Visual Servoing Platform  version 3.4.0
Public Member Functions | Static Public Member Functions | List of all members
vpMath Class Reference
core: Core module » Mathematics » Other tools

#include <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 (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 (double value)
 
static bool isInf (double value)
 
static double lineFitting (const std::vector< vpImagePoint > &imPts, double &a, double &b, double &c)
 
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, bool useBesselCorrection=false)
 
static int modulo (int a, 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 94 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
Examples:
testImageWarp.cpp.

Definition at line 160 of file vpMath.h.

Referenced by vpImageTools::imageDifferenceAbsolute(), vpImageTools::remap(), 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 230 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:
calibrate-hand-eye.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, testMomentAlpha.cpp, testPose.cpp, testRobotAfma6Pose.cpp, testRobotFlirPtu.cpp, testRobotViper850.cpp, testRobotViper850Pose.cpp, testViper650.cpp, testViper850.cpp, trackMeLine.cpp, tutorial-hand-eye-calibration.cpp, tutorial-homography-from-points.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-mb-generic-tracker-live.cpp, tutorial-pose-from-points-live.cpp, and tutorial-pose-from-points-realsense-T265.cpp.

Definition at line 103 of file vpMath.h.

Referenced by vpPose::calculArbreDementhon(), vpHandEyeCalibration::calibrate(), vpMbGenericTracker::computeCurrentProjectionError(), vpMbTracker::computeCurrentProjectionError(), vpMbGenericTracker::computeProjectionError(), vpMbEdgeTracker::computeProjectionError(), vpAfma6::getInverseKinematics(), vpRobotFlirPtu::getNetworkHostName(), vpMeEllipse::leastSquareRobust(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpMbEdgeKltTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpPose::poseDementhonNonPlan(), vpPose::poseDementhonPlan(), vpFeatureSegment::print(), vpPoseVector::print(), vpMeEllipse::printParameters(), vpServoData::save(), vpSimulatorAfma6::savePosFile(), vpRobotAfma4::savePosFile(), vpSimulatorViper850::savePosFile(), vpRobotAfma6::savePosFile(), vpRobotFranka::savePosFile(), vpRobotViper650::savePosFile(), vpRobotViper850::savePosFile(), vpRobotFlirPtu::setJointVelocity(), vpRobotKinova::setJointVelocity(), vpRobotKinova::setPosition(), vpRobotFlirPtu::setPosition(), vpRobotViper650::setPosition(), vpRobotViper850::setPosition(), vpRobotPioneer::setVelocity(), vpMeEllipse::track(), vpMbGenericTracker::track(), vpSimulatorAfma6::updateArticularPosition(), vpSimulatorViper850::updateArticularPosition(), and vpRobotBiclops::vpRobotBiclopsSpeedControlLoop().

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:
testAprilTag.cpp, testColVector.cpp, testImageFilter.cpp, testImageNormalizedCorrelation.cpp, testImageTemplateMatching.cpp, testIoTools.cpp, testKeyPoint-7.cpp, testMath.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixInitialization.cpp, testMomentAlpha.cpp, testRowVector.cpp, testThread2.cpp, and testTukeyEstimator.cpp.

Definition at line 293 of file vpMath.h.

Referenced by vpMbDepthDenseTracker::display(), vpMbDepthNormalTracker::display(), vpMbEdgeKltTracker::display(), vpMbKltTracker::display(), vpMbEdgeTracker::display(), vpMbEdgeTracker::displayFeaturesOnImage(), vpPolygon::isInside(), vpImageConvert::MONO16ToRGBa(), vpRowVector::operator==(), vpColVector::operator==(), vpCameraParameters::operator==(), vpKeyPoint::saveLearningData(), vpQbSoftHand::setPosition(), and vpMbGenericTracker::track().

double vpMath::fact ( unsigned int  x)
inlinestatic

Computes and returns x!

Parameters
x: parameter of factorial function.

Definition at line 215 of file vpMath.h.

