text: /* ----------------------------------------------------------------------------
  
   * GTSAM Copyright 2010, Georgia Tech Research Corporation,
   * Atlanta, Georgia 30332-0415
   * All Rights Reserved
   * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
  
   * See LICENSE for the license information
  
   * -------------------------------------------------------------------------- */
  
  /**
   * @file  testCal3DFisheye.cpp
   * @brief Unit tests for fisheye calibration class
   * @author ghaggin
   */
  
  #include <gtsam/base/Testable.h>
  #include <gtsam/base/numericalDerivative.h>
  #include <gtsam/geometry/Cal3Fisheye.h>
  #include <gtsam/geometry/Point3.h>
  
  #include <CppUnitLite/TestHarness.h>
  
  using namespace gtsam;
  
  GTSAM_CONCEPT_TESTABLE_INST(Cal3Fisheye)
  GTSAM_CONCEPT_MANIFOLD_INST(Cal3Fisheye)
  
  static const double fx = 250, fy = 260, s = 0.1, u0 = 320, v0 = 240;
  static Cal3Fisheye K(fx, fy, s, u0, v0, -0.013721808247486035,
                       0.020727425669427896, -0.012786476702685545,
                       0.0025242267320687625);
  static Point2 kTestPoint2(2, 3);
  
  /* ************************************************************************* */
  TEST(Cal3Fisheye, assert_equal) { CHECK(assert_equal(K, K, 1e-5)); }
  
  /* ************************************************************************* */
  TEST(Cal3Fisheye, retract) {
    Cal3Fisheye expected(K.fx() + 1, K.fy() + 2, K.skew() + 3, K.px() + 4,
                         K.py() + 5, K.k1() + 6, K.k2() + 7, K.k3() + 8,
                         K.k4() + 9);
    Vector d(9);
    d << 1, 2, 3, 4, 5, 6, 7, 8, 9;
    Cal3Fisheye actual = K.retract(d);
    CHECK(assert_equal(expected, actual, 1e-7));
    CHECK(assert_equal(d, K.localCoordinates(actual), 1e-7));
  }
  
  /* ************************************************************************* */
  TEST(Cal3Fisheye, uncalibrate1) {
    // Calculate the solution
    const double xi = kTestPoint2.x(), yi = kTestPoint2.y();
    const double r = sqrt(xi * xi + yi * yi);
    const double t = atan(r);
    const double tt = t * t, t4 = tt * tt, t6 = tt * t4, t8 = t4 * t4;
    const double td =
        t * (1 + K.k1() * tt + K.k2() * t4 + K.k3() * t6 + K.k4() * t8);
    Vector3 pd(td / r * xi, td / r * yi, 1);
    Vector3 v = K.K() * pd;
  
    Point2 uv_sol(v[0] / v[2], v[1] / v[2]);
  
    Point2 uv = K.uncalibrate(kTestPoint2);
    CHECK(assert_equal(uv, uv_sol));
  }
  
  /* ************************************************************************* */
  // For numerical derivatives
  Point2 f(const Cal3Fisheye& k, const Point2& pt) { return k.uncalibrate(pt); }
  
  /* ************************************************************************* */
  TEST(Cal3Fisheye, Derivatives) {
    Matrix H1, H2;
    K.uncalibrate(kTestPoint2, H1, H2);
    CHECK(assert_equal(numericalDerivative21(f, K, kTestPoint2, 1e-7), H1, 1e-5));
    CHECK(assert_equal(numericalDerivative22(f, K, kTestPoint2, 1e-7), H2, 1e-5));
  }
  
  /* ************************************************************************* */
  // Check that a point at (0,0) projects to the image center.
  TEST(Cal3Fisheye, uncalibrate2) {
    Point2 pz(0, 0);
    Matrix H1, H2;
    auto uv = K.uncalibrate(pz, H1, H2);
    CHECK(assert_equal(uv, Point2(u0, v0)));
    CHECK(assert_equal(numericalDerivative21(f, K, pz, 1e-7), H1, 1e-5));
    // TODO(frank): the second jacobian is all NaN for the image center!
    // CHECK(assert_equal(numericalDerivative22(f, K, pz, 1e-7), H2, 1e-5));
  }
  
