FixPoint of a separator The fixpoint of a separator is computed by calling the "::"separate function on a given box until the Hausdorff distance between two iterations is less than a given ratio. This operation can be seen as a contractor on the boundary of the solution set. More...

Classes
class	ContractorNetwork
	Graph of contractors and domains that model a problem in the constraint programming framework. Heterogeneous domains can be handled in the same network, which allows to deal with a wide variety of problems such as non-linear equations, differential systems, delays or inter-temporal equations. More...

class	IntervalVar
	todo More...

class	IntervalVectorVar
	todo More...

class	CtcDelay
	\(\mathcal{C}_{delay}\) that contracts the tubes \([x](\cdot)\) and \([y](\cdot)\) with respect to their delay \([\tau]\) according to the delay constraint \(\mathbf{x}(t)=\mathbf{y}(t+\tau)\) More...

class	CtcDeriv
	\(\mathcal{C}_{\frac{d}{dt}}\) that contracts a tube \([x](\cdot)\) with respect to its derivative tube \([v](\cdot)\) according to the constraint \(\dot{x}(\cdot)=v(\cdot)\) More...

class	CtcEval
	\(\mathcal{C}_\textrm{eval}\) that contracts a tube \([y](\cdot)\) with respect to its derivative tube \([w](\cdot)\) and a measurement \([t]\times[z]\) according to the constraints \(z=y(t)\) and \(\dot{y}(\cdot)=w(\cdot)\) More...

class	CtcLohner
	\(\mathcal{C}_\textrm{lohner}\) that contracts a tube \([\mathbf{x}](\cdot)\) according to a differential constraint \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\) More...

class	CtcPicard
	CtcPicard class. More...

class	CtcStatic
	Generic static \(\mathcal{C}\) that contracts a tube \([\mathbf{x}](\cdot)\) with some IBEX contractor (for boxes, possibly including time). The contractor will be applied on each slice and gate. More...

class	DynCtc
	Contractor interface. More...

class	CtcBox
	Contractor around a box. More...

class	CtcCartProd
	Cartesian product of contractors \(\mathcal{C}_1\times\dots\times\mathcal{C}_n\). More...

class	CtcCN
	static contractor on a contractor network object More...

class	CtcDist
	Distance constraint between two 2d vectors. More...

class	CtcFunction
	Generic static \(\mathcal{C}\) that contracts a box \([\mathbf{x}]\) or a tube \([\mathbf{x}](\cdot)\) according to the constraint \(\mathbf{f}(\mathbf{x})=\mathbf{0}\) or \(\mathbf{f}(\mathbf{x})\in[\mathbf{y}]\). It stands on the CtcFwdBwd of IBEX (HC4Revise). More...

class	CtcPolar
	Minimal contractor for the polar constraint: x = rhocos(theta) y = rhosin(theta) theta = angle(x,y) sqr(rho) = sqr(x)+sqr(y) More...

class	CtcSegment
	Minimal contractor for a segment. More...

class	Slice
	Slice \(\llbracket x\rrbracket(\cdot)\) of a one dimensional tube and made of an envelope and two gates. More...

class	DynamicalItem
	Abstract class for common properties of Tube, TubeVector, Slice, Trajectory, TrajectoryVector objects. More...

class	Tube
	One dimensional tube \([x](\cdot)\), defined as an interval of scalar trajectories. More...

class	TubeVector
	n-dimensional tube \([\mathbf{x}](\cdot)\), defined as an interval of n-dimensional trajectories More...

class	DomainsSizeException
	Exception raised if the size (dimension) of domains are not consistent together, and with the contractor definition. More...

class	DomainsTypeException
	Exception raised if the domains connected to a contractor in a CN are not consistent with the contractor definition. More...

class	Exception
	Root class of all exceptions raised by Codac. More...

class	PdcInPolygon
	Tests if a box is inside a polygon. More...

class	SepPolarXY
	Separator for point in sector. A sector is defined by its center, a distance and an angle (with uncertainty). More...

class	SepPolygon
	Separator for Point inside a polygon. More...

class	ColorMap
	Associates colors to a range of values. More...

struct	rgb
	Represents an RGB value. More...

struct	hsv
	Represents an HSV value. More...

class	Figure
	Two-dimensional graphical item. More...

class	VIBesFig
	Two-dimensional graphical item based on the VIBes viewer. More...

class	VIBesFigPaving
	Two-dimensional graphical item to display a Paving object. More...

class	VIBesFigTube
	Two-dimensional graphical item to display scalar tubes or trajectories. More...

class	VIBesFigTubeVector
	Multi-view item to display vector tubes or trajectories. More...

class	ConnectedSubset
	Multi-dimensional paving representation of a connected subset. More...

class	Paving
	Multi-dimensional paving as representation of a set. More...

class	Set
	Multi-dimensional interval-based representation of a set. More...

class	SIVIAPaving
	Paving resulting from a Set-Inversion Via Interval Analysis. More...

class	TubePaving
	Multi-dimensional paving as projection of a vector tube. More...

class	CtcTransform
	Transformation of a separator with an inversible transformation T(S)(X) = { ffwdSinfbwd(X), ffwdSoutfbwd(X)} Using a function and its inverse is less pessimism than using a forward / backward propagation (see: sepInverse) More...

class	CtcQInterProjF
	Q-intersection contractor. More...

class	SepBox
	Separator \(\mathcal{S}_{box}\) that separates two boxes according to the constraint \(\mathbf{x}\in[\mathbf{b}]\). More...

class	CtcFromSep
	Build a contractor with a separator Wrt the. More...

class	SepCtcPairProj
	projection of a separator using ibexlib algorithm More...

class	SepFixPoint
	Fix point of a Separator. More...

class	SepFunction
	Generic static \(\mathcal{S}\) that separates two boxes according to the constraint \(\mathbf{f}(\mathbf{x})=\mathbf{0}\) or \(\mathbf{f}(\mathbf{x})\in[\mathbf{y}]\). It stands on the SepFwdBwd of IBEX (involving HC4Revise). More...

class	SepProj
	Projection of a separator. More...

class	SepTransform
	Image of a separator by a function \(f\) where an analytic expression of \(\mathbf{f}^{-1}\) is avaiable. the computation is less pessimism than using a classical a forward / backward propagation (. More...

class	Tools
	Basic features provided here in order to avoid overkill dependencies. More...

class	RandTrajectory
	One dimensional random trajectory \(x(\cdot)\), used to represent noises. More...

class	Trajectory
	One dimensional trajectory \(x(\cdot)\), defined as a temporal map of values. More...

class	TrajectoryVector
	n-dimensional trajectory \(\mathbf{x}(\cdot)\), defined as a temporal map of vector values More...

class	CtcConstell
	CtcConstell class. More...

class	VIBesFigMap
	Two-dimensional graphical item to project dynamical items (tubes, trajectories, etc.) on a map. More...

class	TPlane
	Temporal representation of loops. More...

Enumerations
enum class	TimePropag { FORWARD = 0x01 , BACKWARD = 0x02 }
	Specifies the temporal propagation way (forward or backward in time) More...

enum class	InterpolMode
	Defines in which color space (HSV, RGB) the color interpolation will be made.

enum class	TubeColorType
	Defines a set of colors for tube display.

enum class	SetValue { DEFAULT = 0x00 , UNKNOWN = 0x01 , OUT = 0x02 , IN = 0x04 , PENUMBRA = 0x08 }
	Defines a set of feasible values of a set. More...

Functions
TubeVector	CAPD_integrateODE (const Interval &tdomain, const Function &f, const IntervalVector &x0, double tube_dt=0., int capd_order=20, double capd_dt=0.)
	Integrates the autonomous ODE \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\) using CAPD. More...

TubeVector	CAPD_integrateODE (const Interval &tdomain, const TFunction &f, const IntervalVector &x0, double tube_dt=0., int capd_order=20, double capd_dt=0.)
	Integrates the non-autonomous ODE \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x},t)\) using CAPD. More...

const IntervalMatrix	operator\| (const IntervalMatrix &x, const IntervalMatrix &y)
	\([\mathbf{X}]\sqcup[\mathbf{Y}]\) More...

const IntervalMatrix	operator& (const IntervalMatrix &x, const IntervalMatrix &y)
	\([\mathbf{X}]\cap[\mathbf{Y}]\) More...

int	operator& (TimePropag a, TimePropag b)
	Allows tests on combinations of propagation ways. More...

TimePropag	operator\| (TimePropag a, TimePropag b)
	Allows a combination of propagation ways. More...

CtcCartProd	cart_prod (Ctc &c1, Ctc &c2)
	Cartesian product of contractors from two Ctc objects. More...

CtcCartProd	cart_prod (const ibex::Array< Ctc > &array)
	Cartesian product of contractors from an ibex::Array. More...

const std::string	rgb2hex (rgb rgb_value, const char *prefix="#")
	Represents an RGB value in a HTML standard. More...

rgb	hsv2rgb (hsv hsv_value)
	Converts HSV to RGB. More...

hsv	rgb2hsv (rgb rgb_value)
	Converts RGB to HSV. More...

rgb	make_rgb (int r, int g, int b, int alpha=255)
	Makes an RGV value from integers. More...

rgb	make_rgb (float r, float g, float b, float alpha=1.)
	Makes an RGV value from floats. More...

hsv	make_hsv (int h, int s, int v, int alpha=100)
	Makes an HSV value from integers. More...

hsv	make_hsv (float h, float s, float v, float alpha=1.)
	Makes an HSV value from floats. More...

int	operator& (SetValue a, SetValue b)
	Allows tests on combinations of two SetValue. More...

