Visual Servoing Platform  version 3.5.1 under development (2023-03-29)
Static Public Member Functions | List of all members
vpMath Class Reference
core: Core module » Mathematics » Other tools

#include <visp3/core/vpMath.h>

Static Public Member Functions

static double deg (double rad)
 
static vpColVector deg (const vpRotationVector &r)
 
static vpColVector deg (const vpColVector &r)
 
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)
 
template<typename T >
static T clamp (const T &v, const T &lower, const T &upper)
 
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 isNaN (float value)
 
static bool isInf (double value)
 
static bool isInf (float value)
 
static bool isFinite (double value)
 
static bool isFinite (float 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)
 
static vpHomogeneousMatrix ned2ecef (double lonDeg, double latDeg, double radius)
 
static vpHomogeneousMatrix enu2ecef (double lonDeg, double latDeg, double radius)
 
static vpHomogeneousMatrix enu2ned (const vpHomogeneousMatrix &enu_M)
 
template<typename T >
static std::vector< double > linspace (T start_in, T end_in, unsigned int num_in)
 
static std::vector< std::pair< double, double > > computeRegularPointsOnSphere (unsigned int maxPoints)
 
static std::vector< vpHomogeneousMatrix > getLocalTangentPlaneTransformations (const std::vector< std::pair< double, double > > &lonlatVec, double radius, vpHomogeneousMatrix(*toECEF)(double lonDeg, double latDeg, double radius))
 
static vpHomogeneousMatrix lookAt (const vpColVector &from, const vpColVector &to, vpColVector tmp)
 
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)
 

Detailed Description

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

Definition at line 102 of file vpMath.h.

Member Function Documentation

◆ abs()

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 190 of file vpMath.h.

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

◆ clamp()

template<typename T >
static T vpMath::clamp ( const T &  v,
const T &  lower,
const T &  upper 
)
inlinestatic

Clamp a value to boundaries.

Parameters
v: The value to clamp.
lower,upper: The boundaries to clamp v to.

Throw a vpException if the value of lower is greater than upper.

Examples
testMath.cpp.

Definition at line 142 of file vpMath.h.

References vpException::badValue.

Referenced by vpPlaneEstimation::estimatePlane().

◆ comb()

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 311 of file vpMath.h.

References fact().

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

◆ computeRegularPointsOnSphere()

std::vector< std::pair< double, double > > vpMath::computeRegularPointsOnSphere ( unsigned int  maxPoints)
static

Compute the vector of longitude / latitude (in degree) couples for maxPoints regularly spaced on a sphere, using the following paper:

Following image illustrates the camera poses regularly spaced on a sphere:

Parameters
maxPoints: The number of point coordinates to be sampled on a sphere.
Returns
The vector of longitude / latitude (in degree) pairs for the maxPoints on a sphare.
Examples
testMathUtils.cpp.

Definition at line 535 of file vpMath.cpp.

References deg(), and round().

◆ deg() [1/3]

vpColVector vpMath::deg ( const vpColVector &  r)
static

Convert angles of a column vector from radians to degrees.

Parameters
r: Column vector with angles in radians.
Returns
Corresponding column vector with angles converted in degrees.

Definition at line 661 of file vpMath.cpp.

References deg(), and vpArray2D< Type >::size().

◆ deg() [2/3]

vpColVector vpMath::deg ( const vpRotationVector &  r)
static

Convert angles of a rotation vector into degrees.

Parameters
r: Rotation vector with angles in radians.
Returns
Corresponding column vector with angles converted in degrees.

Definition at line 643 of file vpMath.cpp.

References deg(), vpException::fatalError, and vpArray2D< Type >::size().

◆ deg() [3/3]

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, servoAfma6AprilTagPBVS.cpp, servoFrankaPBVS.cpp, servoPioneerPanSegment3D.cpp, servoPioneerPoint2DDepth.cpp, servoPioneerPoint2DDepthWithoutVpServo.cpp, servoUniversalRobotsPBVS.cpp, sonarPioneerReader.cpp, testFrankaJointVelocityLimits.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testMath.cpp, testMocapQualisys.cpp, testMocapVicon.cpp, testMomentAlpha.cpp, testPixhawkDronePositionAbsoluteControl.cpp, testPixhawkDronePositionRelativeControl.cpp, testPixhawkDroneTakeoff.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 111 of file vpMath.h.

