Visual Servoing Platform  version 3.0.1
 All Classes Namespaces Functions Variables Typedefs Enumerations Enumerator Friends Groups Pages
vpMath Class Reference

#include <visp3/core/vpMath.h>

Public Member Functions

template<>
unsigned char saturate (char v)
 
template<>
unsigned char saturate (unsigned short v)
 
template<>
unsigned char saturate (int v)
 
template<>
unsigned char saturate (short v)
 
template<>
unsigned char saturate (unsigned int v)
 
template<>
unsigned char saturate (float v)
 
template<>
unsigned char saturate (double v)
 
template<>
char saturate (unsigned char v)
 
template<>
char saturate (unsigned short v)
 
template<>
char saturate (int v)
 
template<>
char saturate (short v)
 
template<>
char saturate (unsigned int v)
 
template<>
char saturate (float v)
 
template<>
char saturate (double v)
 
template<>
unsigned short saturate (char v)
 
template<>
unsigned short saturate (short v)
 
template<>
unsigned short saturate (int v)
 
template<>
unsigned short saturate (unsigned int v)
 
template<>
unsigned short saturate (float v)
 
template<>
unsigned short saturate (double v)
 
template<>
short saturate (unsigned short v)
 
template<>
short saturate (int v)
 
template<>
short saturate (unsigned int v)
 
template<>
short saturate (float v)
 
template<>
short saturate (double v)
 
template<>
int saturate (float v)
 
template<>
int saturate (double v)
 
template<>
unsigned int saturate (float v)
 
template<>
unsigned int saturate (double v)
 

Static Public Member Functions

static double deg (double rad)
 
static double rad (double deg)
 
static double sqr (double x)
 
static double fact (unsigned int x)
 
static long double comb (unsigned int n, unsigned int p)
 
static int round (const double x)
 
static int() sign (double x)
 
static bool nul (double x, double s=0.001)
 
static bool equal (double x, double y, double s=0.001)
 
static bool greater (double x, double y, double s=0.001)
 
template<class Type >
static Type maximum (const Type &a, const Type &b)
 
template<class Type >
static Type minimum (const Type &a, const Type &b)
 
template<class Type >
static Type abs (const Type &x)
 
static double sinc (double x)
 
static double sinc (double sinx, double x)
 
static double mcosc (double cosx, double x)
 
static double msinc (double sinx, double x)
 
static double sigmoid (double x, double x0=0., double x1=1., double n=12.)
 
template<class Type >
static void swap (Type &a, Type &b)
 
static bool isNaN (const double value)
 
static bool isInf (const double value)
 
template<typename _Tp >
static _Tp saturate (unsigned char v)
 
template<typename _Tp >
static _Tp saturate (char v)
 
template<typename _Tp >
static _Tp saturate (unsigned short v)
 
template<typename _Tp >
static _Tp saturate (short v)
 
template<typename _Tp >
static _Tp saturate (unsigned v)
 
template<typename _Tp >
static _Tp saturate (int v)
 
template<typename _Tp >
static _Tp saturate (float v)
 
template<typename _Tp >
static _Tp saturate (double v)
 
static double getMean (const std::vector< double > &v)
 
static double getMedian (const std::vector< double > &v)
 
static double getStdev (const std::vector< double > &v, const bool useBesselCorrection=false)
 
static int modulo (const int a, const int n)
 

Detailed Description

Provides simple mathematics computation tools that are not available in the C mathematics library (math.h)

Author
Eric Marchand (Eric..nosp@m.Marc.nosp@m.hand@.nosp@m.iris.nosp@m.a.fr) Irisa / Inria Rennes

Definition at line 87 of file vpMath.h.

Member Function Documentation

template<class Type >
static Type vpMath::abs ( const Type &  x)
inlinestatic

Find the absolute value of a number (or other).

Parameters
x: The number.
Returns
The absolute value of x

Definition at line 161 of file vpMath.h.

Referenced by vpServo::secondaryTaskJointLimitAvoidance(), and vpMeNurbs::seekExtremities().

long double vpMath::comb ( unsigned int  n,
unsigned int  p 
)
inlinestatic

Computes the number of combination of p elements inside n elements.

Parameters
n: total number of elements.
p: requested number of elements.
Returns
Combination number $ n! / ((n-p)! p!) $

Definition at line 234 of file vpMath.h.