SetValue	operator\| (SetValue a, SetValue b)
	Union of two SetValue values. More...

Scalar outputs
const Trajectory	cos (const Trajectory &x)
	\(\cos(x(\cdot))\) More...

const Trajectory	sin (const Trajectory &x)
	\(\sin(x(\cdot))\) More...

const Trajectory	abs (const Trajectory &x)
	\(\mid x(\cdot)\mid\) More...

const Trajectory	sqr (const Trajectory &x)
	\(x^2(\cdot)\) More...

const Trajectory	sqrt (const Trajectory &x)
	\(\sqrt{x(\cdot)}\) More...

const Trajectory	exp (const Trajectory &x)
	\(\exp(x(\cdot))\) More...

const Trajectory	log (const Trajectory &x)
	\(\log(x(\cdot))\) More...

const Trajectory	tan (const Trajectory &x)
	\(\tan(x(\cdot))\) More...

const Trajectory	acos (const Trajectory &x)
	\(\arccos(x(\cdot))\) More...

const Trajectory	asin (const Trajectory &x)
	\(\arcsin(x(\cdot))\) More...

const Trajectory	atan (const Trajectory &x)
	\(\arctan(x(\cdot))\) More...

const Trajectory	cosh (const Trajectory &x)
	\(\cosh(x(\cdot))\) More...

const Trajectory	sinh (const Trajectory &x)
	\(\sinh(x(\cdot))\) More...

const Trajectory	tanh (const Trajectory &x)
	\(\tanh(x(\cdot))\) More...

const Trajectory	acosh (const Trajectory &x)
	\(\mathrm{arccosh}(x(\cdot))\) More...

const Trajectory	asinh (const Trajectory &x)
	\(\mathrm{arcsinh}(x(\cdot))\) More...

const Trajectory	atanh (const Trajectory &x)
	\(\mathrm{arctanh}(x(\cdot))\) More...

const Trajectory	atan2 (const Trajectory &y, const Trajectory &x)
	\(\mathrm{arctan2}(y(\cdot),x(\cdot))\) More...

const Trajectory	atan2 (const Trajectory &y, double x)
	\(\mathrm{arctan2}(y(\cdot),x)\) More...

const Trajectory	atan2 (double y, const Trajectory &x)
	\(\mathrm{arctan2}(y, x(\cdot))\) More...

const Trajectory	min (const Trajectory &y, const Trajectory &x)
	\(\min(y(\cdot),x(\cdot))\) More...

const Trajectory	min (const Trajectory &y, double x)
	\(\min(y(\cdot),x)\) More...

const Trajectory	min (double y, const Trajectory &x)
	\(\min(y, x(\cdot))\) More...

const Trajectory	max (const Trajectory &y, const Trajectory &x)
	\(\max(y(\cdot),x(\cdot))\) More...

const Trajectory	max (const Trajectory &y, double x)
	\(\max(y(\cdot),x)\) More...

const Trajectory	max (double y, const Trajectory &x)
	\(\max(y, x(\cdot))\) More...

const Trajectory	pow (const Trajectory &x, int p)
	\(x^p(\cdot)\) More...

const Trajectory	pow (const Trajectory &x, double p)
	\(x^p(\cdot)\) More...

const Trajectory	root (const Trajectory &x, int p)
	\(\sqrt[p]{x(\cdot)}\) More...

const Trajectory	operator+ (const Trajectory &x)
	\(x(\cdot)\) More...

const Trajectory	operator+ (const Trajectory &x, const Trajectory &y)
	\(x(\cdot)+y(\cdot)\) More...

const Trajectory	operator+ (const Trajectory &x, double y)
	\(x(\cdot)+y\) More...

const Trajectory	operator+ (double x, const Trajectory &y)
	\(x+y(\cdot)\) More...

const Trajectory	operator- (const Trajectory &x)
	\(-x(\cdot)\) More...

const Trajectory	operator- (const Trajectory &x, const Trajectory &y)
	\(x(\cdot)-y(\cdot)\) More...

const Trajectory	operator- (const Trajectory &x, double y)
	\(x(\cdot)-y\) More...

const Trajectory	operator- (double x, const Trajectory &y)
	\(x-y(\cdot)\) More...

const Trajectory	operator* (const Trajectory &x, const Trajectory &y)
	\(x(\cdot)\cdot y(\cdot)\) More...

const Trajectory	operator* (const Trajectory &x, double y)
	\(x(\cdot)\cdot y\) More...

const Trajectory	operator* (double x, const Trajectory &y)
	\(x\cdot y(\cdot)\) More...

const Trajectory	operator/ (const Trajectory &x, const Trajectory &y)
	\(x(\cdot)/y(\cdot)\) More...

const Trajectory	operator/ (const Trajectory &x, double y)
	\(x(\cdot)/y\) More...

const Trajectory	operator/ (double x, const Trajectory &y)
	\(x/y(\cdot)\) More...

const Tube	cos (const Tube &x)
	\(\cos([x](\cdot))\) More...

const Tube	sin (const Tube &x)
	\(\sin([x](\cdot))\) More...

const Tube	abs (const Tube &x)
	\(\mid[x](\cdot)\mid\) More...

const Tube	sqr (const Tube &x)
	\([x]^2(\cdot)\) More...

const Tube	sqrt (const Tube &x)
	\(\sqrt{[x](\cdot)}\) More...

const Tube	exp (const Tube &x)
	\(\exp([x](\cdot))\) More...

const Tube	log (const Tube &x)
	\(\log([x](\cdot))\) More...

const Tube	tan (const Tube &x)
	\(\tan([x](\cdot))\) More...

const Tube	acos (const Tube &x)
	\(\arccos([x](\cdot))\) More...

const Tube	asin (const Tube &x)
	\(\arcsin([x](\cdot))\) More...

const Tube	atan (const Tube &x)
	\(\arctan([x](\cdot))\) More...

const Tube	cosh (const Tube &x)
	\(\cosh([x](\cdot))\) More...

const Tube	sinh (const Tube &x)
	\(\sinh([x](\cdot))\) More...

const Tube	tanh (const Tube &x)
	\(\tanh([x](\cdot))\) More...

const Tube	acosh (const Tube &x)
	\(\mathrm{arccosh}([x](\cdot))\) More...

const Tube	asinh (const Tube &x)
	\(\mathrm{arcsinh}([x](\cdot))\) More...

const Tube	atanh (const Tube &x)
	\(\mathrm{arctanh}([x](\cdot))\) More...

const Tube	atan2 (const Tube &y, const Tube &x)
	\(\mathrm{arctan2}([y](\cdot),[x](\cdot))\) More...

const Tube	atan2 (const Tube &y, const Interval &x)
	\(\mathrm{arctan2}([y](\cdot),[x])\) More...

const Tube	atan2 (const Interval &y, const Tube &x)
	\(\mathrm{arctan2}([y],[x](\cdot))\) More...

const Tube	pow (const Tube &x, int p)
	\([x]^p(\cdot)\) More...

const Tube	pow (const Tube &x, double p)
	\([x]^p(\cdot)\) More...

const Tube	pow (const Tube &x, const Interval &p)
	\([x]^{[p]}(\cdot)\) More...

const Tube	root (const Tube &x, int p)
	\(\sqrt[p]{[x](\cdot)}\) More...

const Tube	min (const Tube &y, const Tube &x)
	\(\min([y](\cdot),[x](\cdot))\) More...

const Tube	min (const Tube &y, const Interval &x)
	\(\min([y](\cdot),[x])\) More...

const Tube	min (const Interval &y, const Tube &x)
	\(\min([y],[x](\cdot))\) More...

const Tube	max (const Tube &y, const Tube &x)
	\(\max([y](\cdot),[x](\cdot))\) More...

const Tube	max (const Tube &y, const Interval &x)
	\(\max([y](\cdot),[x])\) More...

const Tube	max (const Interval &y, const Tube &x)
	\(\max([y],[x](\cdot))\) More...

const Tube	operator+ (const Tube &x)
	\([x](\cdot)\) More...

const Tube	operator+ (const Tube &x, const Tube &y)
	\([x](\cdot)+[y](\cdot)\) More...

const Tube	operator+ (const Tube &x, const Interval &y)
	\([x](\cdot)+[y]\) More...

const Tube	operator+ (const Interval &x, const Tube &y)
	\([x]+[y](\cdot)\) More...

const Tube	operator+ (const Tube &x, const Trajectory &y)
	\([x](\cdot)+y(\cdot)\) More...

const Tube	operator+ (const Trajectory &x, const Tube &y)
	\(x(\cdot)+[y](\cdot)\) More...

const Tube	operator- (const Tube &x)
	\(-[x](\cdot)\) More...

const Tube	operator- (const Tube &x, const Tube &y)
	\([x](\cdot)-[y](\cdot)\) More...

const Tube	operator- (const Tube &x, const Interval &y)
	\([x](\cdot)-[y]\) More...

const Tube	operator- (const Interval &x, const Tube &y)
	\([x]-[y](\cdot)\) More...

