#include <visp3/core/vpMomentAlpha.h>

Inheritance diagram for vpMomentAlpha:

Public Member Functions
	vpMomentAlpha ()

	vpMomentAlpha (const std::vector< double > &mu3_ref, double alpha_ref, double threshold=1e-6)

void	compute ()

double	get () const

const std::string	name () const

bool	is_ref () const

bool	is_symmetric () const

void	printDependencies (std::ostream &os) const

Inherited functionalities from vpMoment
const vpMomentObject &	getObject () const

void	linkTo (vpMomentDatabase &moments)

void	update (vpMomentObject &object)

Protected Member Functions
vpMomentDatabase &	getMoments () const

Protected Attributes
std::vector< double >	values

Friends
VISP_EXPORT std::ostream &	operator<< (std::ostream &os, const vpMomentAlpha &v)

Detailed Description

This class defines the orientation of the object inside the plane parallel to the object.

In general the value of the moment is computed in $[-\pi/2 ; \pi/2]$ interval by the formula $\alpha = \frac{1}{2} \mathrm{atan2}(2\mu_{11}, \mu_{20}-\mu_{02})$ .

To obtain a $[-\pi ; \pi]$ precision for non symmetric object, you have to specify a reference information. This reference information is an alpha computed using the previous formula in $[-\pi/2 ; \pi/2]$ . Obtaining this precision comes from third-order centered moments and this reference information.

Therefore there are two modes for vpMomentAlpha and one constructor per mode:

Reference mode using the empty constructor vpMomentAlpha(): The vpMomentAlpha doesn't need any additional information, it will compute its values from available moments in $[-\pi/2 ; \pi/2]$ .
Relative mode using non-empty constructor vpMomentAlpha(std::vector<double>&, double): The vpMomentAlpha is computed in $[-\pi ; \pi]$ from the available moments and the reference information. By knowing the reference, it may distinguish in-plane rotations of $\alpha$ from rotations of $\alpha + \pi$ .

The following code demonstrates a calculation of a reference alpha and then uses this alpha to estimate the orientation of the same object after performing a 180 degrees rotation. Therefore the first and second alpha should have opposite values.

#include <visp3/core/vpMomentAlpha.h>
#include <visp3/core/vpMomentCentered.h>
#include <visp3/core/vpMomentDatabase.h>
#include <visp3/core/vpMomentGravityCenter.h>
#include <visp3/core/vpMomentObject.h>
#include <visp3/core/vpPoint.h>
 
//generic function for printing
void print (double i) { std::cout << i << "\t";}
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int main()
{
  vpPoint p;
 std::vector<vpPoint> vec_p; // Vector that contains the vertices of the contour polygon
  p.set_x(1); p.set_y(1);     // Coordinates in meters in the image plane (vertex 1)
  vec_p.push_back(p);
  p.set_x(2); p.set_y(2);     // Coordinates in meters in the image plane (vertex 2)
  vec_p.push_back(p);
  p.set_x(-3); p.set_y(0);    // Coordinates in meters in the image plane (vertex 3)
  vec_p.push_back(p);
  p.set_x(-3); p.set_y(-1);   // Coordinates in meters in the image plane (vertex 4)
  vec_p.push_back(p);
 
  vpMomentObject objRef(3);                      // Reference object. Must be of order 3 because we will
                                                 // need the 3rd order centered moments
 
  objRef.setType(vpMomentObject::DENSE_POLYGON); // Object is the inner part of a polygon
  objRef.fromVector(vec_p);                      // Init the dense object with the polygon
 
  vpMomentDatabase dbRef;                        // Reference database
  vpMomentGravityCenter gRef;                    // Declaration of gravity center
  vpMomentCentered mcRef;                        // Centered moments
  vpMomentAlpha alphaRef;                        // Declare alpha as reference
 
  gRef.linkTo(dbRef);                            // Add gravity center to database
  mcRef.linkTo(dbRef);                           // Add centered moments
  alphaRef.linkTo(dbRef);                        // Add alpha depending on centered moments
 
  dbRef.updateAll(objRef);                       // All of the moments must be updated, not just alpha
 
  gRef.compute();                                // Compute the moment
  mcRef.compute();                               // Compute centered moments AFTER gravity center
  alphaRef.compute();                            // Compute alpha AFTER centered moments.
 
