+
+
     return
         tensor
         (
-            cos(y)*cos(z) - sin(x)*sin(y)*sin(z),
+            cy*cz - sx*sy*sz, -cx*sz,  sx*cy*sz + sy*cz,
-            -cos(x)*sin(z),
+            cy*sz + sx*sy*cz,  cx*cz,  sy*sz - sx*cy*cz,
-            sin(x)*cos(y)*sin(z) + sin(y)*cos(z),
+            -cx*sy,            sx,     cx*cy
-
-            cos(y)*sin(z) + sin(x)*sin(y)*cos(z),
-            cos(x)*cos(z),
-            sin(y)*sin(z) - sin(x)*cos(y)*cos(z),
-
-            -cos(x)*sin(y),
-            sin(x),
-            cos(x)*cos(y)
         );
 }