TestJacobian.h

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/*
 * Copyright (c) Meta Platforms, Inc. and affiliates.
 *
 * This source code is licensed under the MIT license found in the
 * LICENSE file in the root directory of this source tree.
 */
 
#ifndef META_OCEAN_TEST_TESTGEOMETRY_TEST_JACOBIAN_H
#define META_OCEAN_TEST_TESTGEOMETRY_TEST_JACOBIAN_H
 
#include "ocean/test/testgeometry/TestGeometry.h"
 
#include "ocean/geometry/Jacobian.h"
 
#include "ocean/math/HomogenousMatrix4.h"
#include "ocean/math/PinholeCamera.h"
 
#include "ocean/test/TestSelector.h"
 
namespace Ocean
{
 
namespace Test
{
 
namespace TestGeometry
{
 
/**
 * This class implements Jacobian tests.
 * @ingroup testgeometry
 */
class OCEAN_TEST_GEOMETRY_EXPORT TestJacobian : protected Geometry::Jacobian
{
    protected:
 
        /**
         * Base class for calculating numerical derivatives using central finite differences.
         * @tparam T The data type of the derivative
         * @tparam TScalar The scalar type for epsilon, either 'float' or 'double'
         * @tparam TVariable The data type of a variable object which can change while while everything else is constant
         */
        template <typename T, typename TScalar, typename TVariable>
        class DerivativeCalculatorT
        {
            public:
 
                /**
                 * Default constructor.
                 */
                virtual ~DerivativeCalculatorT() = default;
 
                /**
                 * Calculates the numerical derivative using central finite differences: f'(x) ≈ [f(x + epsilon) - f(x - epsilon)] / (2 * epsilon)
                 * @param variable The variable to calculate the derivative for
                 * @param parameterIndex The index of the parameter to perturb
                 * @param epsilon The epsilon value to use for the finite difference calculation
                 * @return The calculated derivative
                 */
                T calculateDerivative(const TVariable& variable, const size_t parameterIndex, const TScalar epsilon = NumericT<TScalar>::weakEps() * TScalar(0.05)) const;
 
                /**
                 * Verifies an analytical derivative by comparing it with a numerical approximation.
                 * Tests multiple epsilon values to find one that produces a match within tolerance.
                 * @param variable The variable to calculate the derivative for
                 * @param parameterIndex The index of the parameter to verify
                 * @param analyticalDerivative The analytical derivative to verify
                 * @return True if the analytical derivative matches the numerical approximation within tolerance
                 * @tparam TAnalyticalDerivative The type of the analytical derivative (e.g., Vector2, Vector3)
                 */
                template <typename TAnalyticalDerivative>
                bool verifyDerivative(const TVariable& variable, const size_t parameterIndex, const TAnalyticalDerivative& analyticalDerivative) const;
 
            protected:
 
                /**
                 * Calculates the function value with an offset applied to a specific parameter.
                 * Must be implemented by derived classes.
                 * @param variable The variable to evaluate
                 * @param parameterIndex The index of the parameter to perturb
                 * @param offset The offset to apply
                 * @return The calculated function value
                 */
                virtual T calculateValue(const TVariable& variable, const size_t parameterIndex, const TScalar offset) const = 0;
        };
 
        /**
         * Base class for calculating numerical derivatives using central finite differences.
         * This class is a specialization of DerivativeCalculatorT without a variable object.
         * @tparam T The result type (e.g., VectorT2<Scalar>, VectorT3<Scalar>)
         * @tparam TScalar The scalar type for epsilon, either 'float' or 'double'
         */
        template <typename T, typename TScalar>
        class DerivativeCalculatorT<T, TScalar, void>
        {
            public:
 
                /**
                 * Default constructor.
                 */
                virtual ~DerivativeCalculatorT() = default;
 
                /**
                 * Calculates the numerical derivative using central finite differences: f'(x) ≈ [f(x + epsilon) - f(x - epsilon)] / (2 * epsilon)
                 * @param parameterIndex The index of the parameter to perturb
                 * @param epsilon The epsilon value to use for the finite difference calculation
                 * @return The calculated derivative
                 */
                T calculateDerivative(const size_t parameterIndex, const TScalar epsilon = NumericT<TScalar>::weakEps() * TScalar(0.05)) const;
 
                /**
                 * Verifies an analytical derivative by comparing it with a numerical approximation.
                 * Tests multiple epsilon values to find one that produces a match within tolerance.
                 * @param parameterIndex The index of the parameter to verify
                 * @param analyticalDerivative The analytical derivative to verify
                 * @return True if the analytical derivative matches the numerical approximation within tolerance
                 * @tparam TAnalyticalDerivative The type of the analytical derivative (e.g., Vector2, Vector3)
                 */
                template <typename TAnalyticalDerivative>
                bool verifyDerivative(const size_t parameterIndex, const TAnalyticalDerivative& analyticalDerivative) const;
 
            protected:
 