  // The order of values in the vector must be as follows: mu30 mu21 mu12 mu03
  std::vector<double> mu3ref = {mcRef.get(3,0), mcRef.get(2,1), mcRef.get(1,2), mcRef.get(0,3)};
 
  std::cout << "--- Reference object ---" << std::endl;
  std::cout << "alphaRef=" << vpMath::deg(alphaRef.get()) << " deg" << std::endl << "mu3="; // print reference alpha
  std::for_each (mu3ref.begin(), mu3ref.end(), print);
  std::cout << std::endl;
 
  vec_p.clear();
 
  p.set_x(-3); p.set_y(1);                       // Coordinates in meters in the image plane (vertex 4)
  vec_p.push_back(p);
  p.set_x(-3); p.set_y(0);                       // Coordinates in meters in the image plane (vertex 3)
  vec_p.push_back(p);
  p.set_x(2); p.set_y(-2);                       // Coordinates in meters in the image plane (vertex 2)
  vec_p.push_back(p);
  p.set_x(1); p.set_y(-1);                       // Coordinates in meters in the image plane (vertex 1)
  vec_p.push_back(p);
 
  vpMomentObject obj(3);                         // Second object. Order 3 is also required because of the Alpha
                                                 // will compare third-order centered moments to given reference.
 
  obj.setType(vpMomentObject::DENSE_POLYGON);    // Object is the inner part of a polygon
  obj.fromVector(vec_p);                         // Init the dense object with the polygon
 
  vpMomentDatabase db;                           // Database
  vpMomentGravityCenter g;                       // Declaration of gravity center
  vpMomentCentered mc;                           // mc contains centered moments
  vpMomentAlpha alpha(mu3ref, alphaRef.get());   // Declare alpha as relative to a reference
 
  g.linkTo(db);                                  // Add gravity center to database
  mc.linkTo(db);                                 // Add centered moments
  alpha.linkTo(db);                              // Add alpha depending on centered moments
 
  db.updateAll(obj);                             // All of the moments must be updated
 
  g.compute();                                   // Compute the moment
  mc.compute();                                  // Compute centered moments AFTER gravity center
  alpha.compute();                               // Compute alpha AFTER centered moments.
 
  std::cout << "--- current object ---" << std::endl;
  std::cout << "alpha=" << vpMath::deg(alpha.get()) << " deg" << std::endl;
 
  return 0;
}

This program outputs:

--- Reference object ---
alphaRef=25.3019 deg
mu3=1.80552  0.921882  0.385828  0.122449
--- current object ---
alpha=-25.3019 deg

There is also testMomentAlpha.cpp example that shows how to compute alpha in the range $[-\pi ; \pi]$ using arrow images as input. The code is given below:

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2024 by Inria. All rights reserved.
 *
 * This software is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * See the file LICENSE.txt at the root directory of this source
 * distribution for additional information about the GNU GPL.
 *
 * For using ViSP with software that can not be combined with the GNU
 * GPL, please contact Inria about acquiring a ViSP Professional
 * Edition License.
 *
 * See https://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
 * If you have questions regarding the use of this file, please contact
 * Inria at visp@inria.fr
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Description:
 * Test some vpMomentAlpha functionalities.
 */
 
#include <string>
#include <visp3/core/vpMomentAlpha.h>
#include <visp3/core/vpMomentBasic.h>
#include <visp3/core/vpMomentCentered.h>
#include <visp3/core/vpMomentDatabase.h>
#include <visp3/core/vpMomentGravityCenter.h>
#include <visp3/core/vpMomentObject.h>
#include <visp3/io/vpImageIo.h>
 
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
 
int test_moment_alpha(const std::string &name, bool symmetry, const std::vector<int> &vec_angle, double tolerance_deg,
                      double symmetry_threshold = 1e-6)
{
  vpImage<unsigned char> I;
 
  std::cout << "** Test " << (symmetry == true ? "symmetric " : "non symmetric ") << name << " object" << std::endl;
 
  // ***************
  std::cout << "*** Test symmetry detection from mu 3rd order moments" << std::endl;
  // ***************
  std::vector<double> mu_ref;
  double alpha_ref = 0.;
  for (unsigned int i = (unsigned int)vec_angle.size(); i >= 1; --i) {
    // Compute reference alpha image <name>-<vec_angle>[i]deg.pgm
    std::stringstream ss;
    ss << name << "-" << vec_angle[i - 1] << "deg.pgm";
    std::cout << "Process image " << ss.str() << std::endl;
    vpImageIo::read(I, ss.str());
 