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:
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, testRealSense2_D435.cpp, testRealSense2_D435_opencv.cpp, testRealSense2_D435_pcl.cpp, testRealSense2_SR300.cpp, testRealSense_R200.cpp, testRealSense_SR300.cpp, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-T265-realsense.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 200 of file vpMath.cpp.

References vpException::notInitialized.

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:
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, testRealSense2_D435.cpp, testRealSense2_D435_opencv.cpp, testRealSense2_D435_pcl.cpp, testRealSense2_SR300.cpp, testRealSense_R200.cpp, testRealSense_SR300.cpp, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-T265-realsense.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 220 of file vpMath.cpp.

References vpException::notInitialized.

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

double vpMath::getStdev ( const std::vector< double > &  v,
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, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-T265-realsense.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 250 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 302 of file vpMath.h.

bool vpMath::isInf ( 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 111 of file vpMath.cpp.

bool vpMath::isNaN ( 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::lineFitting ( const std::vector< vpImagePoint > &  imPts,
double &  a,
double &  b,
double &  c 
)
static

Compute the line equation using least-squares fitting that minimizes the cost function:

\[ \mathbf{E} = \sum_{i=1}^{n}\left ( ax_i + by_i - c \right )^2 \]

Parameters
imPts: Image points (size >= 3).
a: a coefficient.
b: b coefficient.
c: c coefficient.
Returns
The mean distance error (point-to-line distance) between the points and the fitted line.
Examples:
testLineFitting.cpp.

Definition at line 287 of file vpMath.cpp.

References vpException::dimensionError, vpMatrix::eigenValues(), vpImagePoint::get_u(), and vpImagePoint::get_v().

template<class Type >
static Type vpMath::maximum ( const Type &  a,
const Type &  b 
)
inlinestatic

Find the maximum between two numbers (or other).

Parameters
a: First number.
b: Second number.
Returns
The maximum of the two numbers.
Examples:
testImageDifference.cpp.

Definition at line 145 of file vpMath.h.

Referenced by vpMbEdgeTracker::addCircle(), vpMbEdgeTracker::addCylinder(), vpMbTracker::addProjectionErrorCircle(), vpMbTracker::addProjectionErrorCylinder(), vpMbTracker::extractCylinders(), vpBSpline::findSpan(), vpRobotWireFrameSimulator::getExternalCameraParameters(), vpWireFrameSimulator::getExternalCameraParameters(), vpSimulatorAfma6::getExternalImage(), vpSimulatorViper850::getExternalImage(), vpWireFrameSimulator::getExternalImage(), vpDot2::getFreemanChain(), vpWireFrameSimulator::getInternalCameraParameters(), vpWireFrameSimulator::getInternalImage(), vpRobotWireFrameSimulator::getInternalView(), vpMeNurbs::localReSample(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpRowVector::print(), vpColVector::print(), vpMatrix::print(), vpRansac< vpTransformation >::ransac(), vpDot2::searchDotsInArea(), vpMeNurbs::seekExtremitiesCanny(), vpHinkley::testDownUpwardJump(), and vpRobotBiclops::vpRobotBiclopsSpeedControlLoop().

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 136 of file vpMath.cpp.

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

template<class Type >
static Type vpMath::minimum ( const Type &  a,
const Type &  b 
)
inlinestatic

Find the minimum between two numbers (or other).

Parameters
a: First number.
b: Second number.
Returns
The minimum of the two numbers.
Examples:
testImageDifference.cpp.

Definition at line 153 of file vpMath.h.

Referenced by vpRobotWireFrameSimulator::getExternalCameraParameters(), vpWireFrameSimulator::getExternalCameraParameters(), vpSimulatorAfma6::getExternalImage(), vpSimulatorViper850::getExternalImage(), vpWireFrameSimulator::getExternalImage(), vpWireFrameSimulator::getInternalCameraParameters(), vpWireFrameSimulator::getInternalImage(), vpRobotWireFrameSimulator::getInternalView(), vpIoTools::loadConfigFile(), vpWireFrameSimulator::navigation(), vpRansac< vpTransformation >::ransac(), and vpMbEdgeTracker::testTracking().

int vpMath::modulo ( int  a,
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.