                /**
                 * Calculates the function value with an offset applied to a specific parameter.
                 * Must be implemented by derived classes.
                 * @param parameterIndex The index of the parameter to perturb
                 * @param offset The offset to apply
                 * @return The calculated function value
                 */
                virtual T calculateValue(const size_t parameterIndex, const TScalar offset) const = 0;
        };
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorOrientationalJacobian2x3;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorOrientationJacobian2nx3;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraPoseJacobian2nx6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorFisheyeCameraPoseJacobian2x6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorAnyCameraPoseJacobian2nx6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPoseJacobianDampedDistortion2nx6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPoseZoomJacobian2nx7;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraObjectTransformation2nx6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorFisheyeCameraObjectTransformation2nx6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraPointJacobian2nx3;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorFisheyeCameraPointJacobian2x3;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorAnyCameraPointJacobian2x3;
 
        /// Forward declaration.
        class DerivativeCalculatorSphericalObjectPoint3x3;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorSphericalObjectPointOrientation2x3IF;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraDistortionJacobian2x4;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraJacobian2x6;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPinholeCameraJacobian2x7;
 
        /// Forward declaration.
        class DerivativeCalculatorPinholeCameraJacobian2x8;
 
        /// Forward declaration.
        class DerivativeCalculatorFisheyeCameraJacobian2x12;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorOrientationPinholeCameraJacobian2x11;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPosePinholeCameraJacobian2x12;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPosePinholeCameraJacobian2x14;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorPoseFisheyeCameraJacobian2x18;
 
        /// Forward declaration.
        class DerivativeCalculatorHomography2x8;
 
        /// Forward declaration.
        class DerivativeCalculatorHomography2x9;
 
        /// Forward declaration.
        class DerivativeCalculatorIdentityHomography2x8;
 
        /// Forward declaration.
        class DerivativeCalculatorIdentityHomography2x9;
 
        /// Forward declaration.
        class DerivativeCalculatorSimilarity2x4;
 
        /// Forward declaration.
        template <typename T>
        class DerivativeCalculatorFisheyeDistortNormalized2x2;
 
    public:
 
        /**
         * Tests the entire Jacobian functionality.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @param selector Selector for individual tests
         * @return True, if succeeded
         */
        static bool test(const double testDuration, const TestSelector& selector);
 
        /**
         * Tests the Jacobian for the rotational part of extrinsic camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testOrientationalJacobian2x3(const double testDuration);
 
        /**
         * Tests the Jacobian for the orientation of a camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testOrientationJacobian2nx3(const double testDuration);
 
        /**
         * Deprecated.
         *
         * Tests the Jacobian for the extrinsic camera parameters and a pinhole camera.
         * @tparam T The data type of the scalar, either 'float' or 'double'
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        template <typename T>
        static bool testPinholeCameraPoseJacobian2nx6(const double testDuration);
 
        /**
         * Deprecated.
         *
         * Tests the Jacobian for the extrinsic camera parameters and fisheye camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testFisheyeCameraPoseJacobian2x6(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic camera parameters and any camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testAnyCameraPoseJacobian2nx6(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic camera parameters using a damped distortion.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @tparam T The data type of the scalar, either 'float' or 'double'
         * @return True, if succeeded
         */
        template <typename T>
        static bool testPoseJacobianDampedDistortion2nx6(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic camera parameters (including the zoom parameter).
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testPoseZoomJacobian2nx7(const double testDuration);
 
        /**
         * Tests the 2x6 Jacobian for a 6-DOF transformation with fixed camera pose.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPinholeCameraObjectTransformation2nx6(const double testDuration);
 
        /**
         * Tests the 2x6 Jacobian for a 6-DOF transformation with fixed camera pose.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testFisheyeCameraObjectTransformation2nx6(const double testDuration);
 
        /**
         * Tests the Jacobian for an 2D image point projection in relation to an object point using a pinhole camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPinholeCameraPointJacobian2nx3(const double testDuration);
 
        /**
         * Tests the Jacobian for an 2D image point projection in relation to an object point using a fisheye camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testFisheyeCameraPointJacobian2x3(const double testDuration);
 
        /**
         * Tests the Jacobian for an 2D image point projection in relation to an object point using any camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testAnyCameraPointJacobian2x3(const double testDuration);
 
        /**
         * Tests the Jacobian for two 6DOF poses and a set of 3D object points.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPosesPointsJacobian2nx12(const double testDuration);
 
        /**
         * Tests the Jacobian for an exponential map representing a 3D object point.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testSphericalObjectPoint3x3(const double testDuration);
 