    // Consider the case of a reference alpha
    {
      vpMomentObject obj(3);
      obj.setType(vpMomentObject::DENSE_FULL_OBJECT);
      obj.fromImage(I, 127,
                    vpCameraParameters()); // Init the dense object with the image and corresponding camera parameters
      vpMomentDatabase db;                 // Database
      vpMomentGravityCenter mg;            // Declaration of gravity center moment
      vpMomentCentered mc;                 // Declaration of centered moments
      vpMomentAlpha malpha_ref;            // Declaration of alpha reference moments
      mg.linkTo(db);                       // Add gravity center moment to database
      mc.linkTo(db);                       // Add centered moments
      malpha_ref.linkTo(db);               // Add alpha moment
      db.updateAll(obj);                   // All of the moments must be updated, not just alpha
      mg.compute();                        // Compute gravity center moment
      mc.compute();                        // Compute centered moments AFTER gravity center
      malpha_ref.compute();                // Compute alpha gravity center
 
      mu_ref.clear();
      mu_ref.push_back(mc.get(3, 0));
      mu_ref.push_back(mc.get(2, 1));
      mu_ref.push_back(mc.get(1, 2));
      mu_ref.push_back(mc.get(0, 3));
      alpha_ref = malpha_ref.get();
    }
    // Consider the case of a relative alpha
    {
      vpMomentObject obj(3);
      obj.setType(vpMomentObject::DENSE_FULL_OBJECT);
      obj.fromImage(I, 127,
                    vpCameraParameters()); // Init the dense object with the image and corresponding camera parameters
      vpMomentDatabase db;                 // Database
      vpMomentGravityCenter mg;            // Declaration of gravity center moment
      vpMomentCentered mc;                 // Declaration of centered moments
      vpMomentAlpha malpha(mu_ref, alpha_ref, symmetry_threshold); // Declaration of alpha relative moments
      mg.linkTo(db);                                               // Add gravity center moment to database
      mc.linkTo(db);                                               // Add centered moments
      malpha.linkTo(db);                                           // Add alpha moment
      db.updateAll(obj);                                           // All of the moments must be updated, not just alpha
      mg.compute();                                                // Compute gravity center moment
      mc.compute();                                                // Compute centered moments AFTER gravity center
      malpha.compute();                                            // Compute alpha gravity center
 
      if (malpha.is_symmetric() != symmetry) {
        std::cout << "Error in symmety detection" << std::endl;
        return EXIT_FAILURE;
      }
    }
  }
 
  // ***************
  std::cout << "*** Compute angle in relative mode using the last reference from the previous test" << std::endl;
  // ***************
  for (size_t i = 0; i < vec_angle.size(); i++) {
    std::stringstream ss;
    ss << name << "-" << vec_angle[i] << "deg.pgm";
    std::cout << "Process image " << ss.str() << std::endl;
    vpImageIo::read(I, ss.str());
 
    vpMomentObject obj(3);
    obj.setType(vpMomentObject::DENSE_FULL_OBJECT);
    obj.fromImage(I, 127, vpCameraParameters());                 // Init the dense object with the image
    vpMomentDatabase db;                                         // Database
    vpMomentGravityCenter g;                                     // Declaration of gravity center
    vpMomentCentered mc;                                         // Centered moments
    vpMomentAlpha malpha(mu_ref, alpha_ref, symmetry_threshold); // Alpha moment relative to the reference alpha
    g.linkTo(db);                                                // Add gravity center to database
    mc.linkTo(db);                                               // Add centered moments
    malpha.linkTo(db);                                           // Add alpha depending on centered moments
    db.updateAll(obj);                                           // All of the moments must be updated, not just alpha
    g.compute();                                                 // Compute the moment
    mc.compute();                                                // Compute centered moments AFTER gravity center
    malpha.compute();                                            // Compute alpha AFTER centered moments.
 
