Visual Servoing Platform  version 3.2.0
vpMath Class Reference

#include <vpMath.h>

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)
 
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)

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

Definition at line 85 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

Definition at line 151 of file vpMath.h.

◆ 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 219 of file vpMath.h.

◆ deg()

◆ equal()

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

◆ fact()

double vpMath::fact ( unsigned int  x)
inlinestatic

Computes and returns x!

Parameters
x: parameter of factorial function.

Definition at line 204 of file vpMath.h.

◆ getMean()

◆ getMedian()

◆ getStdev()

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

Definition at line 251 of file vpMath.cpp.

◆ 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 298 of file vpMath.h.

◆ isInf()

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 109 of file vpMath.cpp.

◆ isNaN()

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 83 of file vpMath.cpp.

◆ maximum()

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

◆ 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 134 of file vpMath.cpp.

◆ minimum()

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

◆ modulo()

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 280 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 152 of file vpMath.cpp.

◆ 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 280 of file vpMath.h.

◆ 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, 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 101 of file vpMath.h.

Referenced by vpMbTracker::addPolygon(), vpMbTracker::addProjectionErrorPolygon(), vpMbEdgeMultiTracker::computeProjectionError(), vpMbGenericTracker::computeProjectionError(), vpSimulatorAfma6::init(), vpSimulatorAfma6::initDisplay(), vpMbDepthDenseTracker::loadConfigFile(), vpMbDepthNormalTracker::loadConfigFile(), vpWireFrameSimulator::navigation(), vpSimulatorAfma6::readPosFile(), vpMbDepthDenseTracker::resetTracker(), vpMbDepthNormalTracker::resetTracker(), vpMbEdgeKltTracker::vpMbEdgeKltTracker(), vpMbKltTracker::vpMbKltTracker(), and vpWireFrameSimulator::vpWireFrameSimulator().

◆ round()

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 234 of file vpMath.h.

Referenced by vpMeSite::convolution(), vpMeSite::getSign(), vpMeSite::init(), vpMeTracker::outOfImage(), saturate(), and vpMeSite::vpMeSite().

◆ saturate() [1/37]

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

Definition at line 179 of file vpMath.h.

◆ saturate() [2/37]

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

Definition at line 321 of file vpMath.h.

◆ saturate() [3/37]

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

Definition at line 396 of file vpMath.h.

◆ saturate() [4/37]

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

Definition at line 185 of file vpMath.h.

◆ saturate() [5/37]

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

Definition at line 357 of file vpMath.h.

References round().

◆ saturate() [6/37]

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

Definition at line 389 of file vpMath.h.

References round().

◆ saturate() [7/37]

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

Definition at line 430 of file vpMath.h.

References round().

◆ saturate() [8/37]

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

Definition at line 451 of file vpMath.h.

◆ saturate() [9/37]

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

Definition at line 460 of file vpMath.h.

References round().

◆ saturate() [10/37]

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

Definition at line 467 of file vpMath.h.

References round().

◆ saturate() [11/37]

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

Definition at line 184 of file vpMath.h.

◆ saturate() [12/37]

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

Definition at line 351 of file vpMath.h.

References round().

◆ saturate() [13/37]

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

Definition at line 383 of file vpMath.h.

References round().

◆ saturate() [14/37]

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

Definition at line 424 of file vpMath.h.

References round().

◆ saturate() [15/37]

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

Definition at line 446 of file vpMath.h.

◆ saturate() [16/37]

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

Definition at line 458 of file vpMath.h.

References round().

◆ saturate() [17/37]

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

Definition at line 465 of file vpMath.h.

References round().

◆ saturate() [18/37]

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

Definition at line 183 of file vpMath.h.

◆ saturate() [19/37]

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

Definition at line 339 of file vpMath.h.

◆ saturate() [20/37]

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

Definition at line 371 of file vpMath.h.

◆ saturate() [21/37]

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

Definition at line 414 of file vpMath.h.

◆ saturate() [22/37]

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

Definition at line 438 of file vpMath.h.

◆ saturate() [23/37]

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

Definition at line 181 of file vpMath.h.

◆ saturate() [24/37]

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

Definition at line 344 of file vpMath.h.

◆ saturate() [25/37]

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

Definition at line 376 of file vpMath.h.

◆ saturate() [26/37]

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

Definition at line 409 of file vpMath.h.

◆ saturate() [27/37]

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

Definition at line 178 of file vpMath.h.

◆ saturate() [28/37]

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

Definition at line 364 of file vpMath.h.

◆ saturate() [29/37]

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

Definition at line 346 of file vpMath.h.

◆ saturate() [30/37]

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

Definition at line 378 of file vpMath.h.

◆ saturate() [31/37]

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

Definition at line 419 of file vpMath.h.

◆ saturate() [32/37]

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

Definition at line 442 of file vpMath.h.

◆ saturate() [33/37]

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

Definition at line 180 of file vpMath.h.

◆ saturate() [34/37]

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

Definition at line 334 of file vpMath.h.

◆ saturate() [35/37]

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

Definition at line 366 of file vpMath.h.

◆ saturate() [36/37]

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

Definition at line 437 of file vpMath.h.

◆ saturate() [37/37]

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

Definition at line 182 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 309 of file vpMath.h.

◆ sign()

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 261 of file vpMath.h.

Referenced by vpMbEdgeTracker::computeVVSFirstPhase().

◆ 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 186 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 169 of file vpMath.cpp.

◆ sqr()

◆ 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 168 of file vpMath.h.