Definition at line 340 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 284 of file vpMath.h.

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

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:
calibrate-hand-eye.cpp, exponentialMap.cpp, homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyRansac2DObject.cpp, manServo4PointsDisplay.cpp, manServoMomentsSimple.cpp, manSimu4Dots.cpp, manSimu4Points.cpp, mbtEdgeKltTracking.cpp, mbtGenericTracking.cpp, mbtGenericTracking2.cpp, mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, mbtKltTracking.cpp, moveAfma4.cpp, moveBiclops.cpp, movePtu46.cpp, photometricVisualServoing.cpp, photometricVisualServoingWithoutVpServo.cpp, servoAfma62DhalfCamVelocity.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoFrankaPBVS.cpp, servoKinovaJacoJoint.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, servoSimuSphere2DCamVelocityDisplaySecondaryTask.cpp, servoSimuSquareLine2DCamVelocityDisplay.cpp, servoSimuThetaUCamVelocity.cpp, servoSimuViper850FourPoints2DCamVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_cur.cpp, servoViper850FourPoints2DCamVelocityLs_cur.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, testImageWarp.cpp, testKalmanAcceleration.cpp, testKalmanVelocity.cpp, testKeyPoint-2.cpp, testKeyPoint-4.cpp, testMatrix.cpp, testPose.cpp, testPoseFeatures.cpp, testPoseVector.cpp, testRobotBebop2.cpp, testRobotFlirPtu.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-rs2.cpp, tutorial-mb-generic-tracker-apriltag-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 110 of file vpMath.h.

Referenced by vpVirtualGrabber::acquire(), vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpMbGenericTracker::computeProjectionError(), vpRobotViper650::get_eJe(), vpRobotViper850::get_eJe(), vpAfma6::getInverseKinematics(), vpViper::getInverseKinematicsWrist(), vpRobotKinova::getJointPosition(), vpRobotFlirPtu::getNetworkHostName(), vpRobotPioneer::getVelocity(), vpViper650::init(), vpViper850::init(), vpAfma6::init(), vpSimulatorAfma6::init(), vpSimulatorViper850::init(), vpSimulatorAfma6::initDisplay(), vpSimulatorViper850::initDisplay(), vpMbtPolygon::isVisible(), vpMeEllipse::leastSquareRobust(), vpMbTracker::loadCAOModel(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpMbEdgeKltTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpWireFrameSimulator::navigation(), vpMeEllipse::plugHoles(), vpSimulatorAfma6::readPosFile(), vpRobotAfma4::readPosFile(), vpRobotAfma6::readPosFile(), vpRobotFranka::readPosFile(), vpMbDepthDenseTracker::resetTracker(), vpMbDepthNormalTracker::resetTracker(), vpMbGenericTracker::resetTracker(), vpMbKltTracker::resetTracker(), vpMbEdgeTracker::resetTracker(), vpMeEllipse::sample(), vpMeEllipse::track(), vpMbGenericTracker::track(), vpRobotBiclops::vpRobotBiclopsSpeedControlLoop(), vpRobotCamera::vpRobotCamera(), vpSickLDMRS::vpSickLDMRS(), vpSimulatorCamera::vpSimulatorCamera(), vpViper::vpViper(), vpViper650::vpViper650(), vpViper850::vpViper850(), vpWireFrameSimulator::vpWireFrameSimulator(), and vpPioneer::~vpPioneer().

int vpMath::round ( 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, testImageGetValue.cpp, and testMath.cpp.

Definition at line 245 of file vpMath.h.

References sign().

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

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

Definition at line 189 of file vpMath.h.

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

Definition at line 190 of file vpMath.h.

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

Definition at line 191 of file vpMath.h.

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

Definition at line 192 of file vpMath.h.

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

Definition at line 193 of file vpMath.h.