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

◆ enu2ecef()

vpHomogeneousMatrix vpMath::enu2ecef ( double  lonDeg,
double  latDeg,
double  radius 
)
static

Compute from a given longitude, latitude and a sphere radius the homogeneous transformation from the ENU frame to the ECEF frame:

\[ \begin{bmatrix} X_{\text{ecef}} \\ Y_{\text{ecef}} \\ Z_{\text{ecef}} \end{bmatrix} = \begin{bmatrix} -\sin \lambda & -\sin \varphi \cos \lambda & \cos \varphi \cos \lambda \\ \cos \lambda & -\sin \varphi \sin \lambda & \cos \varphi \sin \lambda \\ 0 & \cos \varphi & \sin \varphi \end{bmatrix} + \begin{bmatrix} \text{r} \cos \varphi \cos \lambda \\ \text{r} \cos \varphi \sin \lambda \\ \text{r} \sin \varphi \end{bmatrix} \]

See also
Parameters
lonDeg: The longitude in degree or angle $\lambda$ in previous equation.
latDeg: The latitude in degree or angle $\varphi$ in previous equation.
radius: The sphere radius $r$ in meter.
Returns
The homogeneous transformation from ENU to ECEF frame.
See also
ned2ecef(), getLocalTangentPlaneTransformations()
Examples
testMathUtils.cpp.

Definition at line 508 of file vpMath.cpp.

References rad().

◆ enu2ned()

vpHomogeneousMatrix vpMath::enu2ned ( const vpHomogeneousMatrix &  enu_M)
static

Convert from ENU (East-North-Up) to NED (North-East-Down) frame.

Parameters
enu_M: HomogeneousMatrix expressed in ENU frame.
Returns
Converted homogeneous matrix in NED frame.

Definition at line 675 of file vpMath.cpp.

◆ equal()

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, testIoEXR.cpp, testIoPFM.cpp, testIoTools.cpp, testKeyPoint-7.cpp, testMath.cpp, testMathUtils.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixInitialization.cpp, testMomentAlpha.cpp, testRowVector.cpp, testThread2.cpp, testTukeyEstimator.cpp, and testUniversalRobotsGetData.cpp.

Definition at line 371 of file vpMath.h.

References nul().

Referenced by vpMbDepthDenseTracker::display(), vpMbDepthNormalTracker::display(), vpMbEdgeKltTracker::display(), vpMbEdgeTracker::display(), vpMbKltTracker::display(), vpMbEdgeTracker::displayFeaturesOnImage(), vpHomogeneousMatrix::isAnHomogeneousMatrix(), vpCameraParameters::operator==(), vpColVector::operator==(), vpRowVector::operator==(), vpQbSoftHand::setPosition(), and vpMunkres::stepTwo().

◆ fact()

double vpMath::fact ( unsigned int  x)
inlinestatic

Computes and returns x!

Parameters
x: parameter of factorial function.

Definition at line 296 of file vpMath.h.

Referenced by comb().

◆ getLocalTangentPlaneTransformations()

std::vector< vpHomogeneousMatrix > vpMath::getLocalTangentPlaneTransformations ( const std::vector< std::pair< double, double > > &  lonlatVec,
double  radius,
vpHomogeneousMatrix(*)(double lonDeg, double latDeg, double radius)  toECEF 
)
static

Compute transformations from the local tangent plane (e.g. NED, ECU, ...) to the ECEF frame.

See also

Following image illustrates the camera poses sampled using longitude / latitude coordinates:

Parameters
lonlatVec: Vector of longitude/latitude coordinates in degree.
radius: Sphere radius in meter.
toECEF: Pointer to the function computing from a longitude / latitude coordinates in degree and a radius the corresponding transformation from the local frame (e.g. NED or ENU) to the ECEF frame.
Returns
The vector of ecef_M_local homogeneous transformations.
See also
enu2ecef(), ned2ecef()
Examples
testMathUtils.cpp.