const Tube	operator- (const Tube &x, const Trajectory &y)
	\([x](\cdot)-y(\cdot)\) More...

const Tube	operator- (const Trajectory &x, const Tube &y)
	\(x(\cdot)-[y](\cdot)\) More...

const Tube	operator* (const Tube &x, const Tube &y)
	\([x](\cdot)\cdot[y](\cdot)\) More...

const Tube	operator* (const Tube &x, const Interval &y)
	\([x](\cdot)\cdot[y]\) More...

const Tube	operator* (const Interval &x, const Tube &y)
	\([x]\cdot[y](\cdot)\) More...

const Tube	operator* (const Tube &x, const Trajectory &y)
	\([x](\cdot)\cdot y(\cdot)\) More...

const Tube	operator* (const Trajectory &x, const Tube &y)
	\(x(\cdot)\cdot[y](\cdot)\) More...

const Tube	operator/ (const Tube &x, const Tube &y)
	\([x](\cdot)/[y](\cdot)\) More...

const Tube	operator/ (const Tube &x, const Interval &y)
	\([x](\cdot)/[y]\) More...

const Tube	operator/ (const Interval &x, const Tube &y)
	\([x]/[y](\cdot)\) More...

const Tube	operator/ (const Tube &x, const Trajectory &y)
	\([x](\cdot)/y(\cdot)\) More...

const Tube	operator/ (const Trajectory &x, const Tube &y)
	\(x(\cdot)/[y](\cdot)\) More...

const Tube	operator\| (const Tube &x, const Tube &y)
	\([x](\cdot)\sqcup[y](\cdot)\) More...

const Tube	operator\| (const Tube &x, const Interval &y)
	\([x](\cdot)\sqcup[y]\) More...

const Tube	operator\| (const Interval &x, const Tube &y)
	\([x]\sqcup[y](\cdot)\) More...

const Tube	operator\| (const Tube &x, const Trajectory &y)
	\([x](\cdot)\sqcup y(\cdot)\) More...

const Tube	operator\| (const Trajectory &x, const Tube &y)
	\(x(\cdot)\sqcup [y](\cdot)\) More...

const Tube	operator& (const Tube &x, const Tube &y)
	\([x](\cdot)\cap[y](\cdot)\) More...

const Tube	operator& (const Tube &x, const Interval &y)
	\([x](\cdot)\cap[y]\) More...

const Tube	operator& (const Interval &x, const Tube &y)
	\([x]\cap[y](\cdot)\) More...

const Tube	operator& (const Tube &x, const Trajectory &y)
	\([x](\cdot)\cap y(\cdot)\) More...

const Tube	operator& (const Trajectory &x, const Tube &y)
	\(x(\cdot)\cap [y](\cdot)\) More...

Vector outputs
const TrajectoryVector	operator+ (const TrajectoryVector &x)
	\(\mathbf{x}(\cdot)\) More...

const TrajectoryVector	operator+ (const TrajectoryVector &x, const TrajectoryVector &y)
	\(\mathbf{x}(\cdot)+\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator+ (const TrajectoryVector &x, const Vector &y)
	\(\mathbf{x}(\cdot)+\mathbf{y}\) More...

const TrajectoryVector	operator+ (const Vector &x, const TrajectoryVector &y)
	\(\mathbf{x}+\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator- (const TrajectoryVector &x)
	\(-\mathbf{x}(\cdot)\) More...

const TrajectoryVector	operator- (const TrajectoryVector &x, const TrajectoryVector &y)
	\(\mathbf{x}(\cdot)-\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator- (const TrajectoryVector &x, const Vector &y)
	\(\mathbf{x}(\cdot)-\mathbf{y}\) More...

const TrajectoryVector	operator- (const Vector &x, const TrajectoryVector &y)
	\(\mathbf{x}-\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator* (double x, const TrajectoryVector &y)
	\(x\cdot\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator* (const Trajectory &x, const TrajectoryVector &y)
	\(x(\cdot)\cdot\mathbf{y}(\cdot)\) More...

const TrajectoryVector	operator* (const Trajectory &x, const Vector &y)
	\(x(\cdot)\cdot\mathbf{y}\) More...

const TrajectoryVector	operator* (const Matrix &x, const TrajectoryVector &y)
	\(x(\cdot)\cdot\mathbf{y}\) More...

const TrajectoryVector	operator/ (const TrajectoryVector &x, double y)
	\(\mathbf{x}(\cdot)/y\) More...

const TrajectoryVector	operator/ (const TrajectoryVector &x, const Trajectory &y)
	\(\mathbf{x}(\cdot)/y(\cdot)\) More...

const TrajectoryVector	operator/ (const Vector &x, const Trajectory &y)
	\(\mathbf{x}/y(\cdot)\) More...

const Vector	vecto_product (const Vector &x, const Vector &y)
	\(\mathbf{x}\times\mathbf{y}\) (or \(\mathbf{x}\wedge\mathbf{y}\) in physics) More...

const TrajectoryVector	vecto_product (const TrajectoryVector &x, const Vector &y)
	\(\mathbf{x}(\cdot)\times\mathbf{y}\) (or \(\mathbf{x}(\cdot)\wedge\mathbf{y}\) in physics) More...

const TrajectoryVector	vecto_product (const Vector &x, const TrajectoryVector &y)
	\(\mathbf{x}\times\mathbf{y}(\cdot)\) (or \(\mathbf{x}\wedge\mathbf{y}(\cdot)\) in physics) More...

const TrajectoryVector	abs (const TrajectoryVector &x)
	\(\mid\mathbf{x}(\cdot)\mid\) More...

const TubeVector	operator+ (const TubeVector &x)
	\([\mathbf{x}](\cdot)\) More...

const TubeVector	operator+ (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)+[\mathbf{y}](\cdot)\) More...

const TubeVector	operator+ (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)+[\mathbf{y}]\) More...

const TubeVector	operator+ (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]+[\mathbf{y}](\cdot)\) More...

const TubeVector	operator+ (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)+\mathbf{y}(\cdot)\) More...

const TubeVector	operator+ (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)+[\mathbf{y}](\cdot)\) More...

const TubeVector	operator- (const TubeVector &x)
	\(-[\mathbf{x}](\cdot)\) More...

const TubeVector	operator- (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)-[\mathbf{y}](\cdot)\) More...

const TubeVector	operator- (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)-[\mathbf{y}]\) More...

const TubeVector	operator- (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]-[\mathbf{y}](\cdot)\) More...

const TubeVector	operator- (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)-\mathbf{y}(\cdot)\) More...

const TubeVector	operator- (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)-[\mathbf{y}](\cdot)\) More...

const TubeVector	operator* (const Tube &x, const TubeVector &y)
	\([x](\cdot)\cdot[\mathbf{y}](\cdot)\) More...

const TubeVector	operator* (const Interval &x, const TubeVector &y)
	\([x]\cdot[\mathbf{y}](\cdot)\) More...

const TubeVector	operator* (const Tube &x, const IntervalVector &y)
	\([x](\cdot)\cdot[\mathbf{y}]\) More...

const TubeVector	operator* (const Trajectory &x, const TubeVector &y)
	\(x(\cdot)\cdot[\mathbf{y}](\cdot)\) More...

const TubeVector	operator/ (const TubeVector &x, const Tube &y)
	\([\mathbf{x}](\cdot)/[y](\cdot)\) More...

const TubeVector	operator/ (const TubeVector &x, const Interval &y)
	\([\mathbf{x}](\cdot)/[y]\) More...

const TubeVector	operator/ (const IntervalVector &x, const Tube &y)
	\([\mathbf{x}]/[y](\cdot)\) More...

const TubeVector	operator/ (const TubeVector &x, const Trajectory &y)
	\([\mathbf{x}](\cdot)/y(\cdot)\) More...

const TubeVector	operator\| (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}](\cdot)\) More...

const TubeVector	operator\| (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}]\) More...

const TubeVector	operator\| (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]\sqcup[\mathbf{y}](\cdot)\) More...

const TubeVector	operator\| (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)\sqcup\mathbf{y}(\cdot)\) More...

const TubeVector	operator\| (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)\sqcup[\mathbf{y}](\cdot)\) More...

const TubeVector	operator& (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)\cap[\mathbf{y}](\cdot)\) More...

const TubeVector	operator& (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)\cap[\mathbf{y}]\) More...

const TubeVector	operator& (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]\cap[\mathbf{y}](\cdot)\) More...

const TubeVector	operator& (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)\cap\mathbf{y}(\cdot)\) More...

const TubeVector	operator& (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)\cap[\mathbf{y}](\cdot)\) More...

const TubeVector	abs (const TubeVector &x)
	\(\mid\mathbf{x}(\cdot)\mid\) More...

Interval
void	serialize_Interval (std::ofstream &bin_file, const Interval &intv)
	Writes an Interval object into a binary file. More...

void	deserialize_Interval (std::ifstream &bin_file, Interval &intv)
	Creates an Interval object from a binary file. More...

IntervalVector
void	deserialize_IntervalVector (std::ifstream &bin_file, IntervalVector &box)
	Writes an IntervalVector object into a binary file. More...

void	serialize_IntervalVector (std::ofstream &bin_file, const IntervalVector &box)
	Creates an IntervalVector object from a binary file. More...