  /* ************************************************************************* */
  //  This test uses cv2::fisheye::projectPoints to test that uncalibrate
  //  properly projects a point into the image plane.  One notable difference
  //  between opencv and the Cal3Fisheye::uncalibrate function is the skew
  //  parameter. The equivalence is alpha = s/fx.
  //
  // Python script to project points with fisheye model in OpenCv
  // (script run with OpenCv version 4.2.0 and Numpy version 1.18.2)
  // clang-format off
  /*
  ===========================================================
  
  import numpy as np
  import cv2
  
  objpts = np.float64([[23,27,31]]).reshape(1,-1,3)
  
  cameraMatrix = np.float64([
      [250, 0, 320],
      [0, 260, 240],
      [0,0,1]
  ])
  alpha = 0.1/250
  distCoeffs = np.float64([-0.013721808247486035, 0.020727425669427896,-0.012786476702685545, 0.0025242267320687625]) 
  
  rvec = np.float64([[0.,0.,0.]])
  tvec = np.float64([[0.,0.,0.]]);
  imagePoints, jacobian = cv2.fisheye.projectPoints(objpts, rvec, tvec, cameraMatrix, distCoeffs, alpha=alpha) 
  np.set_printoptions(precision=14) 
  print(imagePoints)
  
  ===========================================================
   * Script output: [[[457.82638130304935 408.18905848512986]]]
   */
  // clang-format on
  TEST(Cal3Fisheye, uncalibrate3) {
    Point3 p3(23, 27, 31);
    Point2 xi(p3.x() / p3.z(), p3.y() / p3.z());
    auto uv = K.uncalibrate(xi);
    CHECK(assert_equal(uv, Point2(457.82638130304935, 408.18905848512986)));
  }
  
  /* ************************************************************************* */
  TEST(Cal3Fisheye, calibrate1) {
    Point2 pi;
    Point2 uv;
    Point2 pi_hat;
  
    pi = Point2(0.5, 0.5);     // point in intrinsic coordinates
    uv = K.uncalibrate(pi);    // map intrinsic coord to image plane (pi)
    pi_hat = K.calibrate(uv);  // map image coords (pi) back to intrinsic coords
    CHECK(traits<Point2>::Equals(pi, pi_hat,
                                 1e-5));  // check that the inv mapping works
  
    pi = Point2(-0.7, -1.2);
    uv = K.uncalibrate(pi);
    pi_hat = K.calibrate(uv);
    CHECK(traits<Point2>::Equals(pi, pi_hat, 1e-5));
  
    pi = Point2(-3, 5);
    uv = K.uncalibrate(pi);
    pi_hat = K.calibrate(uv);
    CHECK(traits<Point2>::Equals(pi, pi_hat, 1e-5));
  
    pi = Point2(7, -12);
    uv = K.uncalibrate(pi);
    pi_hat = K.calibrate(uv);
    CHECK(traits<Point2>::Equals(pi, pi_hat, 1e-5));
  }
  
  /* ************************************************************************* */
  // Check that calibrate returns (0,0) for the image center
  TEST(Cal3Fisheye, calibrate2) {
    Point2 uv(u0, v0);
    auto xi_hat = K.calibrate(uv);
    CHECK(assert_equal(xi_hat, Point2(0, 0)))
  }
  
  /* ************************************************************************* */
  // Run calibrate on OpenCv test from uncalibrate3
  //  (script shown above)
  // 3d point: (23, 27, 31)
  // 2d point in image plane: (457.82638130304935, 408.18905848512986)
  TEST(Cal3Fisheye, calibrate3) {
    Point3 p3(23, 27, 31);
    Point2 xi(p3.x() / p3.z(), p3.y() / p3.z());
    Point2 uv(457.82638130304935, 408.18905848512986);
    auto xi_hat = K.calibrate(uv);
    CHECK(assert_equal(xi_hat, xi));
  }
  
  /* ************************************************************************* */
  int main() {
    TestResult tr;
    return TestRegistry::runAllTests(tr);
  }
  /* ************************************************************************* */
  