Definition at line 585 of file vpMath.cpp.

◆ getMean()

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-T265-realsense.cpp, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-rgbd-structure-core.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, tutorial-mb-generic-tracker-rgbd-structure-core.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 276 of file vpMath.cpp.

References vpException::notInitialized.

Referenced by getStdev().

◆ getMedian()

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-T265-realsense.cpp, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-rgbd-structure-core.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, tutorial-mb-generic-tracker-rgbd-structure-core.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 296 of file vpMath.cpp.

References vpException::notInitialized.

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

◆ getStdev()

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-T265-realsense.cpp, tutorial-apriltag-detector-live-rgbd-realsense.cpp, tutorial-apriltag-detector-live-rgbd-structure-core.cpp, tutorial-apriltag-detector-live.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, tutorial-mb-generic-tracker-rgbd-structure-core.cpp, and tutorial-mb-generic-tracker-rgbd.cpp.

Definition at line 326 of file vpMath.cpp.

References getMean(), and vpException::notInitialized.

◆ greater()

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 380 of file vpMath.h.

◆ isFinite() [1/2]

bool vpMath::isFinite ( double  value)
static

Returns whether a double is a finite value (neither infinite nor NaN).

Parameters
value: Double number to check.
Returns
true if value is neither infinite nor NaN (as defined by IEEE754 standard) and false otherwise.
Examples
testMath.cpp.

Definition at line 175 of file vpMath.cpp.

References isInf(), and isNaN().

Referenced by vpImage< Type >::getMinMaxValue().

◆ isFinite() [2/2]

bool vpMath::isFinite ( float  value)
static

Returns whether a float is a finite value (neither infinite nor NaN).

Parameters
value: Float number to check.
Returns
true if value is neither infinite nor NaN (as defined by IEEE754 standard) and false otherwise.

Definition at line 194 of file vpMath.cpp.

References isInf(), and isNaN().

◆ isInf() [1/2]

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
true if value is a plus or minus infinity (as defined by IEEE754 standard) and false otherwise.
Examples
testMath.cpp.

Definition at line 134 of file vpMath.cpp.

Referenced by isFinite().

◆ isInf() [2/2]

bool vpMath::isInf ( float  value)
static

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

Parameters
value: Float number to check.
Returns
true if value is a plus or minus infinity (as defined by IEEE754 standard) and false otherwise.

Definition at line 155 of file vpMath.cpp.

◆ isNaN() [1/2]

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
true if value is Not A Number (as defined by IEEE754 standard) and false otherwise.
Examples
testMath.cpp, and tutorial-apriltag-detector-live-rgbd-structure-core.cpp.

Definition at line 90 of file vpMath.cpp.

Referenced by vpKeyPoint::compute3DForPointsOnCylinders(), vpMbtDistanceKltCylinder::computeInteractionMatrixAndResidu(), vpComedi::getPhyData(), vpMbtDistanceKltCylinder::init(), isFinite(), and vpHomogeneousMatrix::isValid().

◆ isNaN() [2/2]

bool vpMath::isNaN ( float  value)
static

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

Parameters
value: Float number to check.
Returns
true if value is Not A Number (as defined by IEEE754 standard) and false otherwise.

Definition at line 111 of file vpMath.cpp.

◆ lineFitting()

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 363 of file vpMath.cpp.

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

◆ linspace()

template<typename T >
static std::vector<double> vpMath::linspace ( T  start_in,
T  end_in,
unsigned int  num_in 
)
inlinestatic

Similar to the NumPy linspace function: "Return evenly spaced numbers over a specified interval." Code from: https://stackoverflow.com/a/27030598

Parameters
start_in: The starting value of the sequence.
end_in: The end value of the sequence.
num_in: Number of samples to generate.
Returns
Returns num_in evenly spaced samples, calculated over the interval [start_in, end_in].
Examples
testMathUtils.cpp.

Definition at line 252 of file vpMath.h.

◆ lookAt()

vpHomogeneousMatrix vpMath::lookAt ( const vpColVector &  from,
const vpColVector &  to,
vpColVector  tmp 
)
static

Compute the transformation such that the camera located at from position looks toward to position.