Trajectory
void	serialize_Trajectory (std::ofstream &bin_file, const Trajectory &traj, int version_number=SERIALIZATION_VERSION)
	Writes a Trajectory object into a binary file. More...

void	deserialize_Trajectory (std::ifstream &bin_file, Trajectory *&traj)
	Creates a Trajectory object from a binary file. More...

TrajectoryVector
void	serialize_TrajectoryVector (std::ofstream &bin_file, const TrajectoryVector &traj, int version_number=SERIALIZATION_VERSION)
	Writes a TrajectoryVector object into a binary file. More...

void	deserialize_TrajectoryVector (std::ifstream &bin_file, TrajectoryVector *&traj)
	Creates a TrajectoryVector object from a binary file. More...

Tube
void	serialize_Tube (std::ofstream &bin_file, const Tube &tube, int version_number=SERIALIZATION_VERSION)
	Writes a Tube object into a binary file (version 2) More...

void	deserialize_Tube (std::ifstream &bin_file, Tube *&tube)
	Creates a Tube object from a binary file. More...

TubeVector
void	serialize_TubeVector (std::ofstream &bin_file, const TubeVector &tube, int version_number=SERIALIZATION_VERSION)
	Writes a TubeVector object into a binary file. More...

void	deserialize_TubeVector (std::ifstream &bin_file, TubeVector *&tube)
	Creates a TubeVector object from a binary file. More...

SIVIA for contractors
std::map< SetValue, std::list< IntervalVector > >	SIVIA (const IntervalVector &x, const IntervalVector &y, Ctc &ctc, float precision, bool regular_paving=false, bool display_result=true, const std::string &fig_name="", bool return_result=false, const SetColorMap &color_map=DEFAULT_SET_COLOR_MAP)
	Executes a SIVIA algorithm from a contractor, and displays the result. SIVIA: Set Inversion Via Interval Analysis. More...

std::map< SetValue, std::list< IntervalVector > >	SIVIA (const IntervalVector &x, Ctc &ctc, float precision, bool regular_paving=false, bool display_result=true, const std::string &fig_name="", bool return_result=false, const SetColorMap &color_map=DEFAULT_SET_COLOR_MAP)
	Executes a SIVIA algorithm from a contractor, and displays the result. SIVIA: Set Inversion Via Interval Analysis. More...

SIVIA for separators
std::map< SetValue, std::list< IntervalVector > >	SIVIA (const IntervalVector &x, ibex::Sep &sep, float precision, bool regular_paving=false, bool display_result=true, const std::string &fig_name="", bool return_result=false, const SetColorMap &color_map=DEFAULT_SET_COLOR_MAP)
	Executes a SIVIA algorithm from a separator, and displays the result. SIVIA: Set Inversion Via Interval Analysis. More...

Variables
SetColorMap	DEFAULT_SET_COLOR_MAP
	predefined DEFAULT_SET_COLOR_MAP

SetColorMap	LIE_SET_COLOR_MAP
	predefined LIE_SET_COLOR_MAP

Detailed Description

FixPoint of a separator The fixpoint of a separator is computed by calling the "::"separate function on a given box until the Hausdorff distance between two iterations is less than a given ratio. This operation can be seen as a contractor on the boundary of the solution set.

CtcPicard class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

TubeSynthesis class

Date: 2022

Author: Simon Rohou

Copyright: Copyright 2022 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

TubeTreeSynthesis class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

DelayTFunction class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

TFnc class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

TFunction class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

ConvexPolygon class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

GrahamScan class

Date: 2019

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

Polygon class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

ThickEdge class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

At the end, two boxes x_in and x_out, need to be reconstructed by merging the resulting box and parts of the initial box which belong (or not) to the solution set.

CtcConstell class

Date: 2018

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

DataLoader class

Date: 2016

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

DataLoaderLissajous class

Date: 2016

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

DataLoaderRedermor class

Date: 2016

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

Beacon class

Date: 2015

Author: Simon Rohou

Copyright: Copyright 2021 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

Beacon class

Date: 2024

Author: Simon Rohou

Copyright: Copyright 2024 Codac Team

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

Enumeration Type Documentation

◆ TimePropag

enum codac::TimePropag

strong

Specifies the temporal propagation way (forward or backward in time)

Enumerator
FORWARD	forward in time (from \(t^-\) to \(t^+\))
BACKWARD	backward in time (from \(t^+\) to \(t^-\))

   {
     FORWARD = 0x01, 
     BACKWARD = 0x02 
   };

◆ SetValue

enum codac::SetValue

strong

Defines a set of feasible values of a set.

Note: These values can be used as flags for boolean selections. Example of use: (UNKNOWN | IN) to get items of these types

Enumerator
DEFAULT	does not have a meaning, only used for default values of arguments
UNKNOWN	unable to conclude
OUT	outside the solution set
IN	inside the solution set
PENUMBRA	inside the penumbra set

   {
     DEFAULT = 0x00, 
  
     UNKNOWN = 0x01, 
     OUT = 0x02,     
     IN = 0x04,      
     PENUMBRA = 0x08 
   };

Function Documentation

◆ CAPD_integrateODE() [1/2]

TubeVector codac::CAPD_integrateODE	(	const Interval &	tdomain,
		const Function &	f,
		const IntervalVector &	x0,
		double	tube_dt = `0.`,
		int	capd_order = `20`,
		double	capd_dt = `0.`
	)

Integrates the autonomous ODE \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\) using CAPD.

Parameters

tdomain	temporal domain \([t_0,t_f]\)
f	the function \(\mathbf{f}\) (defined with a `Function` object)
x0	the initial condition \(\mathbf{x}_0\) at \(t_0\)
tube_dt	sampling value \(\delta\) for the temporal discretization of the resulting tube
capd_order	(optional) order of the integration method
capd_dt	(optional) custom time step for CAPD integration

Returns: TubeVector enclosing the solution

◆ CAPD_integrateODE() [2/2]

TubeVector codac::CAPD_integrateODE	(	const Interval &	tdomain,
		const TFunction &	f,
		const IntervalVector &	x0,
		double	tube_dt = `0.`,
		int	capd_order = `20`,
		double	capd_dt = `0.`
	)

Integrates the non-autonomous ODE \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x},t)\) using CAPD.

Parameters

tdomain	temporal domain \([t_0,t_f]\)
f	the temporal function \(\mathbf{f}\) (defined with a `TFunction` object)
x0	the initial condition \(\mathbf{x}_0\) at \(t_0\)
tube_dt	sampling value \(\delta\) for the temporal discretization of the resulting tube
capd_order	(optional) order of the integration method
capd_dt	(optional) custom time step for CAPD integration

Returns: TubeVector enclosing the solution

◆ operator|() [1/13]

const IntervalMatrix codac::operator\|	(	const IntervalMatrix &	x,
		const IntervalMatrix &	y
	)

\([\mathbf{X}]\sqcup[\mathbf{Y}]\)

Parameters

x
y

Returns: IntervalMatrix output

◆ operator&() [1/13]

const IntervalMatrix codac::operator&	(	const IntervalMatrix &	x,
		const IntervalMatrix &	y
	)

\([\mathbf{X}]\cap[\mathbf{Y}]\)

Parameters

x
y

Returns: IntervalMatrix output

◆ cos() [1/2]

const Trajectory codac::cos ( const Trajectory & x )

\(\cos(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ sin() [1/2]

const Trajectory codac::sin ( const Trajectory & x )

\(\sin(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ abs() [1/4]

const Trajectory codac::abs ( const Trajectory & x )

\(\mid x(\cdot)\mid\)

Parameters

x

Returns: Trajectory output

◆ sqr() [1/2]

const Trajectory codac::sqr ( const Trajectory & x )

\(x^2(\cdot)\)

Parameters

x

Returns: Trajectory output

◆ sqrt() [1/2]

const Trajectory codac::sqrt ( const Trajectory & x )

\(\sqrt{x(\cdot)}\)

Parameters

x

Returns: Trajectory output

◆ exp() [1/2]

const Trajectory codac::exp ( const Trajectory & x )

\(\exp(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ log() [1/2]

const Trajectory codac::log ( const Trajectory & x )

\(\log(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ tan() [1/2]

const Trajectory codac::tan ( const Trajectory & x )

\(\tan(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ acos() [1/2]

const Trajectory codac::acos ( const Trajectory & x )

\(\arccos(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ asin() [1/2]

const Trajectory codac::asin ( const Trajectory & x )

\(\arcsin(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ atan() [1/2]

const Trajectory codac::atan ( const Trajectory & x )

\(\arctan(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ cosh() [1/2]

const Trajectory codac::cosh ( const Trajectory & x )

\(\cosh(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ sinh() [1/2]

const Trajectory codac::sinh ( const Trajectory & x )

\(\sinh(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ tanh() [1/2]

const Trajectory codac::tanh ( const Trajectory & x )

\(\tanh(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ acosh() [1/2]

const Trajectory codac::acosh ( const Trajectory & x )

\(\mathrm{arccosh}(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ asinh() [1/2]

const Trajectory codac::asinh ( const Trajectory & x )

\(\mathrm{arcsinh}(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ atanh() [1/2]

const Trajectory codac::atanh ( const Trajectory & x )

\(\mathrm{arctanh}(x(\cdot))\)

Parameters

x

Returns: Trajectory output

◆ atan2() [1/6]

const Trajectory codac::atan2	(	const Trajectory &	y,
		const Trajectory &	x
	)