References fact().

Referenced by vpMomentCentered::compute(), vpMomentAlpha::compute(), vpFeatureMomentCentered::compute_Lmu_pq(), vpNurbs::computeCurveDersPoint(), and vpPixelMeterConversion::convertMoment().

bool vpMath::equal ( double  x,
double  y,
double  s = 0.001 
)
inlinestatic

Compares $ | x - y | $ to $ s $.

Parameters
x: x value.
y: y value.
s: Tolerance threshold.
Returns
true if $ | x - y | < s $.
Examples:
testColVector.cpp, testImageFilter.cpp, testKeyPoint-7.cpp, testMath.cpp, testPoseRansac2.cpp, testRowVector.cpp, and testThread2.cpp.

Definition at line 306 of file vpMath.h.

References nul().

double vpMath::fact ( unsigned int  x)
inlinestatic

Computes and returns x!

Parameters
x: parameter of factorial function.

Definition at line 220 of file vpMath.h.

Referenced by comb().

double vpMath::getMean ( const std::vector< double > &  v)
static

Compute the mean value for a vector of double.

Parameters
v: Vector of double values.
Returns
The mean value.
Examples:
testMath.cpp, and testRealSense.cpp.

Definition at line 197 of file vpMath.cpp.

References vpException::notInitialized.

Referenced by getStdev().

double vpMath::getMedian ( const std::vector< double > &  v)
static

Compute the median value for a vector of double.

Parameters
v: Vector of double values.
Returns
The median value.
Examples:
testMath.cpp, and testRealSense.cpp.

Definition at line 217 of file vpMath.cpp.

References vpException::notInitialized.

Referenced by vpRowVector::median(), and vpColVector::median().

double vpMath::getStdev ( const std::vector< double > &  v,
const bool  useBesselCorrection = false 
)
static

Compute the standard deviation value for a vector of double.

Parameters
v: Vector of double values.
useBesselCorrection: If true, the Bessel correction is used (normalize by N-1).
Returns
The standard deviation value.
Examples:
testMath.cpp.

Definition at line 245 of file vpMath.cpp.

References getMean(), and vpException::notInitialized.

bool vpMath::greater ( double  x,
double  y,
double  s = 0.001 
)
inlinestatic

Compares $ x $ to $ y - s $.

Parameters
x: x value.
y: y value.
s: Tolerance threshold.
Returns
true if $ x > y - s $.

Definition at line 318 of file vpMath.h.

bool vpMath::isInf ( const double  value)
static

Returns whether a double is an infinity value (either positive infinity or negative infinity).

Parameters
value: Double number to check.
Returns
Return true if value is infinity.
Examples:
testMath.cpp.

Definition at line 112 of file vpMath.cpp.

bool vpMath::isNaN ( const double  value)
static

Check whether a double number is not a number (NaN) or not.

Parameters
value: Double number to check.
Returns
Return true if value is not a number.
Examples:
testMath.cpp.

Definition at line 85 of file vpMath.cpp.

Referenced by vpKeyPoint::compute3DForPointsOnCylinders(), vpMbtDistanceKltCylinder::computeInteractionMatrixAndResidu(), vpComedi::getPhyData(), vpMbtDistanceKltCylinder::init(), and vpPose::poseRansac().

double vpMath::mcosc ( double  cosx,
double  x 
)
static

Compute $ (1-cos(x))/x^2 $

Parameters
cosx: Value of cos(x).
x: Value of x.
Returns
$ (1-cosx)/x^2 $

Definition at line 138 of file vpMath.cpp.

Referenced by vpRotationMatrix::buildFrom(), vpExponentialMap::direct(), and vpExponentialMap::inverse().

int vpMath::modulo ( const int  a,
const int  n 
)
static

Compute the modified modulo:

  • modulo(11, 10) == 1 == 11 % 10
  • modulo(-1, 10) == 9
Parameters
a: The dividend.
n: The divisor.
Returns
The modified modulo of a mod n.
Examples:
testImageMorphology.cpp.

Definition at line 274 of file vpMath.cpp.

double vpMath::msinc ( double  sinx,
double  x 
)
static

Compute $ (1-sinc(x))/x^2 $ with $ sinc(x) = sinx / x $.

Parameters
sinx: value of sin(x).
x: Value of x.
Returns
$ (1-sinc(x))/x^2 $

Definition at line 154 of file vpMath.cpp.