Right-handed coordinate system for OpenGL (figure from https://learnopengl.com/Getting-started/Coordinate-Systems):

See also:

Parameters
from: Current camera position as a 3-dim vector with 3D coordinates (X,Y,Z) in meter..
to: Where the camera must point toward as a 3-dim vector with 3D coordinates (X,Y,Z) in meter.
tmp: Arbitrary up-vector as a 3-dim vector with coordinates along (X,Y,Z) in meter.
Returns
The homogeneous transformation from the camera frame to the OpenGL frame.
Examples
testMathUtils.cpp.

Definition at line 620 of file vpMath.cpp.

References vpColVector::crossProd(), vpColVector::normalize(), and vpArray2D< Type >::size().

◆ maximum()

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 175 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(), vpWireFrameSimulator::getInternalCameraParameters(), vpWireFrameSimulator::getInternalImage(), vpRobotWireFrameSimulator::getInternalView(), vpMeNurbs::localReSample(), vpColVector::print(), vpForceTwistMatrix::print(), vpPoseVector::print(), vpRowVector::print(), vpVelocityTwistMatrix::print(), vpMatrix::print(), vpRansac< vpTransformation >::ransac(), vpDot2::searchDotsInArea(), vpMeNurbs::seekExtremitiesCanny(), and vpRobotBiclops::vpRobotBiclopsSpeedControlLoop().

◆ mcosc()

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 215 of file vpMath.cpp.

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

◆ minimum()

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 183 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().

◆ modulo()

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 416 of file vpMath.cpp.

◆ msinc()

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 231 of file vpMath.cpp.

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

◆ ned2ecef()

vpHomogeneousMatrix vpMath::ned2ecef ( double  lonDeg,
double  latDeg,
double  radius 
)
static

Compute from a given longitude, latitude and a sphere radius the homogeneous transformation from the NED frame to the ECEF frame:

\[ \begin{bmatrix} X_{\text{ecef}} \\ Y_{\text{ecef}} \\ Z_{\text{ecef}} \end{bmatrix} = \begin{bmatrix} -\sin \varphi \cos \lambda & -\sin \lambda & -\cos \varphi \cos \lambda \\ -\sin \varphi \sin \lambda & \cos \lambda & -\cos \varphi \sin \lambda \\ \cos \varphi & 0 & -\sin \varphi \end{bmatrix} + \begin{bmatrix} \text{r} \cos \varphi \cos \lambda \\ \text{r} \cos \varphi \sin \lambda \\ \text{r} \sin \varphi \end{bmatrix} \]

See also:

Parameters
lonDeg: The longitude in degree or angle $\lambda$ in previous equation.
latDeg: The latitude in degree or angle $\varphi$ in previous equation.
radius: The sphere radius $r$ in meter.
Returns
The homogeneous transformation from NED to ECEF frame.
See also
enu2ecef(), getLocalTangentPlaneTransformations()
Examples
testMathUtils.cpp.

Definition at line 456 of file vpMath.cpp.

References rad().

◆ nul()

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 362 of file vpMath.h.

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

◆ rad()