\(\mathrm{arctan2}(y(\cdot),x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ atan2() [2/6]

const Trajectory codac::atan2	(	const Trajectory &	y,
		double	x
	)

\(\mathrm{arctan2}(y(\cdot),x)\)

Parameters

y
x

Returns: Trajectory output

◆ atan2() [3/6]

const Trajectory codac::atan2	(	double	y,
		const Trajectory &	x
	)

\(\mathrm{arctan2}(y, x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ min() [1/6]

const Trajectory codac::min	(	const Trajectory &	y,
		const Trajectory &	x
	)

\(\min(y(\cdot),x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ min() [2/6]

const Trajectory codac::min	(	const Trajectory &	y,
		double	x
	)

\(\min(y(\cdot),x)\)

Parameters

y
x

Returns: Trajectory output

◆ min() [3/6]

const Trajectory codac::min	(	double	y,
		const Trajectory &	x
	)

\(\min(y, x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ max() [1/6]

const Trajectory codac::max	(	const Trajectory &	y,
		const Trajectory &	x
	)

\(\max(y(\cdot),x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ max() [2/6]

const Trajectory codac::max	(	const Trajectory &	y,
		double	x
	)

\(\max(y(\cdot),x)\)

Parameters

y
x

Returns: Trajectory output

◆ max() [3/6]

const Trajectory codac::max	(	double	y,
		const Trajectory &	x
	)

\(\max(y, x(\cdot))\)

Parameters

y
x

Returns: Trajectory output

◆ pow() [1/5]

const Trajectory codac::pow	(	const Trajectory &	x,
		int	p
	)

\(x^p(\cdot)\)

Parameters

x
p

Returns: Trajectory output

◆ pow() [2/5]

const Trajectory codac::pow	(	const Trajectory &	x,
		double	p
	)

\(x^p(\cdot)\)

Parameters

x
p

Returns: Trajectory output

◆ root() [1/2]

const Trajectory codac::root	(	const Trajectory &	x,
		int	p
	)

\(\sqrt[p]{x(\cdot)}\)

Parameters

x
p

Returns: Trajectory output

◆ operator+() [1/20]

const Trajectory codac::operator+ ( const Trajectory & x )

\(x(\cdot)\)

Parameters

x

Returns: Trajectory output

◆ operator+() [2/20]

const Trajectory codac::operator+	(	const Trajectory &	x,
		const Trajectory &	y
	)

\(x(\cdot)+y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator+() [3/20]

const Trajectory codac::operator+	(	const Trajectory &	x,
		double	y
	)

\(x(\cdot)+y\)

Parameters

x
y

Returns: Trajectory output

◆ operator+() [4/20]

const Trajectory codac::operator+	(	double	x,
		const Trajectory &	y
	)

\(x+y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator-() [1/20]

const Trajectory codac::operator- ( const Trajectory & x )

\(-x(\cdot)\)

Parameters

x

Returns: Trajectory output

◆ operator-() [2/20]

const Trajectory codac::operator-	(	const Trajectory &	x,
		const Trajectory &	y
	)

\(x(\cdot)-y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator-() [3/20]

const Trajectory codac::operator-	(	const Trajectory &	x,
		double	y
	)

\(x(\cdot)-y\)

Parameters

x
y

Returns: Trajectory output

◆ operator-() [4/20]

const Trajectory codac::operator-	(	double	x,
		const Trajectory &	y
	)

\(x-y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator*() [1/16]

const Trajectory codac::operator*	(	const Trajectory &	x,
		const Trajectory &	y
	)

\(x(\cdot)\cdot y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator*() [2/16]

const Trajectory codac::operator*	(	const Trajectory &	x,
		double	y
	)

\(x(\cdot)\cdot y\)

Parameters

x
y

Returns: Trajectory output

◆ operator*() [3/16]

const Trajectory codac::operator*	(	double	x,
		const Trajectory &	y
	)

\(x\cdot y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator/() [1/15]

const Trajectory codac::operator/	(	const Trajectory &	x,
		const Trajectory &	y
	)

\(x(\cdot)/y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator/() [2/15]

const Trajectory codac::operator/	(	const Trajectory &	x,
		double	y
	)

\(x(\cdot)/y\)

Parameters

x
y

Returns: Trajectory output

◆ operator/() [3/15]

const Trajectory codac::operator/	(	double	x,
		const Trajectory &	y
	)

\(x/y(\cdot)\)

Parameters

x
y

Returns: Trajectory output

◆ operator+() [5/20]

const TrajectoryVector codac::operator+ ( const TrajectoryVector & x )

\(\mathbf{x}(\cdot)\)

Parameters

x

Returns: TrajectoryVector output

◆ operator+() [6/20]

const TrajectoryVector codac::operator+	(	const TrajectoryVector &	x,
		const TrajectoryVector &	y
	)

\(\mathbf{x}(\cdot)+\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator+() [7/20]

const TrajectoryVector codac::operator+	(	const TrajectoryVector &	x,
		const Vector &	y
	)

\(\mathbf{x}(\cdot)+\mathbf{y}\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator+() [8/20]

const TrajectoryVector codac::operator+	(	const Vector &	x,
		const TrajectoryVector &	y
	)

\(\mathbf{x}+\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator-() [5/20]

const TrajectoryVector codac::operator- ( const TrajectoryVector & x )

\(-\mathbf{x}(\cdot)\)

Parameters

x

Returns: TrajectoryVector output

◆ operator-() [6/20]

const TrajectoryVector codac::operator-	(	const TrajectoryVector &	x,
		const TrajectoryVector &	y
	)

\(\mathbf{x}(\cdot)-\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator-() [7/20]

const TrajectoryVector codac::operator-	(	const TrajectoryVector &	x,
		const Vector &	y
	)

\(\mathbf{x}(\cdot)-\mathbf{y}\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator-() [8/20]

const TrajectoryVector codac::operator-	(	const Vector &	x,
		const TrajectoryVector &	y
	)

\(\mathbf{x}-\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator*() [4/16]

const TrajectoryVector codac::operator*	(	double	x,
		const TrajectoryVector &	y
	)

\(x\cdot\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator*() [5/16]

const TrajectoryVector codac::operator*	(	const Trajectory &	x,
		const TrajectoryVector &	y
	)

\(x(\cdot)\cdot\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator*() [6/16]

const TrajectoryVector codac::operator*	(	const Trajectory &	x,
		const Vector &	y
	)

\(x(\cdot)\cdot\mathbf{y}\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator*() [7/16]

const TrajectoryVector codac::operator*	(	const Matrix &	x,
		const TrajectoryVector &	y
	)

\(x(\cdot)\cdot\mathbf{y}\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator/() [4/15]

const TrajectoryVector codac::operator/	(	const TrajectoryVector &	x,
		double	y
	)

\(\mathbf{x}(\cdot)/y\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator/() [5/15]

const TrajectoryVector codac::operator/	(	const TrajectoryVector &	x,
		const Trajectory &	y
	)

\(\mathbf{x}(\cdot)/y(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ operator/() [6/15]

const TrajectoryVector codac::operator/	(	const Vector &	x,
		const Trajectory &	y
	)

\(\mathbf{x}/y(\cdot)\)

Parameters

x
y

Returns: TrajectoryVector output

◆ vecto_product() [1/3]

const Vector codac::vecto_product	(	const Vector &	x,
		const Vector &	y
	)

\(\mathbf{x}\times\mathbf{y}\) (or \(\mathbf{x}\wedge\mathbf{y}\) in physics)

Parameters

x
y

Returns: Vector output

◆ vecto_product() [2/3]

const TrajectoryVector codac::vecto_product	(	const TrajectoryVector &	x,
		const Vector &	y
	)

\(\mathbf{x}(\cdot)\times\mathbf{y}\) (or \(\mathbf{x}(\cdot)\wedge\mathbf{y}\) in physics)

Parameters

x
y

Returns: TrajectoryVector output

◆ vecto_product() [3/3]

const TrajectoryVector codac::vecto_product	(	const Vector &	x,
		const TrajectoryVector &	y
	)

\(\mathbf{x}\times\mathbf{y}(\cdot)\) (or \(\mathbf{x}\wedge\mathbf{y}(\cdot)\) in physics)

Parameters

x
y

Returns: TrajectoryVector output

◆ abs() [2/4]

const TrajectoryVector codac::abs ( const TrajectoryVector & x )

\(\mid\mathbf{x}(\cdot)\mid\)

Parameters

x

Returns: TrajectoryVector output

◆ cos() [2/2]

const Tube codac::cos ( const Tube & x )

\(\cos([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ sin() [2/2]

const Tube codac::sin ( const Tube & x )

\(\sin([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ abs() [3/4]

const Tube codac::abs ( const Tube & x )

\(\mid[x](\cdot)\mid\)

Parameters

x

Returns: Tube output

◆ sqr() [2/2]

const Tube codac::sqr ( const Tube & x )

\([x]^2(\cdot)\)

Parameters

x

Returns: Tube output

◆ sqrt() [2/2]

const Tube codac::sqrt ( const Tube & x )

\(\sqrt{[x](\cdot)}\)

Parameters

x

Returns: Tube output

◆ exp() [2/2]

const Tube codac::exp ( const Tube & x )