        /**
         * Tests the Jacobian for an exponential map representing a 3D object point which is projected into the camera frame.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testSphericalObjectPointOrientation2x3IF(const double testDuration);
 
        /**
         * Tests the Jacobian for the radial and tangential distortion camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPinholeCameraDistortionJacobian2x4(const double testDuration);
 
        /**
         * Tests the Jacobian for the intrinsic and radial distortion of pinhole camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPinholeCameraJacobian2x6(const double testDuration);
 
        /**
         * Tests the Jacobian for the intrinsic and radial and tangential distortion of pinhole camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testPinholeCameraJacobian2x7(const double testDuration);
 
        /**
         * Tests the Jacobian for the intrinsic, radial and tangential distortion of pinhole camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testPinholeCameraJacobian2x8(const double testDuration);
 
        /**
         * Tests the Jacobian for the intrinsic, radial and tangential distortion of fisheye camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testFisheyeCameraJacobian2x12(const double testDuration);
 
        /**
         * Tests the Jacobian for the rotational part of the extrinsic camera matrix, intrinsic and radial and tangential camera parameters.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testOrientationPinholeCameraJacobian2x11(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic, intrinsic and radial camera parameters for a pinhole camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testPosePinholeCameraJacobian2x12(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic, intrinsic and radial and tangential distortion camera parameters for a pinhole camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, either 'float' or 'double'
         */
        template <typename T>
        static bool testPosePinholeCameraJacobian2x14(const double testDuration);
 
        /**
         * Tests the Jacobian for the extrinsic, intrinsic and radial camera parameters and distortion parameters for a fisheye camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        template <typename T>
        static bool testPoseFisheyeCameraJacobian2x18(const double testDuration);
 
        /**
         * Tests the 2x8 Jacobian for the homography.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testHomography2x8(const double testDuration);
 
        /**
         * Tests the 2x9 Jacobian for the homography.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testHomography2x9(const double testDuration);
 
        /**
         * Tests the 2x8 Jacobian for the identity homography.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testIdentityHomography2x8(const double testDuration);
 
        /**
         * Tests the 2x9 Jacobian for the identity homography.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testIdentityHomography2x9(const double testDuration);
 
        /**
         * Tests the 2x4 Jacobian of a similarity transformation.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         */
        static bool testSimilarity2x4(const double testDuration);
 
        /**
         * Tests the 2x2 Jacobian of the distortion of a normalized image point for a fisheye camera.
         * @param testDuration Number of seconds for each test, with range (0, infinity)
         * @return True, if succeeded
         * @tparam T the data type of the scalar to be used, 'float', or 'double'
         */
        template <typename T>
        static bool testCalculateFisheyeDistortNormalized2x2(const double testDuration);
 
    private:
 
        /**
         * Checks if an analytical derivative matches an approximated derivative within tolerance.
         * @param analyticalDerivative The analytical derivative value
         * @param approximatedDerivative The numerically approximated derivative value
         * @return True if the derivatives match within tolerance
         * @tparam T The data type of the derivative
         */
        template <typename T>
        static bool checkDerivative(const T& analyticalDerivative, const T& approximatedDerivative);
 
        /**
         * Checks if an analytical derivative matches an approximated derivative within tolerance.
         * @param analyticalDerivative The analytical derivative value
         * @param approximatedDerivative The numerically approximated derivative value
         * @return True if the derivatives match within tolerance
         * @tparam T The data type of the scalar, either 'float' or 'double'
         */
        template <typename T>
        static bool checkScalarDerivative(const T analyticalDerivative, const T approximatedDerivative);
 
        /**
         * Calculates the two Jacobian rows for a given pose and dynamic object point.
         * The derivatives are calculated for the 3D object point only.<br>
         * The resulting Jacobian rows have the following form:<br>
         * | dfx / dX, dfx / dY, dfx / dZ |<br>
         * | dfy / dX, dfy / dY, dfy / dZ |<br>
         * @param jx First row position of the Jacobian, with 3 column entries receiving the point derivatives
         * @param jy Second row position of the Jacobian, with 3 column entries receiving the point derivatives
         * @param pinholeCamera The pinhole camera to determine the Jacobian values for
         * @param flippedCamera_T_world Pose to determine the Jacobian for (inverted and flipped)
         * @param objectPoint 3D object point to determine the Jacobian for
         * @param distortImagePoint True, to force the distortion of the image point using the distortion parameters of this camera object
         * @tparam tUseBorderDistortionIfOutside True, to apply the distortion from the nearest point lying on the frame border if the point lies outside the visible camera area; False to apply the distortion from the given position
         */
        template <bool tUseBorderDistortionIfOutside>
        static void calculatePointJacobian2x3(Scalar* jx, Scalar* jy, const PinholeCamera& pinholeCamera, const HomogenousMatrix4& flippedCamera_T_world, const Vector3& objectPoint, const bool distortImagePoint);
};
 