    if (!symmetry) {
      // Tranform input angle from [0; 360] to [-180; +180] range
      double angle = vec_angle[i];
      if (angle > 180)
        angle -= 360;
      if (angle < -180)
        angle += 360;
 
      std::cout << "alpha expected " << angle << " computed " << vpMath::deg(malpha.get()) << " deg" << std::endl;
 
      if (!vpMath::equal(angle, vpMath::deg(malpha.get()), tolerance_deg)) { // 0.5 deg of tolerance
        std::cout << "Error: result is not in the tolerance: " << tolerance_deg << std::endl;
        return EXIT_FAILURE;
      }
    }
    else {
   // Tranform input angle from [0; 360] to [0; 180] range
      double angle_des1 = vec_angle[i];
      double angle_des2 = vec_angle[i] - 180;
 
      // Tranform input angle from [0; 360] to [0; 180] range
      double alpha = vpMath::deg(malpha.get());
 
      std::cout << "alpha expected " << angle_des1 << " or " << angle_des2 << " computed " << alpha << " deg"
        << std::endl;
 
      if (!vpMath::equal(angle_des1, alpha, tolerance_deg) &&
          !vpMath::equal(angle_des2, alpha, tolerance_deg)) { // 0.5 deg of tolerance
        std::cout << "Error: result is not in the tolerance: " << tolerance_deg << std::endl;
        return EXIT_FAILURE;
      }
    }
  }
  std::cout << "Test succeed" << std::endl;
  return EXIT_SUCCESS;
}
 
int main()
{
  std::string name;
  bool symmetry;
  double tolerance_deg;
  std::vector<int> vec_angle;
  double symmetry_threshold;
 
  // *******************************
  // Test arrow
  // *******************************
  name = "arrow";
  symmetry = false;
  tolerance_deg = 0.5;
  vec_angle.clear();
  vec_angle.push_back(0);
  vec_angle.push_back(45);
  vec_angle.push_back(90);
  vec_angle.push_back(135);
  vec_angle.push_back(180);
  vec_angle.push_back(225);
  vec_angle.push_back(270);
  vec_angle.push_back(315);
 
  if (test_moment_alpha(name, symmetry, vec_angle, tolerance_deg) == EXIT_FAILURE) {
    return EXIT_FAILURE;
  }
 
  // *******************************
  // Test ellipse created with gimp
  // *******************************
  name = "ellipse";
  symmetry = true;
  tolerance_deg = 0.5;
  vec_angle.clear();
  vec_angle.push_back(0);
  vec_angle.push_back(45);
  vec_angle.push_back(90);
  vec_angle.push_back(135);
 
  if (test_moment_alpha(name, symmetry, vec_angle, tolerance_deg) == EXIT_FAILURE) {
    return EXIT_FAILURE;
  }
 
  // *******************************
  // Test ellipse created with xfig
  // *******************************
  name = "ellipse-xfig";
  symmetry = true;
  tolerance_deg = 2.5;
  symmetry_threshold = 1e-2; // Modify default value
  vec_angle.clear();
  vec_angle.push_back(0);
  vec_angle.push_back(45);
  vec_angle.push_back(90);
  vec_angle.push_back(135);
 
  if (test_moment_alpha(name, symmetry, vec_angle, tolerance_deg, symmetry_threshold) == EXIT_FAILURE) {
    return EXIT_FAILURE;
  }
 
  // *******************************
  // Test baleine created with gimp
  // *******************************
  name = "baleine";
  symmetry = false;
  tolerance_deg = 5.;
  vec_angle.clear();
  vec_angle.push_back(0);
  vec_angle.push_back(45);
  vec_angle.push_back(90);
  vec_angle.push_back(135);
  vec_angle.push_back(180);
  vec_angle.push_back(225);
  vec_angle.push_back(270);
  vec_angle.push_back(315);
 
  if (test_moment_alpha(name, symmetry, vec_angle, tolerance_deg) == EXIT_FAILURE) {
    return EXIT_FAILURE;
  }
 
  return EXIT_SUCCESS;
}

From the first image we compute the 3rd order centered moments and the value of the reference alpha that is than used to compute the alpha moment in the range $[-\pi ; \pi]$ . Running this example you will get:

alpha expected 0 computed -0.128108 deg
alpha expected 45 computed 44.8881 deg
alpha expected 90 computed 89.8719 deg
alpha expected 135 computed 134.888 deg
alpha expected 180 computed 179.872 deg
alpha expected -135 computed -135.112 deg
alpha expected -90 computed -90.1281 deg
alpha expected -45 computed -45.1119 deg

Shortcuts for quickly getting those references exist in vpMomentCommon.