\(\exp([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ log() [2/2]

const Tube codac::log ( const Tube & x )

\(\log([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ tan() [2/2]

const Tube codac::tan ( const Tube & x )

\(\tan([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ acos() [2/2]

const Tube codac::acos ( const Tube & x )

\(\arccos([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ asin() [2/2]

const Tube codac::asin ( const Tube & x )

\(\arcsin([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ atan() [2/2]

const Tube codac::atan ( const Tube & x )

\(\arctan([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ cosh() [2/2]

const Tube codac::cosh ( const Tube & x )

\(\cosh([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ sinh() [2/2]

const Tube codac::sinh ( const Tube & x )

\(\sinh([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ tanh() [2/2]

const Tube codac::tanh ( const Tube & x )

\(\tanh([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ acosh() [2/2]

const Tube codac::acosh ( const Tube & x )

\(\mathrm{arccosh}([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ asinh() [2/2]

const Tube codac::asinh ( const Tube & x )

\(\mathrm{arcsinh}([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ atanh() [2/2]

const Tube codac::atanh ( const Tube & x )

\(\mathrm{arctanh}([x](\cdot))\)

Parameters

x

Returns: Tube output

◆ atan2() [4/6]

const Tube codac::atan2	(	const Tube &	y,
		const Tube &	x
	)

\(\mathrm{arctan2}([y](\cdot),[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ atan2() [5/6]

const Tube codac::atan2	(	const Tube &	y,
		const Interval &	x
	)

\(\mathrm{arctan2}([y](\cdot),[x])\)

Parameters

y
x

Returns: Tube output

◆ atan2() [6/6]

const Tube codac::atan2	(	const Interval &	y,
		const Tube &	x
	)

\(\mathrm{arctan2}([y],[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ pow() [3/5]

const Tube codac::pow	(	const Tube &	x,
		int	p
	)

\([x]^p(\cdot)\)

Parameters

x
p

Returns: Tube output

◆ pow() [4/5]

const Tube codac::pow	(	const Tube &	x,
		double	p
	)

\([x]^p(\cdot)\)

Parameters

x
p

Returns: Tube output

◆ pow() [5/5]

const Tube codac::pow	(	const Tube &	x,
		const Interval &	p
	)

\([x]^{[p]}(\cdot)\)

Parameters

x
p

Returns: Tube output

◆ root() [2/2]

const Tube codac::root	(	const Tube &	x,
		int	p
	)

\(\sqrt[p]{[x](\cdot)}\)

Parameters

x
p

Returns: Tube output

◆ min() [4/6]

const Tube codac::min	(	const Tube &	y,
		const Tube &	x
	)

\(\min([y](\cdot),[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ min() [5/6]

const Tube codac::min	(	const Tube &	y,
		const Interval &	x
	)

\(\min([y](\cdot),[x])\)

Parameters

y
x

Returns: Tube output

◆ min() [6/6]

const Tube codac::min	(	const Interval &	y,
		const Tube &	x
	)

\(\min([y],[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ max() [4/6]

const Tube codac::max	(	const Tube &	y,
		const Tube &	x
	)

\(\max([y](\cdot),[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ max() [5/6]

const Tube codac::max	(	const Tube &	y,
		const Interval &	x
	)

\(\max([y](\cdot),[x])\)

Parameters

y
x

Returns: Tube output

◆ max() [6/6]

const Tube codac::max	(	const Interval &	y,
		const Tube &	x
	)

\(\max([y],[x](\cdot))\)

Parameters

y
x

Returns: Tube output

◆ operator+() [9/20]

const Tube codac::operator+ ( const Tube & x )

\([x](\cdot)\)

Parameters

x

Returns: Tube output

◆ operator+() [10/20]

const Tube codac::operator+	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)+[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator+() [11/20]

const Tube codac::operator+	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)+[y]\)

Parameters

x
y

Returns: Tube output

◆ operator+() [12/20]

const Tube codac::operator+	(	const Interval &	x,
		const Tube &	y
	)

\([x]+[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator+() [13/20]

const Tube codac::operator+	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)+y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator+() [14/20]

const Tube codac::operator+	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)+[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator-() [9/20]

const Tube codac::operator- ( const Tube & x )

\(-[x](\cdot)\)

Parameters

x

Returns: Tube output

◆ operator-() [10/20]

const Tube codac::operator-	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)-[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator-() [11/20]

const Tube codac::operator-	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)-[y]\)

Parameters

x
y

Returns: Tube output

◆ operator-() [12/20]

const Tube codac::operator-	(	const Interval &	x,
		const Tube &	y
	)

\([x]-[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator-() [13/20]

const Tube codac::operator-	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)-y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator-() [14/20]

const Tube codac::operator-	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)-[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator*() [8/16]

const Tube codac::operator*	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)\cdot[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator*() [9/16]

const Tube codac::operator*	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)\cdot[y]\)

Parameters

x
y

Returns: Tube output

◆ operator*() [10/16]

const Tube codac::operator*	(	const Interval &	x,
		const Tube &	y
	)

\([x]\cdot[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator*() [11/16]

const Tube codac::operator*	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)\cdot y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator*() [12/16]

const Tube codac::operator*	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)\cdot[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator/() [7/15]

const Tube codac::operator/	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)/[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator/() [8/15]

const Tube codac::operator/	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)/[y]\)

Parameters

x
y

Returns: Tube output

◆ operator/() [9/15]

const Tube codac::operator/	(	const Interval &	x,
		const Tube &	y
	)

\([x]/[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator/() [10/15]

const Tube codac::operator/	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)/y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator/() [11/15]

const Tube codac::operator/	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)/[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator|() [2/13]

const Tube codac::operator\|	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)\sqcup[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator|() [3/13]

const Tube codac::operator\|	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)\sqcup[y]\)

Parameters

x
y

Returns: Tube output

◆ operator|() [4/13]

const Tube codac::operator\|	(	const Interval &	x,
		const Tube &	y
	)

\([x]\sqcup[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator|() [5/13]

const Tube codac::operator\|	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)\sqcup y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator|() [6/13]

const Tube codac::operator\|	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)\sqcup [y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator&() [2/13]

const Tube codac::operator&	(	const Tube &	x,
		const Tube &	y
	)

\([x](\cdot)\cap[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator&() [3/13]

const Tube codac::operator&	(	const Tube &	x,
		const Interval &	y
	)

\([x](\cdot)\cap[y]\)

Parameters

x
y

Returns: Tube output

◆ operator&() [4/13]

const Tube codac::operator&	(	const Interval &	x,
		const Tube &	y
	)

\([x]\cap[y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator&() [5/13]

const Tube codac::operator&	(	const Tube &	x,
		const Trajectory &	y
	)

\([x](\cdot)\cap y(\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator&() [6/13]

const Tube codac::operator&	(	const Trajectory &	x,
		const Tube &	y
	)

\(x(\cdot)\cap [y](\cdot)\)

Parameters

x
y

Returns: Tube output

◆ operator+() [15/20]

const TubeVector codac::operator+ ( const TubeVector & x )

\([\mathbf{x}](\cdot)\)

Parameters

x

Returns: TubeVector output

◆ operator+() [16/20]

const TubeVector codac::operator+	(	const TubeVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}](\cdot)+[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator+() [17/20]

const TubeVector codac::operator+	(	const TubeVector &	x,
		const IntervalVector &	y
	)

\([\mathbf{x}](\cdot)+[\mathbf{y}]\)

Parameters

x
y

Returns: TubeVector output

◆ operator+() [18/20]

const TubeVector codac::operator+	(	const IntervalVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}]+[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator+() [19/20]

const TubeVector codac::operator+	(	const TubeVector &	x,
		const TrajectoryVector &	y
	)

\([\mathbf{x}](\cdot)+\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator+() [20/20]

const TubeVector codac::operator+	(	const TrajectoryVector &	x,
		const TubeVector &	y
	)

\(\mathbf{x}(\cdot)+[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator-() [15/20]

const TubeVector codac::operator- ( const TubeVector & x )

\(-[\mathbf{x}](\cdot)\)

Parameters

x

Returns: TubeVector output

◆ operator-() [16/20]

const TubeVector codac::operator-	(	const TubeVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}](\cdot)-[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator-() [17/20]

const TubeVector codac::operator-	(	const TubeVector &	x,
		const IntervalVector &	y
	)

\([\mathbf{x}](\cdot)-[\mathbf{y}]\)

Parameters

x
y

Returns: TubeVector output

◆ operator-() [18/20]

const TubeVector codac::operator-	(	const IntervalVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}]-[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator-() [19/20]

const TubeVector codac::operator-	(	const TubeVector &	x,
		const TrajectoryVector &	y
	)

\([\mathbf{x}](\cdot)-\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator-() [20/20]

const TubeVector codac::operator-	(	const TrajectoryVector &	x,
		const TubeVector &	y
	)

\(\mathbf{x}(\cdot)-[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator*() [13/16]

const TubeVector codac::operator*	(	const Tube &	x,
		const TubeVector &	y
	)

\([x](\cdot)\cdot[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator*() [14/16]

const TubeVector codac::operator*	(	const Interval &	x,
		const TubeVector &	y
	)

\([x]\cdot[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator*() [15/16]

const TubeVector codac::operator*	(	const Tube &	x,
		const IntervalVector &	y
	)

