Merge pull request #10574 from razerhell:patch-1

* Newton's method can be more efficient

when we get the result of function distortPoint with a point (0, 0) and then undistortPoint with  the result, we get the point not (0, 0). and then we discovered that the old method is not convergence sometimes. finally we have gotten the right values by Newton's method.

* modify by advice  Newton's method...#10574

* calib3d(fisheye): fix codestyle, update theta before exit EPS check

modules/calib3d/src/fisheye.cpp

@@ -388,10 +388,18 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
         {
             // compensate distortion iteratively
             double theta = theta_d;
-            for(int j = 0; j < 10; j++ )
+
+            const double EPS = 1e-8; // or std::numeric_limits<double>::epsilon();
+            for (int j = 0; j < 10; j++)
             {
                 double theta2 = theta*theta, theta4 = theta2*theta2, theta6 = theta4*theta2, theta8 = theta6*theta2;
-                theta = theta_d / (1 + k[0] * theta2 + k[1] * theta4 + k[2] * theta6 + k[3] * theta8);
+                double k0_theta2 = k[0] * theta2, k1_theta4 = k[1] * theta4, k2_theta6 = k[2] * theta6, k3_theta8 = k[3] * theta8;
+                /* new_theta = theta - theta_fix, theta_fix = f0(theta) / f0'(theta) */
+                double theta_fix = (theta * (1 + k0_theta2 + k1_theta4 + k2_theta6 + k3_theta8) - theta_d) /
+                                   (1 + 3*k0_theta2 + 5*k1_theta4 + 7*k2_theta6 + 9*k3_theta8);
+                theta = theta - theta_fix;
+                if (fabs(theta_fix) < EPS)
+                    break;
             }
 
             scale = std::tan(theta) / theta_d;