Referenced by vpExponentialMap::direct(), and vpExponentialMap::inverse().

bool vpMath::nul ( double  x,
double  s = 0.001 
)
inlinestatic

Compares $ | x | $ to $ s $.

Parameters
x: Value to test.
s: Tolerance threshold
Returns
true if $ | x | < s $.

Definition at line 294 of file vpMath.h.

Referenced by vpPose::computeRansacIterations(), equal(), vpQuaternionVector::inverse(), vpQuaternionVector::normalize(), and vpQuaternionVector::operator/().

static double vpMath::rad ( double  deg)
inlinestatic

Convert an angle in degrees into radian.

Parameters
deg: Angle in degrees.
Returns
Angle converted in radian.
Examples:
calibrateTsai.cpp, exponentialMap.cpp, homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbtEdgeKltMultiTracking.cpp, mbtEdgeKltTracking.cpp, mbtKltMultiTracking.cpp, mbtKltTracking.cpp, moveAfma4.cpp, moveBiclops.cpp, movePtu46.cpp, photometricVisualServoing.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6FourPoints2DCamVelocityInteractionCurrent.cpp, servoAfma6FourPoints2DCamVelocityInteractionDesired.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu4Points.cpp, servoSimuAfma6FourPoints2DCamVelocity.cpp, servoSimuCircle2DCamVelocityDisplay.cpp, servoSimuCylinder.cpp, servoSimuCylinder2DCamVelocityDisplay.cpp, servoSimuCylinder2DCamVelocityDisplaySecondaryTask.cpp, servoSimuFourPoints2DCamVelocityDisplay.cpp, servoSimuFourPoints2DPolarCamVelocityDisplay.cpp, servoSimuLine2DCamVelocityDisplay.cpp, servoSimuPoint2DhalfCamVelocity1.cpp, servoSimuPoint2DhalfCamVelocity2.cpp, servoSimuPoint2DhalfCamVelocity3.cpp, servoSimuSphere.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper650FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper650FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, sonarPioneerReader.cpp, testDisplacement.cpp, testFeatureSegment.cpp, testFindMatch.cpp, testKalmanAcceleration.cpp, testKalmanVelocity.cpp, testKeyPoint-2.cpp, testKeyPoint-4.cpp, testMatrix.cpp, testPose.cpp, testPoseFeatures.cpp, testPoseRansac2.cpp, testPoseVector.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testViper650.cpp, testViper850.cpp, tutorial-detection-object-mbt.cpp, tutorial-detection-object-mbt2.cpp, tutorial-homography-from-points.cpp, tutorial-ibvs-4pts-display.cpp, tutorial-ibvs-4pts-image-tracking.cpp, tutorial-ibvs-4pts-ogre-tracking.cpp, tutorial-ibvs-4pts-ogre.cpp, tutorial-ibvs-4pts-plotter-continuous-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter-gain-adaptive.cpp, tutorial-ibvs-4pts-plotter.cpp, tutorial-ibvs-4pts-wireframe-camera.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-ibvs-4pts.cpp, tutorial-image-simulator.cpp, tutorial-mb-edge-tracker.cpp, tutorial-mb-hybrid-tracker.cpp, tutorial-mb-klt-tracker.cpp, tutorial-mb-tracker-full.cpp, and wireframeSimulator.cpp.

Definition at line 104 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbEdgeMultiTracker::computeProjectionError(), vpMeEllipse::display(), vpDisplay::displayEllipse(), vpRobotViper650::get_eJe(), vpRobotViper850::get_eJe(), vpAfma6::getInverseKinematics(), vpViper::getInverseKinematicsWrist(), vpRobotViper650::getPosition(), vpRobotViper850::getPosition(), vpRobotPioneer::getVelocity(), vpAfma6::init(), vpViper650::init(), vpViper850::init(), vpSimulatorAfma6::init(), vpSimulatorViper850::init(), vpSimulatorAfma6::initDisplay(), vpSimulatorViper850::initDisplay(), vpMeEllipse::initTracking(), vpMbtPolygon::isVisible(), vpMbEdgeKltTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpWireFrameSimulator::navigation(), vpSimulatorAfma6::readPosFile(), vpRobotAfma4::readPosFile(), vpRobotAfma6::readPosFile(), vpMbEdgeMultiTracker::resetTracker(), vpMbKltMultiTracker::resetTracker(), vpMbKltTracker::resetTracker(), vpMbEdgeTracker::resetTracker(), vpMbEdgeKltTracker::vpMbEdgeKltTracker(), vpMbEdgeTracker::vpMbEdgeTracker(), vpMbKltTracker::vpMbKltTracker(), vpRobotBiclops::vpRobotBiclopsSpeedControlLoop(), vpSickLDMRS::vpSickLDMRS(), vpViper::vpViper(), vpViper650::vpViper650(), vpViper850::vpViper850(), and vpWireFrameSimulator::vpWireFrameSimulator().

template<typename _Tp >
static _Tp vpMath::saturate ( unsigned char  v)
inlinestatic

Definition at line 192 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( char  v)
inlinestatic

Definition at line 193 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( unsigned short  v)
inlinestatic

Definition at line 194 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( short  v)
inlinestatic

Definition at line 195 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( unsigned  v)
inlinestatic

Definition at line 196 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( int  v)
inlinestatic

Definition at line 197 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( float  v)
inlinestatic

Definition at line 198 of file vpMath.h.

template<typename _Tp >
static _Tp vpMath::saturate ( double  v)
inlinestatic

Definition at line 199 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( char  v)
inline

Definition at line 345 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( unsigned short  v)
inline

Definition at line 357 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( int  v)
inline

Definition at line 361 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( short  v)
inline

Definition at line 365 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( unsigned int  v)
inline

Definition at line 369 of file vpMath.h.

template<>
unsigned char vpMath::saturate ( float  v)
inline

Definition at line 373 of file vpMath.h.

References round().

template<>
unsigned char vpMath::saturate ( double  v)
inline

Definition at line 378 of file vpMath.h.

References round().

template<>
char vpMath::saturate ( unsigned char  v)
inline

Definition at line 384 of file vpMath.h.

template<>
char vpMath::saturate ( unsigned short  v)
inline

Definition at line 388 of file vpMath.h.

template<>
char vpMath::saturate ( int  v)
inline

Definition at line 392 of file vpMath.h.

template<>
char vpMath::saturate ( short  v)
inline

Definition at line 397 of file vpMath.h.

template<>
char vpMath::saturate ( unsigned int  v)
inline

Definition at line 401 of file vpMath.h.

template<>
char vpMath::saturate ( float  v)
inline

Definition at line 405 of file vpMath.h.

References round().

template<>
char vpMath::saturate ( double  v)
inline

Definition at line 410 of file vpMath.h.

References round().

template<>
unsigned short vpMath::saturate ( char  v)
inline

Definition at line 416 of file vpMath.h.

template<>
unsigned short vpMath::saturate ( short  v)
inline

Definition at line 428 of file vpMath.h.

template<>
unsigned short vpMath::saturate ( int  v)
inline

Definition at line 432 of file vpMath.h.

template<>
unsigned short vpMath::saturate ( unsigned int  v)
inline

Definition at line 437 of file vpMath.h.

template<>
unsigned short vpMath::saturate ( float  v)
inline

Definition at line 441 of file vpMath.h.

References round().

template<>
unsigned short vpMath::saturate ( double  v)
inline

Definition at line 446 of file vpMath.h.

References round().

template<>
short vpMath::saturate ( unsigned short  v)
inline

Definition at line 452 of file vpMath.h.

template<>
short vpMath::saturate ( int  v)
inline

Definition at line 455 of file vpMath.h.

template<>
short vpMath::saturate ( unsigned int  v)
inline

Definition at line 459 of file vpMath.h.

template<>
short vpMath::saturate ( float  v)
inline

Definition at line 462 of file vpMath.h.

References round().

template<>
short vpMath::saturate ( double  v)
inline

Definition at line 466 of file vpMath.h.

References round().

template<>
int vpMath::saturate ( float  v)
inline

Definition at line 472 of file vpMath.h.

References round().

template<>
int vpMath::saturate ( double  v)
inline

Definition at line 476 of file vpMath.h.

References round().

template<>
unsigned int vpMath::saturate ( float  v)
inline

Definition at line 482 of file vpMath.h.

References round().

template<>
unsigned int vpMath::saturate ( double  v)
inline

Definition at line 486 of file vpMath.h.

References round().

double vpMath::sigmoid ( double  x,
double  x0 = 0.,
double  x1 = 1.,
double  n = 12. 
)
inlinestatic

Sigmoid function between [x0,x1] with $ s(x)=0 if x\le x0$ and $ s(x)=1 if x \ge x1 $

Parameters
x: Value of x.
x0: Lower bound (default 0).
x1: Upper bound (default 1).
n: Degree of the exponential (default 12).
Returns
Sigmoid value $1/(1+exp(-n*((x-x0)/(x1-x0)-0.5)))$

Definition at line 333 of file vpMath.h.

int vpMath::sign ( double  x)
inlinestatic

Return the sign of x.

Returns
-1 if x is negative, +1 if positive and 0 if zero.

Definition at line 275 of file vpMath.h.

Referenced by vpMbEdgeTracker::computeVVSFirstPhase(), and vpMeNurbs::seekExtremities().

double vpMath::sinc ( double  x)
static

Compute sinus cardinal $ \frac{sin(x)}{x} $.

Parameters
x: Value of x.
Returns
Sinus cardinal.

Definition at line 169 of file vpMath.cpp.

Referenced by vpRotationMatrix::buildFrom(), vpThetaUVector::buildFrom(), vpCalibration::calibrationTsai(), vpExponentialMap::direct(), vpFeatureThetaU::interaction(), and vpExponentialMap::inverse().

double vpMath::sinc ( double  sinx,
double  x 
)
static

Compute sinus cardinal $ \frac{sin(x)}{x}$.

Parameters
sinx: Value of sin(x).
x: Value of x.
Returns
Sinus cardinal.

Definition at line 184 of file vpMath.cpp.

static double vpMath::sqr ( double  x)
inlinestatic

Compute x square value.

Returns
Square value $ x^2 $.
Examples:
servoSimuSphere.cpp, servoViper850Point2DArtVelocity-jointAvoidance-gpa.cpp, testRobust.cpp, and tutorial-klt-tracker-with-reinit.cpp.

Definition at line 110 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbtDistanceCircle::computeInteractionMatrixError(), vpCircle::computeIntersectionPoint(), vpPose::computeResidual(), vpPose::computeResidualDementhon(), vpCalibration::computeStdDeviation(), vpCalibration::computeStdDeviation_dist(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbEdgeTracker::computeVVSSecondPhasePoseEstimation(), vpMbEdgeMultiTracker::computeVVSSecondPhaseWeights(), vpMbEdgeTracker::computeVVSSecondPhaseWeights(), vpMeterPixelConversion::convertEllipse(), vpMeterPixelConversion::convertLine(), vpPixelMeterConversion::convertLine(), vpPixelMeterConversion::convertPointWithDistortion(), vpPose::coplanar(), vpFeatureBuilder::create(), vpDot2::defineDots(), vpDisplayGTK::displayArrow(), vpDisplayX::displayArrow(), vpDisplayOpenCV::displayArrow(), vpDisplayOpenCV::displayDotLine(), vpFeatureDisplay::displayEllipse(), vpCalibration::displayGrid(), vpMeSite::distance(), vpImagePoint::distance(), vpImageFilter::getGaussianDerivativeKernel(), vpImageFilter::getGaussianKernel(), vpViper::getInverseKinematicsWrist(), vpMeEllipse::initTracking(), vpFeatureEllipse::interaction(), vpFeatureThetaU::interaction(), vpRotationMatrix::isARotationMatrix(), vpScale::KernelDensityGradient(), vpScale::KernelDensityGradient_EPANECHNIKOV(), vpMeLine::leastSquare(), vpMeNurbs::localReSample(), vpScale::MeanShift(), vpPose::poseRansac(), vpPose::poseVirtualVSrobust(), vpCircle::projection(), vpNurbs::removeCurveKnot(), vpMeLine::reSample(), vpMeLine::sample(), vpMeNurbs::sample(), vpMeLine::seekExtremities(), vpMeNurbs::seekExtremitiesCanny(), vpMeSite::sqrDistance(), vpImagePoint::sqrDistance(), vpMeNurbs::supressNearPoints(), vpMeSite::track(), and vpImageTools::undistort().

template<class Type >
static void vpMath::swap ( Type &  a,
Type &  b 
)
inlinestatic

Exchange two numbers.

Parameters
aFirst number to exchange.
bSecond number to exchange

Definition at line 182 of file vpMath.h.