\([x](\cdot)\cdot[\mathbf{y}]\)

Parameters

x
y

Returns: TubeVector output

◆ operator*() [16/16]

const TubeVector codac::operator*	(	const Trajectory &	x,
		const TubeVector &	y
	)

\(x(\cdot)\cdot[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator/() [12/15]

const TubeVector codac::operator/	(	const TubeVector &	x,
		const Tube &	y
	)

\([\mathbf{x}](\cdot)/[y](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator/() [13/15]

const TubeVector codac::operator/	(	const TubeVector &	x,
		const Interval &	y
	)

\([\mathbf{x}](\cdot)/[y]\)

Parameters

x
y

Returns: TubeVector output

◆ operator/() [14/15]

const TubeVector codac::operator/	(	const IntervalVector &	x,
		const Tube &	y
	)

\([\mathbf{x}]/[y](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator/() [15/15]

const TubeVector codac::operator/	(	const TubeVector &	x,
		const Trajectory &	y
	)

\([\mathbf{x}](\cdot)/y(\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator|() [7/13]

const TubeVector codac::operator\|	(	const TubeVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator|() [8/13]

const TubeVector codac::operator\|	(	const TubeVector &	x,
		const IntervalVector &	y
	)

\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}]\)

Parameters

x
y

Returns: TubeVector output

◆ operator|() [9/13]

const TubeVector codac::operator\|	(	const IntervalVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}]\sqcup[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator|() [10/13]

const TubeVector codac::operator\|	(	const TubeVector &	x,
		const TrajectoryVector &	y
	)

\([\mathbf{x}](\cdot)\sqcup\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator|() [11/13]

const TubeVector codac::operator\|	(	const TrajectoryVector &	x,
		const TubeVector &	y
	)

\(\mathbf{x}(\cdot)\sqcup[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator&() [7/13]

const TubeVector codac::operator&	(	const TubeVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}](\cdot)\cap[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator&() [8/13]

const TubeVector codac::operator&	(	const TubeVector &	x,
		const IntervalVector &	y
	)

\([\mathbf{x}](\cdot)\cap[\mathbf{y}]\)

Parameters

x
y

Returns: TubeVector output

◆ operator&() [9/13]

const TubeVector codac::operator&	(	const IntervalVector &	x,
		const TubeVector &	y
	)

\([\mathbf{x}]\cap[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator&() [10/13]

const TubeVector codac::operator&	(	const TubeVector &	x,
		const TrajectoryVector &	y
	)

\([\mathbf{x}](\cdot)\cap\mathbf{y}(\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ operator&() [11/13]

const TubeVector codac::operator&	(	const TrajectoryVector &	x,
		const TubeVector &	y
	)

\(\mathbf{x}(\cdot)\cap[\mathbf{y}](\cdot)\)

Parameters

x
y

Returns: TubeVector output

◆ abs() [4/4]

const TubeVector codac::abs ( const TubeVector & x )

\(\mid\mathbf{x}(\cdot)\mid\)

Parameters

x

Returns: TubeVector output

◆ operator&() [12/13]

int codac::operator&	(	TimePropag	a,
		TimePropag	b
	)

inline

Allows tests on combinations of propagation ways.

Used for tests such as if(time_propag & TimePropag::FORWARD) { ... }

Parameters

a	first TimePropag operand
b	second TimePropag operand

Returns: intersection of propagation ways

42 { return static_cast<int>(static_cast<int>(a) & static_cast<int>(b)); }

◆ operator|() [12/13]

TimePropag codac::operator\|	(	TimePropag	a,
		TimePropag	b
	)

inline

Allows a combination of propagation ways.

Note: For instance: FORWARD | BACKWARD

Parameters

a	first TimePropag operand
b	second TimePropag operand

Returns: union of propagation ways, such as FORWARD | BACKWARD

54 { return static_cast<TimePropag>(static_cast<int>(a) | static_cast<int>(b)); }

codac::TimePropag

TimePropag

Specifies the temporal propagation way (forward or backward in time)

Definition: codac_DynCtc.h:27

◆ cart_prod() [1/2]

CtcCartProd codac::cart_prod	(	Ctc &	c1,
		Ctc &	c2
	)

Cartesian product of contractors from two Ctc objects.

Parameters

c1	first Ctc contractor
c2	second Ctc contractor

Returns: the Cartesian product of the contractors \(\mathcal{C}_1\times\dots\times\mathcal{C}_n\)

◆ cart_prod() [2/2]

CtcCartProd codac::cart_prod ( const ibex::Array< Ctc > & array )

Cartesian product of contractors from an ibex::Array.

Parameters

array ibex::Array of contractors

Returns: the Cartesian product of the contractors \(\mathcal{C}_1\times\dots\times\mathcal{C}_n\)

◆ rgb2hex()

const std::string codac::rgb2hex	(	rgb	rgb_value,
		const char *	prefix = `"#"`
	)

Represents an RGB value in a HTML standard.

Parameters

rgb_value
prefix	optional characters ("#" by default)

Returns: the HTML string

◆ hsv2rgb()

rgb codac::hsv2rgb ( hsv hsv_value )

Converts HSV to RGB.

Parameters

hsv_value

Returns: RGB value

◆ rgb2hsv()

hsv codac::rgb2hsv ( rgb rgb_value )

Converts RGB to HSV.

Parameters

rgb_value

Returns: HSV value

◆ make_rgb() [1/2]

rgb codac::make_rgb	(	int	r,
		int	g,
		int	b,
		int	alpha = `255`
	)

Makes an RGV value from integers.

Parameters

r	red value, integer between 0 and 255
g	green value, integer between 0 and 255
b	blue value, integer between 0 and 255
alpha	opacity value, integer between 0 (transparent) and 255 (opaque)

Returns: RGB value

◆ make_rgb() [2/2]

rgb codac::make_rgb	(	float	r,
		float	g,
		float	b,
		float	alpha = `1.`
	)

Makes an RGV value from floats.

Parameters

r	red value, float between 0. and 1.
g	green value, float between 0. and 1.
b	blue value, float between 0. and 1.
alpha	opacity value, float between 0. (transparent) and 1. (opaque)

Returns: RGB value

◆ make_hsv() [1/2]

hsv codac::make_hsv	(	int	h,
		int	s,
		int	v,
		int	alpha = `100`
	)

Makes an HSV value from integers.

Parameters

h	hue value, integer between 0 and 360
s	saturation value, integer between 0 and 100
v	value (lightness), integer between 0 and 100
alpha	opacity value, integer between 0 (transparent) and 100 (opaque)

Returns: HSV value

◆ make_hsv() [2/2]

hsv codac::make_hsv	(	float	h,
		float	s,
		float	v,
		float	alpha = `1.`
	)

Makes an HSV value from floats.

Parameters

h	hue value, float between 0. and 360.
s	saturation value, float between 0. and 1.
v	value (lightness), float between 0. and 1.
alpha	opacity value, float between 0. (transparent) and 1. (opaque)

Returns: HSV value

◆ operator&() [13/13]

int codac::operator&	(	SetValue	a,
		SetValue	b
	)

inline

Allows tests on combinations of two SetValue.

Used for tests such as if(set_val & SetValue::OUT) { ... }

Parameters

a	first SetValue operand
b	second SetValue operand

Returns: intersection of set values

46 { return static_cast<int>(static_cast<int>(a) & static_cast<int>(b)); }

◆ operator|() [13/13]

SetValue codac::operator\|	(	SetValue	a,
		SetValue	b
	)

inline

Union of two SetValue values.

Avoids the need to cast for boolean union operations.

Parameters

a
b

Returns: the interval union a|b

58 { return static_cast<SetValue>(static_cast<int>(a) | static_cast<int>(b)); }

codac::SetValue

SetValue

Defines a set of feasible values of a set.

Definition: codac_Set.h:27

◆ serialize_Interval()

void codac::serialize_Interval	(	std::ofstream &	bin_file,
		const Interval &	intv
	)

Writes an Interval object into a binary file.

Interval binary structure:
[char_intv_type]
[double_lb]
[double_ub]

char_intv_type refers the type of Interval: either BOUNDED, EMPTY_SET, ALL_REALS, POS_REALS, NEG_REALS.

In case of unbounded intervals, the two last fields disappear.

Parameters

bin_file	binary file (ofstream object)
intv	Interval object to be serialized

◆ deserialize_Interval()

void codac::deserialize_Interval	(	std::ifstream &	bin_file,
		Interval &	intv
	)

Creates an Interval object from a binary file.

The binary file has to be written by the serialize_Interval() function.

Parameters

bin_file	binary file (ifstream object)
intv	Interval object to be deserialized

◆ deserialize_IntervalVector()

void codac::deserialize_IntervalVector	(	std::ifstream &	bin_file,
		IntervalVector &	box
	)

Writes an IntervalVector object into a binary file.

IntervalVector binary structure:
[short_int_size]
[Interval_1]
...
[Interval_n]

Parameters

bin_file	binary file (ofstream object)
box	IntervalVector object to be serialized

◆ serialize_IntervalVector()

void codac::serialize_IntervalVector	(	std::ofstream &	bin_file,
		const IntervalVector &	box
	)

Creates an IntervalVector object from a binary file.

The binary file has to be written by the serialize_IntervalVector() function.