This moment depends on vpMomentCentered.

Examples: testMomentAlpha.cpp.

Definition at line 209 of file vpMomentAlpha.h.

Constructor & Destructor Documentation

◆ vpMomentAlpha() [1/2]

BEGIN_VISP_NAMESPACE vpMomentAlpha::vpMomentAlpha ( )

Empty constructor. Initializes alpha moment as a reference alpha with a value in $[-\pi/2 ; \pi/2]$ . A default-constructed alpha moment may be used as a reference information for other alphas. A reference alpha is a class harbouring an alpha value computed for a $[-\pi/2 ; \pi/2]$ portion of the circle.

Definition at line 52 of file vpMomentAlpha.cpp.

References vpMoment::values.

◆ vpMomentAlpha() [2/2]

vpMomentAlpha::vpMomentAlpha	(	const std::vector< double > &	mu3_ref,
		double	alpha_ref,
		double	threshold = `1e-6`
	)

Common constructor. Initializes alpha moment as a non-reference alpha with a value computed in $[-\pi ; \pi]$ when the object is non symmetric.

Parameters

mu3_ref	: Vector of 3rd order centered moments corresponding to the reference alpha in the following order: $\mu_{30},\mu_{21},\mu_{12},\mu_{03}$ .
alpha_ref	: Value of the reference alpha that has mu3_ref 3rd order moments.
threshold	: Threshold used to determine object symmetry along its 2 axis. The object is declared symmetric if all the four 3rd order centered moments mu3_ref have values lower than this threshold. If the object is symmetric, the alpha angle is commuted in [ $[-\pi/2 ; \pi/2]$ ]. If the object is non symmetric, the alpha angle is commuted in [ $[-\pi ; \pi]$ ]

Definition at line 69 of file vpMomentAlpha.cpp.

References vpMoment::values.

Member Function Documentation

◆ compute()

void vpMomentAlpha::compute ( )

virtual

Compute the value of the alpha-moment. Depends on vpMomentCentered.

Implements vpMoment.

Examples: testMomentAlpha.cpp.

Definition at line 87 of file vpMomentAlpha.cpp.

References vpMath::comb(), vpMomentDatabase::get(), vpMomentCentered::get(), vpMoment::getMoments(), vpException::notInitialized, and vpMoment::values.

Referenced by vpMomentCommon::getAlpha(), and vpMomentCommon::updateAll().

◆ get()

double vpMomentAlpha::get ( ) const

inline

Retrieve the orientation of the object as a single double value.

Examples: testMomentAlpha.cpp.

Definition at line 226 of file vpMomentAlpha.h.

Referenced by vpMomentCommon::getAlpha().

◆ getMoments()

vpMomentDatabase& vpMoment::getMoments ( ) const

inlineprotectedinherited

Returns the linked moment database.

Returns: the moment database

Definition at line 118 of file vpMoment.h.

Referenced by compute(), vpMomentArea::compute(), vpMomentAreaNormalized::compute(), vpMomentCentered::compute(), vpMomentCInvariant::compute(), vpMomentGravityCenterNormalized::compute(), printDependencies(), vpMomentArea::printDependencies(), vpMomentAreaNormalized::printDependencies(), vpMomentCentered::printDependencies(), and vpMomentGravityCenterNormalized::printDependencies().

◆ getObject()

const vpMomentObject& vpMoment::getObject ( ) const

inlineinherited

Definition at line 145 of file vpMoment.h.

◆ is_ref()

bool vpMomentAlpha::is_ref ( ) const

inline

Returns true if the alpha moment was constructed as a reference with values in $[-\pi/2 ; \pi/2]$ , false otherwise.

Definition at line 236 of file vpMomentAlpha.h.

◆ is_symmetric()

bool vpMomentAlpha::is_symmetric ( ) const

inline

Returns true if the alpha moment is computed on a symmetric object along its two axis. Symmetry is computed using 3rd order centered moments $\mu_{30},\mu_{21},\mu_{12},\mu_{03}$ .

Examples: testMomentAlpha.cpp.

Definition at line 248 of file vpMomentAlpha.h.

◆ linkTo()

void vpMoment::linkTo ( vpMomentDatabase & data_base )

inherited

Links the moment to a database of moment primitives. If the moment depends on other moments, these moments must be linked to the same database.