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, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyHartleyDLT2DObject.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, servoAfma6AprilTagIBVS.cpp, servoAfma6AprilTagPBVS.cpp, servoAfma6Cylinder2DCamVelocity.cpp, servoAfma6Cylinder2DCamVelocitySecondaryTask.cpp, servoAfma6FourPoints2DCamVelocityLs_cur.cpp, servoAfma6FourPoints2DCamVelocityLs_des.cpp, servoAfma6Line2DCamVelocity.cpp, servoAfma6SquareLines2DCamVelocity.cpp, servoAfma6TwoLines2DCamVelocity.cpp, servoBebop2.cpp, servoKinovaJacoJoint.cpp, servoMomentImage.cpp, servoMomentPoints.cpp, servoMomentPolygon.cpp, servoPixhawkDroneIBVS.cpp, servoSimu3D_cMcd_CamVelocity.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu3D_cdMc_CamVelocity.cpp, servoSimu3D_cdMc_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, servoUniversalRobotsIBVS.cpp, servoUniversalRobotsPBVS.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, testMath.cpp, testMatrix.cpp, testPixhawkDronePositionAbsoluteControl.cpp, testPixhawkDronePositionRelativeControl.cpp, testPixhawkRoverVelocityControl.cpp, testPose.cpp, testPoseFeatures.cpp, testPoseVector.cpp, testQuaternion2.cpp, testRobotBebop2.cpp, testRobotFlirPtu.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRotation2.cpp, testUniversalRobotsJointPosition.cpp, testUniversalRobotsJointVelocity.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-draw-frame.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 121 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpMbGenericTracker::computeProjectionError(), enu2ecef(), vpRobotViper650::get_eJe(), vpRobotViper850::get_eJe(), vpAfma6::getInverseKinematics(), vpViper::getInverseKinematicsWrist(), vpRobotKinova::getJointPosition(), vpRobotPioneer::getVelocity(), vpRobotUniversalRobots::init(), vpSimulatorViper850::init(), vpAfma6::init(), vpSimulatorAfma6::init(), vpViper650::init(), vpViper850::init(), vpSimulatorAfma6::initDisplay(), vpSimulatorViper850::initDisplay(), vpMbtPolygon::isVisible(), vpMeEllipse::leastSquareRobust(), vpMbTracker::loadCAOModel(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpMbEdgeKltTracker::loadConfigFile(), vpMbEdgeTracker::loadConfigFile(), vpMbKltTracker::loadConfigFile(), vpWireFrameSimulator::navigation(), ned2ecef(), vpMeEllipse::plugHoles(), vpRobotAfma4::readPosFile(), vpRobotAfma6::readPosFile(), vpRobotFranka::readPosFile(), vpRobotUniversalRobots::readPosFile(), vpSimulatorAfma6::readPosFile(), vpMbDepthDenseTracker::resetTracker(), vpMbDepthNormalTracker::resetTracker(), vpMbEdgeTracker::resetTracker(), vpMbGenericTracker::resetTracker(), vpMbKltTracker::resetTracker(), vpMeEllipse::sample(), vpMeEllipse::track(), vpRobotBiclops::vpRobotBiclopsSpeedControlLoop(), vpRobotMavsdk::vpRobotMavsdk(), vpSickLDMRS::vpSickLDMRS(), vpViper::vpViper(), vpViper650::vpViper650(), vpViper850::vpViper850(), and vpWireFrameSimulator::vpWireFrameSimulator().

◆ round()

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 325 of file vpMath.h.

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

◆ saturate() [1/37]

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

Definition at line 224 of file vpMath.h.

◆ saturate() [2/37]

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

Definition at line 405 of file vpMath.h.

◆ saturate() [3/37]

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

Definition at line 480 of file vpMath.h.

◆ saturate() [4/37]

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

Definition at line 230 of file vpMath.h.

◆ saturate() [5/37]

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

Definition at line 441 of file vpMath.h.

References round().

◆ saturate() [6/37]

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

Definition at line 473 of file vpMath.h.

References round().

◆ saturate() [7/37]

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

Definition at line 514 of file vpMath.h.

References round().

◆ saturate() [8/37]

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

Definition at line 535 of file vpMath.h.

References round().

◆ saturate() [9/37]

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

Definition at line 544 of file vpMath.h.

References round().

◆ saturate() [10/37]

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

Definition at line 551 of file vpMath.h.

References round().

◆ saturate() [11/37]

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

Definition at line 229 of file vpMath.h.

◆ saturate() [12/37]

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

Definition at line 435 of file vpMath.h.

References round().

◆ saturate() [13/37]

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

Definition at line 467 of file vpMath.h.

References round().

◆ saturate() [14/37]

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

Definition at line 508 of file vpMath.h.

References round().

◆ saturate() [15/37]

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

Definition at line 530 of file vpMath.h.

References round().

◆ saturate() [16/37]

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

Definition at line 542 of file vpMath.h.

References round().

◆ saturate() [17/37]

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

Definition at line 549 of file vpMath.h.

References round().