Parameters

bin_file	binary file (ifstream object)
box	IntervalVector object to be deserialized

◆ serialize_Trajectory()

void codac::serialize_Trajectory	(	std::ofstream &	bin_file,
		const Trajectory &	traj,
		int	version_number = `SERIALIZATION_VERSION`
	)

Writes a Trajectory object into a binary file.

Trajectory binary structure:
[short_int_version_number]
[int_nb_points]
[double_t_pt1]
[double_y_pt1]
[double_t_pt2]
[double_y_pt2]
[double_t_pt3]
...

Note: Only map valued trajectories are serializable

Parameters

bin_file	binary file (ofstream object)
traj	Trajectory object to be serialized
version_number	optional version number for tests purposes (backwards compatibility)

◆ deserialize_Trajectory()

void codac::deserialize_Trajectory	(	std::ifstream &	bin_file,
		Trajectory *&	traj
	)

Creates a Trajectory object from a binary file.

The binary file has to be written by the serialize_Trajectory() function.

Parameters

bin_file	binary file (ifstream object)
traj	Trajectory object to be deserialized

◆ serialize_TrajectoryVector()

void codac::serialize_TrajectoryVector	(	std::ofstream &	bin_file,
		const TrajectoryVector &	traj,
		int	version_number = `SERIALIZATION_VERSION`
	)

Writes a TrajectoryVector object into a binary file.

TrajectoryVector binary structure:
[short_int_size]
[Trajectory_1]
...
[Trajectory_n]

Parameters

bin_file	binary file (ofstream object)
traj	TrajectoryVector object to be serialized
version_number	optional version number for tests purposes (backwards compatibility)

◆ deserialize_TrajectoryVector()

void codac::deserialize_TrajectoryVector	(	std::ifstream &	bin_file,
		TrajectoryVector *&	traj
	)

Creates a TrajectoryVector object from a binary file.

The binary file has to be written by the serialize_TrajectoryVector() function.

Parameters

bin_file	binary file (ifstream object)
traj	TrajectoryVector object to be deserialized

◆ serialize_Tube()

void codac::serialize_Tube	(	std::ofstream &	bin_file,
		const Tube &	tube,
		int	version_number = `SERIALIZATION_VERSION`
	)

Writes a Tube object into a binary file (version 2)

Tube binary structure:
[short_int_version_number]
[int_nb_slices]
[double_t0]
[double_t1] // time input shared by 1rst and 2nd slices
[double_t2]
...
[interval_y0] // value of 1rst slice
[interval_y1]
...
[gate_t0] // value of 1rst gate
[gate_t1]
...

Parameters

bin_file	binary file (ofstream object)
tube	Tube object to be serialized
version_number	optional version number for tests purposes (backwards compatibility)

◆ deserialize_Tube()

void codac::deserialize_Tube	(	std::ifstream &	bin_file,
		Tube *&	tube
	)

Creates a Tube object from a binary file.

The binary file has to be written by the serialize_Tube() function.

Parameters

bin_file	binary file (ifstream object)
tube	Tube object to be deserialized

◆ serialize_TubeVector()

void codac::serialize_TubeVector	(	std::ofstream &	bin_file,
		const TubeVector &	tube,
		int	version_number = `SERIALIZATION_VERSION`
	)

Writes a TubeVector object into a binary file.

TubeVector binary structure:
[short_int_size]
[Tube_1]
...
[Tube_n]

Parameters

bin_file	binary file (ofstream object)
tube	TubeVector object to be serialized
version_number	optional version number for tests purposes (backwards compatibility)

◆ deserialize_TubeVector()

void codac::deserialize_TubeVector	(	std::ifstream &	bin_file,
		TubeVector *&	tube
	)

Creates a TubeVector object from a binary file.

The binary file has to be written by the serialize_TubeVector() function.

Parameters

bin_file	binary file (ifstream object)
tube	TubeVector object to be deserialized

◆ SIVIA() [1/3]

std::map<SetValue,std::list<IntervalVector> > codac::SIVIA	(	const IntervalVector &	x,
		const IntervalVector &	y,
		Ctc &	ctc,
		float	precision,
		bool	regular_paving = `false`,
		bool	display_result = `true`,
		const std::string &	fig_name = `""`,
		bool	return_result = `false`,
		const SetColorMap &	color_map = `DEFAULT_SET_COLOR_MAP`
	)

Executes a SIVIA algorithm from a contractor, and displays the result. SIVIA: Set Inversion Via Interval Analysis.

The result is displayed in the current VIBes figure.

Parameters

x	initial box (part that will be bisected)
y	initial box (part that will not be bisected)
ctc	Contractor operator for the set inversion
precision	accuracy of the paving algorithm
regular_paving	regular bisection rule
display_result	display information if true
fig_name	name of the figure on which boxes are drawn. If empty, default figure is used
return_result	if true, boxes will be stored in the returned map
color_map	color map used to draw boxes, see SetColorMap

Returns: return a map of lists of boxes. Keys of the map are IN/OUT/UNKNOWN. The lists are empty if return_result if false.

◆ SIVIA() [2/3]

std::map<SetValue,std::list<IntervalVector> > codac::SIVIA	(	const IntervalVector &	x,
		Ctc &	ctc,
		float	precision,
		bool	regular_paving = `false`,
		bool	display_result = `true`,
		const std::string &	fig_name = `""`,
		bool	return_result = `false`,
		const SetColorMap &	color_map = `DEFAULT_SET_COLOR_MAP`
	)

Executes a SIVIA algorithm from a contractor, and displays the result. SIVIA: Set Inversion Via Interval Analysis.

The result is displayed in the current VIBes figure.

Parameters

x	initial box
ctc	Contractor operator for the set inversion
precision	accuracy of the paving algorithm
regular_paving	regular bisection rule
display_result	display information if true
fig_name	name of the figure on which boxes are drawn. If empty, default figure is used
return_result	if true, boxes will be stored in the returned map
color_map	color map used to draw boxes, see SetColorMap

Returns: return a map of lists of boxes. Keys of the map are IN/OUT/UNKNOWN. The lists are empty if return_result if false.

◆ SIVIA() [3/3]

std::map<SetValue,std::list<IntervalVector> > codac::SIVIA	(	const IntervalVector &	x,
		ibex::Sep &	sep,
		float	precision,
		bool	regular_paving = `false`,
		bool	display_result = `true`,
		const std::string &	fig_name = `""`,
		bool	return_result = `false`,
		const SetColorMap &	color_map = `DEFAULT_SET_COLOR_MAP`
	)

Executes a SIVIA algorithm from a separator, and displays the result. SIVIA: Set Inversion Via Interval Analysis.

The result is displayed in the current VIBes figure.

Parameters

x	initial box
sep	Separator operator for the set inversion
precision	accuracy of the paving algorithm
regular_paving	regular bisection rule
display_result	display information if true
fig_name	name of the figure if None use the current figure. If empty, default figure is used
return_result	if true, boxes will be stored in the returned map
color_map	color map used to draw boxes, see SetColorMap

Returns: return a map of lists of boxes. Keys of the map are IN/OUT/UNKNOWN. The lists are empty if return_result if false.

Classes

Enumerations

Functions

Variables

Detailed Description

CtcPicard class

TubeSynthesis class

TubeTreeSynthesis class

DelayTFunction class

TFnc class

TFunction class

ConvexPolygon class

GrahamScan class

Polygon class

ThickEdge class

CtcConstell class

DataLoader class

DataLoaderLissajous class

DataLoaderRedermor class

Beacon class

Beacon class

Enumeration Type Documentation

◆ TimePropag

◆ SetValue

Function Documentation

◆ CAPD_integrateODE() [1/2]

◆ CAPD_integrateODE() [2/2]

◆ operator|() [1/13]

◆ operator&() [1/13]

◆ cos() [1/2]

◆ sin() [1/2]

◆ abs() [1/4]

◆ sqr() [1/2]

◆ sqrt() [1/2]

◆ exp() [1/2]

◆ log() [1/2]

◆ tan() [1/2]

◆ acos() [1/2]

◆ asin() [1/2]

◆ atan() [1/2]

◆ cosh() [1/2]

◆ sinh() [1/2]

◆ tanh() [1/2]

◆ acosh() [1/2]

◆ asinh() [1/2]

◆ atanh() [1/2]

◆ atan2() [1/6]

◆ atan2() [2/6]

◆ atan2() [3/6]

◆ min() [1/6]

◆ min() [2/6]

◆ min() [3/6]

◆ max() [1/6]

◆ max() [2/6]

◆ max() [3/6]

◆ pow() [1/5]

◆ pow() [2/5]

◆ root() [1/2]

◆ operator+() [1/20]

◆ operator+() [2/20]

◆ operator+() [3/20]

◆ operator+() [4/20]

◆ operator-() [1/20]

◆ operator-() [2/20]

◆ operator-() [3/20]

◆ operator-() [4/20]

◆ operator*() [1/16]

◆ operator*() [2/16]

◆ operator*() [3/16]

◆ operator/() [1/15]

◆ operator/() [2/15]

◆ operator/() [3/15]

◆ operator+() [5/20]

◆ operator+() [6/20]

◆ operator+() [7/20]

◆ operator+() [8/20]

◆ operator-() [5/20]

◆ operator-() [6/20]

◆ operator-() [7/20]

◆ operator-() [8/20]