Code review updates

scottshambaugh · scottshambaugh · commit ef8d0677817f · 2021-11-14T15:26:12.000-07:00
diff --git a/doc/users/next_whats_new/3d_plot_tilt_angle.rst b/doc/users/next_whats_new/3d_plot_tilt_angle.rst
@@ -1,5 +1,5 @@
-3D plots have now have a 3rd "tilt" viewing angle
--------------------------------------------------
+3D plots gained a 3rd "tilt" viewing angle
+------------------------------------------
 
 3D plots can now be viewed from any orientation with the addition of a 3rd tilt
 angle, which rotates the plot about the viewing axis. Interactive rotation
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -1270,9 +1270,10 @@ def _on_move(self, event):
         if self.button_pressed in self._rotate_btn:
             # rotate viewing point
             # get the x and y pixel coords
-            tilt = np.deg2rad(self.tilt)
             if dx == 0 and dy == 0:
                 return
+
+            tilt = np.deg2rad(self.tilt)
             delev = -(dy/h)*180*np.cos(tilt) - (dx/w)*180*np.sin(tilt)
             dazim = +(dy/h)*180*np.sin(tilt) - (dx/w)*180*np.cos(tilt)
             self.elev = self.elev + delev
diff --git a/lib/mpl_toolkits/mplot3d/proj3d.py b/lib/mpl_toolkits/mplot3d/proj3d.py
@@ -55,15 +55,15 @@ def rotation_about_vector(v, angle):
     """
     Produce a rotation matrix for an angle in radians about a vector.
     """
-    v = v/np.linalg.norm(v)
+    vx, vy, vz = v / np.linalg.norm(v)
     s = np.sin(angle)
     c = np.cos(angle)
-    t = 1-c
+    t = 2*np.sin(angle/2)**2  # more numerically stable than t = 1-c
 
     R = np.array([
-        [t*v[0]*v[0] + c,      t*v[0]*v[1] - v[2]*s, t*v[0]*v[2] + v[1]*s],
-        [t*v[1]*v[0] + v[2]*s, t*v[1]*v[1] + c,      t*v[1]*v[2] - v[0]*s],
-        [t*v[2]*v[0] - v[1]*s, t*v[2]*v[1] + v[0]*s, t*v[2]*v[2] + c]])
+        [t*vx*vx + c,    t*vx*vy - vz*s, t*vx*vz + vy*s],
+        [t*vy*vx + vz*s, t*vy*vy + c,    t*vy*vz - vx*s],
+        [t*vz*vx - vy*s, t*vz*vy + vx*s, t*vz*vz + c]])
 
     return R
 