◆ saturate() [18/37]

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

Definition at line 228 of file vpMath.h.

◆ saturate() [19/37]

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

Definition at line 423 of file vpMath.h.

◆ saturate() [20/37]

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

Definition at line 455 of file vpMath.h.

◆ saturate() [21/37]

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

Definition at line 498 of file vpMath.h.

◆ saturate() [22/37]

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

Definition at line 522 of file vpMath.h.

◆ saturate() [23/37]

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

Definition at line 226 of file vpMath.h.

◆ saturate() [24/37]

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

Definition at line 428 of file vpMath.h.

◆ saturate() [25/37]

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

Definition at line 460 of file vpMath.h.

◆ saturate() [26/37]

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

Definition at line 493 of file vpMath.h.

◆ saturate() [27/37]

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

Definition at line 223 of file vpMath.h.

◆ saturate() [28/37]

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

Definition at line 448 of file vpMath.h.

◆ saturate() [29/37]

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

Definition at line 430 of file vpMath.h.

◆ saturate() [30/37]

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

Definition at line 462 of file vpMath.h.

◆ saturate() [31/37]

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

Definition at line 503 of file vpMath.h.

◆ saturate() [32/37]

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

Definition at line 526 of file vpMath.h.

◆ saturate() [33/37]

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

Definition at line 225 of file vpMath.h.

◆ saturate() [34/37]

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

Definition at line 418 of file vpMath.h.

◆ saturate() [35/37]

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

Definition at line 450 of file vpMath.h.

◆ saturate() [36/37]

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

Definition at line 521 of file vpMath.h.

◆ saturate() [37/37]

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

Definition at line 227 of file vpMath.h.

◆ sigmoid()

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 393 of file vpMath.h.

◆ sign()

int vpMath::sign ( double  x)
inlinestatic

Return the sign of x.

Parameters
x: Value to test.
Returns
-1 if x is negative, +1 if positive and 0 if zero.

Definition at line 344 of file vpMath.h.

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

◆ sinc() [1/2]

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 261 of file vpMath.cpp.

◆ sinc() [2/2]

double vpMath::sinc ( double  x)
static

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

Parameters
x: Value of x.
Returns
Sinus cardinal.

Definition at line 246 of file vpMath.cpp.

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

◆ sqr()

static double vpMath::sqr ( double  x)
inlinestatic

Compute x square value.

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

Definition at line 127 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpMbtDistanceCircle::computeInteractionMatrixError(), vpCircle::computeIntersectionPoint(), vpPose::computeResidual(), vpPose::computeResidualDementhon(), vpCalibration::computeStdDeviation(), vpCalibration::computeStdDeviation_dist(), vpMbDepthDenseTracker::computeVVS(), vpMbDepthNormalTracker::computeVVS(), vpMbEdgeTracker::computeVVS(), vpMbEdgeKltTracker::computeVVS(), vpMbGenericTracker::computeVVS(), vpMbEdgeTracker::computeVVSInit(), vpMeterPixelConversion::convertEllipse(), vpMeterPixelConversion::convertLine(), vpPixelMeterConversion::convertLine(), vpPose::coplanar(), vpFeatureBuilder::create(), vpDot2::defineDots(), vpDisplayGTK::displayArrow(), vpDisplayOpenCV::displayArrow(), vpDisplayX::displayArrow(), vpDisplayOpenCV::displayDotLine(), vpCalibration::displayGrid(), vpImagePoint::distance(), vpMeSite::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(), vpPose::poseVirtualVSrobust(), vpPose::poseVirtualVSWithDepth(), vpColorDepthConversion::projectColorToDepth(), vpCircle::projection(), vpSphere::projection(), vpNurbs::removeCurveKnot(), vpMeLine::reSample(), vpMeLine::sample(), vpMeNurbs::sample(), vpMeLine::seekExtremities(), vpMeNurbs::seekExtremitiesCanny(), vpImagePoint::sqrDistance(), vpMeSite::sqrDistance(), vpMeNurbs::supressNearPoints(), vpMeSite::track(), and vpImageTools::undistort().

◆ swap()

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 207 of file vpMath.h.