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

Definition at line 194 of file vpMath.h.

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

Definition at line 195 of file vpMath.h.

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

Definition at line 196 of file vpMath.h.

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

Definition at line 327 of file vpMath.h.

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

Definition at line 340 of file vpMath.h.

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

Definition at line 345 of file vpMath.h.

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

Definition at line 350 of file vpMath.h.

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

Definition at line 352 of file vpMath.h.

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

Definition at line 357 of file vpMath.h.

References round().

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

Definition at line 363 of file vpMath.h.

References round().

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

Definition at line 370 of file vpMath.h.

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

Definition at line 372 of file vpMath.h.

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

Definition at line 377 of file vpMath.h.

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

Definition at line 382 of file vpMath.h.

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

Definition at line 384 of file vpMath.h.

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

Definition at line 389 of file vpMath.h.

References round().

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

Definition at line 395 of file vpMath.h.

References round().

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

Definition at line 402 of file vpMath.h.

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

Definition at line 415 of file vpMath.h.

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

Definition at line 420 of file vpMath.h.

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

Definition at line 425 of file vpMath.h.

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

Definition at line 430 of file vpMath.h.

References round().

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

Definition at line 436 of file vpMath.h.

References round().

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

Definition at line 443 of file vpMath.h.

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

Definition at line 444 of file vpMath.h.

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

Definition at line 448 of file vpMath.h.

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

Definition at line 452 of file vpMath.h.

References round().

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

Definition at line 457 of file vpMath.h.

References round().

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

Definition at line 464 of file vpMath.h.

References round().

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

Definition at line 466 of file vpMath.h.

References round().

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

Definition at line 471 of file vpMath.h.

References round().

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

Definition at line 473 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 315 of file vpMath.h.

static int() vpMath::sign ( double  x)
inlinestatic

Referenced by vpThetaUVector::buildFrom(), vpMbEdgeTracker::computeVVSFirstPhase(), round(), 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(), vpMatrix::computeCovarianceMatrixVVS(), 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 185 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 116 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), 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(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeTracker::computeVVSInit(), vpMeterPixelConversion::convertEllipse(), vpPixelMeterConversion::convertLine(), vpMeterPixelConversion::convertLine(), vpPixelMeterConversion::convertPoint(), vpMeterPixelConversion::convertPoint(), vpPose::coplanar(), vpFeatureBuilder::create(), vpDot2::defineDots(), vpDisplayGTK::displayArrow(), vpDisplayX::displayArrow(), vpDisplayOpenCV::displayArrow(), vpDisplayOpenCV::displayDotLine(), vpCalibration::displayGrid(), vpMeSite::distance(), vpImagePoint::distance(), vpImageDraw::drawArrow(), vpImageDraw::drawDottedLine(), vpMbtFaceDepthNormal::estimateFeatures(), vpImageFilter::getGaussianDerivativeKernel(), vpImageFilter::getGaussianKernel(), vpViper::getInverseKinematicsWrist(), vpImageTools::initUndistortMap(), vpImageTools::integralImage(), vpFeatureEllipse::interaction(), vpFeatureThetaU::interaction(), vpRotationMatrix::isARotationMatrix(), vpScale::KernelDensityGradient(), vpScale::KernelDensityGradient_EPANECHNIKOV(), vpMeLine::leastSquare(), vpMeNurbs::localReSample(), vpScale::MeanShift(), vpRobust::MEstimator(), vpPose::poseVirtualVSrobust(), vpSphere::projection(), vpCircle::projection(), vpNurbs::removeCurveKnot(), vpMeLine::reSample(), vpMeLine::sample(), vpMeNurbs::sample(), vpMeLine::seekExtremities(), vpMeNurbs::seekExtremitiesCanny(), vpRobust::simultMEstimator(), vpMeSite::sqrDistance(), vpImagePoint::sqrDistance(), vpMeNurbs::supressNearPoints(), vpImageTools::templateMatching(), vpMeSite::track(), vpMbGenericTracker::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 177 of file vpMath.h.