Attention: Two moments of the same class cannot be stored in the same database
#include <visp3/core/vpMomentCentered.h>

#include <visp3/core/vpMomentDatabase.h>

#include <visp3/core/vpMomentGravityCenter.h>

#include <visp3/core/vpMomentObject.h>

#include <visp3/core/vpPoint.h>

#ifdef ENABLE_VISP_NAMESPACE

using namespace VISP_NAMESPACE_NAME;

#endif

int main()

{

vpPoint p;

std::vector<vpPoint> vec_p;

p.set_x(1); p.set_y(1); // coordinates in meters in the image plane (vertex 1)

vec_p.push_back(p);

p.set_x(2); p.set_y(2); // coordinates in meters in the image plane (vertex 2)

vec_p.push_back(p);

vpMomentObject obj(2);

obj.setType(vpMomentObject::DISCRETE); // Discrete mode.

obj.fromVector(vec_p); // Init the dense object with the polygon

vpMomentDatabase db;

vpMomentGravityCenter G; // declaration of gravity center

vpMomentCentered mc; // mc contains centered moments

G.linkTo(db); // add gravity center to database

mc.linkTo(db); // centered moments depend on gravity, add them to the

// database to grant access

G.update(obj); // specify the object for gravity center

mc.update(obj); // and for centered moments

G.compute(); // compute the moment

mc.compute(); // compute centered moments AFTER gravity center

return 0;

}

vpMomentObject::DISCRETE
@ DISCRETE
Definition: vpMomentObject.h:236

vpMoment::update
void update(vpMomentObject &object)
Definition: vpMoment.cpp:127

Parameters

data_base : database of moment primitives.

Examples: mbot-apriltag-ibvs.cpp, servoBebop2.cpp, and testMomentAlpha.cpp.

Definition at line 114 of file vpMoment.cpp.

References vpMoment::name().

Referenced by vpMomentCommon::getAlpha(), vpMomentCommon::getMu3(), vpMomentCommon::getSurface(), and vpMomentCommon::vpMomentCommon().

◆ name()

const std::string vpMomentAlpha::name ( ) const

inlinevirtual

Moment name.

Implements vpMoment.

Definition at line 230 of file vpMomentAlpha.h.

◆ printDependencies()

void vpMomentAlpha::printDependencies ( std::ostream & os ) const

virtual

Prints the dependencies of alpha, namely centered moments mu11, mu20 ad mu02

Reimplemented from vpMoment.

Definition at line 163 of file vpMomentAlpha.cpp.

References vpMomentDatabase::get(), vpMomentCentered::get(), vpMoment::getMoments(), and vpException::notInitialized.

◆ update()

void vpMoment::update ( vpMomentObject & moment_object )

inherited

Updates the moment with the current object. This does not compute any values.

Parameters

moment_object : object descriptor of the current camera vision.

Definition at line 127 of file vpMoment.cpp.

Friends And Related Function Documentation

◆ operator<<

VISP_EXPORT std::ostream& operator<<	(	std::ostream &	os,
		const vpMomentAlpha &	v
	)

friend

Prints the value of the major-axis orientation in degrees and rad

Definition at line 180 of file vpMomentAlpha.cpp.

Member Data Documentation

◆ values

std::vector<double> vpMoment::values

protectedinherited

Definition at line 113 of file vpMoment.h.

Referenced by compute(), vpMomentArea::compute(), vpMomentAreaNormalized::compute(), vpMomentCentered::compute(), vpMomentCInvariant::compute(), vpMomentGravityCenter::compute(), vpMomentGravityCenterNormalized::compute(), vpMomentGravityCenter::get(), vpMomentCentered::get(), vpMomentCInvariant::getMomentVector(), vpMomentCentered::set(), vpMomentAlpha(), vpMomentArea::vpMomentArea(), vpMomentAreaNormalized::vpMomentAreaNormalized(), vpMomentCInvariant::vpMomentCInvariant(), and vpMomentGravityCenter::vpMomentGravityCenter().

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ vpMomentAlpha() [1/2]

◆ vpMomentAlpha() [2/2]

Member Function Documentation

◆ compute()

◆ get()

◆ getMoments()

◆ getObject()

◆ is_ref()

◆ is_symmetric()

◆ linkTo()

◆ name()

◆ printDependencies()

◆ update()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ values