Visual Servoing Platform  version 3.2.0 under development (2018-08-19)
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 86 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 152 of file vpMath.h.

Referenced by vpImageTools::imageDifferenceAbsolute(), 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 220 of file vpMath.h.

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

static double vpMath::deg ( double  rad)
inlinestatic

Convert an angle in radians into degrees.

Parameters
rad: Angle in radians.
Returns
Angle converted in degrees.
Examples:
calibrateTsai.cpp, mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, moveBiclops.cpp, movePioneer.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, sonarPioneerReader.cpp, testFrankaJointVelocityLimits.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testPose.cpp, testRobotAfma6Pose.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, testViper650.cpp, testViper850.cpp, trackMeLine.cpp, tutorial-homography-from-points.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 95 of file vpMath.h.

Referenced by vpMbGenericTracker::computeCurrentProjectionError(), vpMbTracker::computeCurrentProjectionError(), vpMbEdgeMultiTracker::computeProjectionError(), vpMbGenericTracker::computeProjectionError(), vpMbEdgeTracker::computeProjectionError(), vpAfma6::getInverseKinematics(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpMbEdgeKltTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpFeatureSegment::print(), vpPoseVector::print(), vpServoData::save(), vpSimulatorAfma6::savePosFile(), vpRobotAfma4::savePosFile(), vpSimulatorViper850::savePosFile(), vpRobotAfma6::savePosFile(), vpRobotViper650::savePosFile(), vpRobotViper850::savePosFile(), vpRobotViper650::setPosition(), vpRobotViper850::setPosition(), vpRobotPioneer::setVelocity(), vpMbGenericTracker::track(), vpSimulatorAfma6::updateArticularPosition(), vpSimulatorViper850::updateArticularPosition(), and vpRobotBiclops::vpRobotBiclopsSpeedControlLoop().

double vpMath::fact ( unsigned int  x)
inlinestatic

Computes and returns x!

Parameters
x: parameter of factorial function.

Definition at line 205 of file vpMath.h.

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:
mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testImageTemplateMatching.cpp, testKeyPoint-2.cpp, testMath.cpp, and tutorial-apriltag-detector-live.cpp.

Definition at line 252 of file vpMath.cpp.

References 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 299 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 110 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 84 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 135 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 281 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 153 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 281 of file vpMath.h.

Referenced by vpPose::computeRansacIterations(), 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, mbtGenericTracking.cpp, mbtGenericTracking2.cpp, mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.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, servoFrankaPBVS.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, servoViper850FourPoints2DArtVelocityInteractionCurrent.cpp, servoViper850FourPoints2DCamVelocityInteractionCurrent.cpp, servoViper850FourPointsKinect.cpp, simulateCircle2DCamVelocity.cpp, simulateFourPoints2DCartesianCamVelocity.cpp, simulateFourPoints2DPolarCamVelocity.cpp, sonarPioneerReader.cpp, testDisplacement.cpp, testFeatureSegment.cpp, testFindMatch.cpp, testFrankaJointVelocity-2.cpp, testFrankaJointVelocity-3.cpp, testFrankaJointVelocity.cpp, testFrankaJointVelocityLimits.cpp, testGenericTracker.cpp, testGenericTrackerDepth.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, testVirtuoseWithGlove.cpp, tutorial-detection-object-mbt-deprecated.cpp, tutorial-detection-object-mbt.cpp, tutorial-detection-object-mbt2-deprecated.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-generic-tracker-apriltag-live-realsense2.cpp, tutorial-mb-generic-tracker-apriltag-live-webcam.cpp, tutorial-mb-generic-tracker-full.cpp, tutorial-mb-hybrid-tracker.cpp, tutorial-mb-klt-tracker.cpp, tutorial-mb-tracker-full.cpp, and wireframeSimulator.cpp.

Definition at line 102 of file vpMath.h.

Referenced by vpVirtualGrabber::acquire(), vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpMbEdgeMultiTracker::computeProjectionError(), vpMbGenericTracker::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(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpMbEdgeKltTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpWireFrameSimulator::navigation(), vpMeEllipse::printParameters(), vpSimulatorAfma6::readPosFile(), vpRobotAfma4::readPosFile(), vpRobotAfma6::readPosFile(), vpMbDepthDenseTracker::resetTracker(), vpMbDepthNormalTracker::resetTracker(), vpMbEdgeMultiTracker::resetTracker(), vpMbKltMultiTracker::resetTracker(), vpMbGenericTracker::resetTracker(), vpMbKltTracker::resetTracker(), vpMbEdgeTracker::resetTracker(), vpMbGenericTracker::track(), vpMbEdgeKltTracker::vpMbEdgeKltTracker(), vpMbEdgeTracker::vpMbEdgeTracker(), vpMbKltTracker::vpMbKltTracker(), vpRobotBiclops::vpRobotBiclopsSpeedControlLoop(), vpRobotCamera::vpRobotCamera(), vpSickLDMRS::vpSickLDMRS(), vpSimulatorCamera::vpSimulatorCamera(), vpViper::vpViper(), vpViper650::vpViper650(), vpViper850::vpViper850(), vpWireFrameSimulator::vpWireFrameSimulator(), vpMeEllipse::~vpMeEllipse(), and vpPioneer::~vpPioneer().

int vpMath::round ( const double  x)
inlinestatic

Round x to the nearest integer.

Parameters
x: Value to round.
Returns
Nearest integer of x.
Examples:
mbot-apriltag-2D-half-vs.cpp, mbot-apriltag-ibvs.cpp, mbot-apriltag-pbvs.cpp, and testMath.cpp.

Definition at line 235 of file vpMath.h.

References sign().

Referenced by vpMeLine::computeRhoTheta(), vpMeSite::convolution(), vpKeyPoint::createImageMatching(), vpKltOpencv::display(), vpMeNurbs::display(), vpDisplayGTK::displayCharString(), vpDisplayOpenCV::displayCharString(), vpDisplayGTK::displayCircle(), vpDisplayX::displayCircle(), vpDisplayOpenCV::displayCircle(), vpDisplayGTK::displayDotLine(), vpDisplayX::displayDotLine(), vpDisplayGTK::displayLine(), vpDisplayX::displayLine(), vpDisplayOpenCV::displayLine(), vpKeyPoint::displayMatching(), vpDisplayGTK::displayPoint(), vpDisplayX::displayPoint(), vpDisplayOpenCV::displayPoint(), vpMbtDistanceKltCylinder::displayPrimitive(), vpMbtDistanceKltPoints::displayPrimitive(), vpDisplayGTK::displayRectangle(), vpDisplayX::displayRectangle(), vpDisplayOpenCV::displayRectangle(), vp::equalizeHistogram(), vpImageTools::extract(), vpBSpline::findSpan(), vpMeSite::getSign(), vpImage< Type >::getValue(), vpImage< vpRGBa >::getValue(), vpMeSite::init(), vpMeLine::initTracking(), vpKeyPoint::insertImageMatching(), vpImageTools::interpolate(), vpImageConvert::MONO16ToRGBa(), vpMeTracker::outOfImage(), vpMeLine::sample(), saturate(), vpKltOpencv::suppressFeature(), vpMeLine::updateDelta(), vpMeSite::vpMeSite(), and vpMeEllipse::~vpMeEllipse().

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

Definition at line 179 of file vpMath.h.

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

Definition at line 180 of file vpMath.h.

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

Definition at line 181 of file vpMath.h.

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

Definition at line 182 of file vpMath.h.

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

Definition at line 183 of file vpMath.h.

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

Definition at line 184 of file vpMath.h.

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

Definition at line 185 of file vpMath.h.

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

Definition at line 186 of file vpMath.h.

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

Definition at line 322 of file vpMath.h.

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

Definition at line 335 of file vpMath.h.

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

Definition at line 340 of file vpMath.h.

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

Definition at line 345 of file vpMath.h.

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

Definition at line 347 of file vpMath.h.

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

Definition at line 352 of file vpMath.h.

References round().

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

Definition at line 358 of file vpMath.h.

References round().

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

Definition at line 365 of file vpMath.h.

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

Definition at line 367 of file vpMath.h.

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

Definition at line 372 of file vpMath.h.

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

Definition at line 377 of file vpMath.h.

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

Definition at line 379 of file vpMath.h.

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

Definition at line 384 of file vpMath.h.

References round().

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

Definition at line 390 of file vpMath.h.

References round().

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

Definition at line 397 of file vpMath.h.

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

Definition at line 410 of file vpMath.h.

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

Definition at line 415 of file vpMath.h.

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

Definition at line 420 of file vpMath.h.

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

Definition at line 425 of file vpMath.h.

References round().

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

Definition at line 431 of file vpMath.h.

References round().

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

Definition at line 438 of file vpMath.h.

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

Definition at line 439 of file vpMath.h.

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

Definition at line 443 of file vpMath.h.

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

Definition at line 447 of file vpMath.h.

References round().

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

Definition at line 452 of file vpMath.h.

References round().

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

Definition at line 459 of file vpMath.h.

References round().

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

Definition at line 461 of file vpMath.h.

References round().

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

Definition at line 466 of file vpMath.h.

References round().

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

Definition at line 468 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 310 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 262 of file vpMath.h.

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

double vpMath::sinc ( double  x)
static
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 187 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 108 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpCalibration::calibrationTsai(), vpMatrix::computeCovarianceMatrixVVS(), vpHomography::computeDisplacement(), vpMbtDistanceCircle::computeInteractionMatrixError(), vpCircle::computeIntersectionPoint(), vpPoseFeatures::computePose(), vpPose::computeResidual(), vpPose::computeResidualDementhon(), vpCalibration::computeStdDeviation(), vpCalibration::computeStdDeviation_dist(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbEdgeKltTracker::computeVVS(), vpMbEdgeMultiTracker::computeVVS(), vpMbEdgeKltMultiTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeTracker::computeVVSInit(), 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(), vpMbtFaceDepthNormal::estimateFeatures(), vpImageFilter::getGaussianDerivativeKernel(), vpImageFilter::getGaussianKernel(), vpViper::getInverseKinematicsWrist(), vpMeEllipse::initTracking(), vpImageTools::integralImage(), vpFeatureEllipse::interaction(), vpFeatureThetaU::interaction(), vpRotationMatrix::isARotationMatrix(), vpScale::KernelDensityGradient(), vpScale::KernelDensityGradient_EPANECHNIKOV(), vpMeLine::leastSquare(), vpMeNurbs::localReSample(), vpScale::MeanShift(), vpImageTools::normalizedCorrelation(), vpPose::poseVirtualVSrobust(), vpMeEllipse::printParameters(), vpCircle::projection(), vpNurbs::removeCurveKnot(), vpMeLine::reSample(), vpMeLine::sample(), vpMeNurbs::sample(), vpMeLine::seekExtremities(), vpMeNurbs::seekExtremitiesCanny(), vpRobust::simultMEstimator(), vpMeSite::sqrDistance(), vpImagePoint::sqrDistance(), vpMeNurbs::supressNearPoints(), vpImageTools::templateMatching(), vpMeEllipse::track(), vpMeSite::track(), vpMbGenericTracker::track(), vpImageTools::undistort(), and vpMeEllipse::~vpMeEllipse().

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 169 of file vpMath.h.