template <>
inline bool TestJacobian::checkDerivative(const float& analyticalDerivative, const float& approximatedDerivative)
{
    return checkScalarDerivative<float>(analyticalDerivative, approximatedDerivative);
}
 
template <>
inline bool TestJacobian::checkDerivative(const double& analyticalDerivative, const double& approximatedDerivative)
{
    return checkScalarDerivative<double>(analyticalDerivative, approximatedDerivative);
}
 
template <>
inline bool TestJacobian::checkDerivative(const VectorF2& analyticalDerivative, const VectorF2& approximatedDerivative)
{
    if (!checkScalarDerivative<float>(analyticalDerivative.x(), approximatedDerivative.x()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<float>(analyticalDerivative.y(), approximatedDerivative.y()))
    {
        return false;
    }
 
    return true;
}
 
template <>
inline bool TestJacobian::checkDerivative(const VectorD2& analyticalDerivative, const VectorD2& approximatedDerivative)
{
    if (!checkScalarDerivative<double>(analyticalDerivative.x(), approximatedDerivative.x()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<double>(analyticalDerivative.y(), approximatedDerivative.y()))
    {
        return false;
    }
 
    return true;
}
 
template <>
inline bool TestJacobian::checkDerivative(const VectorF3& analyticalDerivative, const VectorF3& approximatedDerivative)
{
    if (!checkScalarDerivative<float>(analyticalDerivative.x(), approximatedDerivative.x()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<float>(analyticalDerivative.y(), approximatedDerivative.y()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<float>(analyticalDerivative.z(), approximatedDerivative.z()))
    {
        return false;
    }
 
    return true;
}
 
template <>
inline bool TestJacobian::checkDerivative(const VectorD3& analyticalDerivative, const VectorD3& approximatedDerivative)
{
    if (!checkScalarDerivative<double>(analyticalDerivative.x(), approximatedDerivative.x()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<double>(analyticalDerivative.y(), approximatedDerivative.y()))
    {
        return false;
    }
 
    if (!checkScalarDerivative<double>(analyticalDerivative.z(), approximatedDerivative.z()))
    {
        return false;
    }
 
    return true;
}
 
template <typename T>
inline bool TestJacobian::checkDerivative(const T& /*analyticalDerivative*/, const T& /*approximatedDerivative*/)
{
    OCEAN_WARNING_MISSING_IMPLEMENTATION;
    return false;
}
 
template <typename T>
bool TestJacobian::checkScalarDerivative(const T analyticalDerivative, const T approximatedDerivative)
{
    const double maxAbsValue = std::max(std::abs(analyticalDerivative), std::abs(approximatedDerivative));
    const double absDiff = std::abs(analyticalDerivative - approximatedDerivative);
 
    if (NumericT<T>::isEqualEps(analyticalDerivative) || NumericT<T>::isEqualEps(approximatedDerivative))
    {
        if (absDiff > T(0.001))
        {
            return false;
        }
    }
    else
    {
        if (NumericT<T>::isNotEqualEps(T(maxAbsValue)) && T(absDiff / maxAbsValue) > T(0.05))
        {
            return false;
        }
    }
 
    return true;
}
 
template <bool tUseBorderDistortionIfOutside>
void TestJacobian::calculatePointJacobian2x3(Scalar* jx, Scalar* jy, const PinholeCamera& pinholeCamera, const HomogenousMatrix4& flippedCamera_T_world, const Vector3& objectPoint, const bool distortImagePoint)
{
    ocean_assert(jx != nullptr && jy != nullptr);
    ocean_assert(flippedCamera_T_world.isValid());
 
    /**
     * | dfx / dX, dfx / dY, dfx / dZ |<br>
     * | dfy / dX, dfy / dY, dfy / dZ |<br>
     */
 
    const Scalar eps = Numeric::weakEps();
 
    const Vector2 imagePoint(pinholeCamera.projectToImageIF<tUseBorderDistortionIfOutside>(flippedCamera_T_world, objectPoint, distortImagePoint));
 
    for (unsigned int n = 0u; n < 3u; ++n)
    {
        Vector3 dObjectPoint(objectPoint);
 
        dObjectPoint[n] += eps;
 
        const Vector2 dImagePoint(pinholeCamera.projectToImageIF<tUseBorderDistortionIfOutside>(flippedCamera_T_world, dObjectPoint, distortImagePoint));
 
        const Scalar dx = (dImagePoint.x() - imagePoint.x()) / eps;
        const Scalar dy = (dImagePoint.y() - imagePoint.y()) / eps;
 
        jx[n] = dx;
        jy[n] = dy;
    }
}
 
}
 
}
 
}
 
#endif // META_OCEAN_TEST_TESTGEOMETRY_TEST_JACOBIAN_H