Detailed Description

Combination of a map on a manifold and a polytope defined on the tangent space of the map. The polytope can be normal (Tcpolytope) or simple (Tscpolytope).

See also: chart.h,chart.c.

Definition at line 86 of file chart.h.

Data Fields
TAtlasBase *	w

unsigned int	m

unsigned int	k

unsigned int	da

unsigned int	n

unsigned int	nrJ

double	error

double	eCurv

double	r

unsigned int	degree

boolean	collision

boolean	frontier

boolean	singular

double *	center

double *	T

boolean *	BJ

unsigned int	ml

unsigned int	nl

unsigned int *	l

boolean	simple

Tcpolytope *	p

Tscpolytope *	sp

double *	A

double *	B

double *	c

double *	d

double *	iRBt

double *	BiRBt

Field Documentation

◆ w

TAtlasBase* Tchart::w

The world structure on which the chart is defined

Definition at line 88 of file chart.h.

Referenced by AddBorderConstraint(), Chart2Manifold(), ChartVolume(), CompareTangentSpaces(), CopyChart(), DistanceOnChart(), ForceChartCut(), GetChartWorld(), InitChartInt(), IntersectChartsInt(), LoadChart(), MinCosinusBetweenCharts(), PathInChart(), PlotChart(), PlotChartAsBox(), PlotChartAsPolygon(), and ReconstructAtlasPath().

◆ m

unsigned int Tchart::m

Number of variables. Dimension of the ambient space.

Definition at line 89 of file chart.h.

Referenced by AddBorderConstraint(), Chart2Manifold(), ChartErrorFromParameters(), ChartMemSize(), ChartVolume(), ClassifyPointInChart(), CompareTangentSpaces(), ComputeJacobianKernelBasis(), CopyChart(), DistanceOnChart(), ForceChartCut(), GetChartAmbientDim(), GetChartDegree(), InitChartInt(), IntersectChartsInt(), LoadChart(), Local2Global(), Manifold2Chart(), MinCosinusBetweenCharts(), PathInChart(), PlotChart(), PlotChartAsPolygon(), PointOnChart(), and SaveChart().

◆ k

unsigned int Tchart::k

Dimension of the manifold. Dimension of the tangent space.

Definition at line 90 of file chart.h.

Referenced by AddBorderConstraint(), Chart2Manifold(), ChartMemSize(), ChartVolume(), CompareTangentSpaces(), ComputeJacobianKernelBasis(), CopyChart(), DistanceOnChart(), Error2Chart(), FocusedPointOnBoundary(), ForceChartCut(), GetChartDegree(), GetChartManifoldDim(), InitChartInt(), IntersectChartsInt(), LoadChart(), Local2Global(), Manifold2Chart(), MinCosinusBetweenCharts(), PathInChart(), PlotChart(), PlotChartAsBox(), PlotChartAsPolygon(), SaveChart(), and SetLinearizedDynamics().

◆ da

unsigned int Tchart::da

Dimension of the action space. Only used for linearized dynamics.

Definition at line 91 of file chart.h.

Referenced by CopyChart(), InitChartInt(), LoadChart(), SaveChart(), and SetLinearizedDynamics().

◆ n

unsigned int Tchart::n

Number of non-redundant equations (equalities) defining the manifold

Definition at line 92 of file chart.h.

Referenced by Chart2Manifold(), ChartErrorFromParameters(), CopyChart(), Error2Chart(), GetChartDegree(), InitChartInt(), IntersectChartsInt(), LoadChart(), Local2Global(), Manifold2Chart(), and SaveChart().

◆ nrJ

unsigned int Tchart::nrJ

Number of equations. Number of rows of the Jacobian. This is n for well constrained systems and it is larger than n for overconstrained sytems.

Definition at line 93 of file chart.h.

Referenced by Chart2Manifold(), ComputeJacobianKernelBasis(), CopyChart(), InitChartInt(), LoadChart(), and SaveChart().

◆ error

double Tchart::error

Maximum error for the linear approximation of the manifold.

Definition at line 96 of file chart.h.

Referenced by ClassifyPointInChart(), CopyChart(), DistanceOnChart(), GetChartMaxError(), InitChartInt(), LoadChart(), PathInChart(), PointOnChart(), and SaveChart().

◆ eCurv

double Tchart::eCurv

Maximum cuvature error between the charts and the manifold

Definition at line 97 of file chart.h.

Referenced by CompareTangentSpaces(), CopyChart(), GetChartMaxCurvError(), InitChartInt(), LoadChart(), and SaveChart().

◆ r

double Tchart::r

Temptative radious of influence of the chart. This is stored in the polytpe, but we cache it here for convenience.

Definition at line 98 of file chart.h.

Referenced by BoundaryPointFromExternalCorner(), BoundaryPointsFromExternalCorners(), ClassifyPointInChart(), CopyChart(), FocusedPointOnBoundary(), ForceChartCut(), GetChartRadius(), InitChartInt(), IntersectChartsInt(), LoadChart(), PlotChartAsBox(), PointOnChart(), RandomPointOnBoundary(), and SaveChart().

◆ degree

unsigned int Tchart::degree

Used to detect bifurcations.

Definition at line 100 of file chart.h.

Referenced by CopyChart(), GetChartDegree(), InitChartInt(), LoadChart(), and SaveChart().

◆ collision

boolean Tchart::collision

TRUE if the chart center is in collision.

Definition at line 101 of file chart.h.

Referenced by CollisionChart(), and InitChartInt().

◆ frontier

boolean Tchart::frontier

TRUE for charts with the center out of the domain either because of the domain limits or due to a collision. Those charts are not to be extended.

Definition at line 102 of file chart.h.

Referenced by ChartIsFrontier(), CopyChart(), ExpandibleChart(), FrontierChart(), InitChartInt(), LoadChart(), PlotChartAsPolygon(), and SaveChart().

◆ singular

boolean Tchart::singular

TRUE for charts defined on singularities. This occurs during branch switching. Singular charts do not have a Jacobian basis defined

Definition at line 105 of file chart.h.

Referenced by ComputeJacobianKernelBasis(), CopyChart(), GetChartDegree(), InitChartInt(), LinkChart(), LoadChart(), SaveChart(), and SingularChart().

◆ center

double* Tchart::center

Linearization point on the manifold.

Definition at line 109 of file chart.h.

Referenced by Chart2Manifold(), ComputeJacobianKernelBasis(), CopyChart(), DeleteChart(), DistanceOnChart(), ForceChartCut(), GetChartCenter(), GetChartDegree(), InitChartInt(), IntersectChartsInt(), LoadChart(), Local2Global(), Manifold2Chart(), PathInChart(), PlotChartAsBox(), and SaveChart().

◆ T

double* Tchart::T

Basis of the tangent space of the manifold at p (m x k matrix) stored in the form of a vector.

Definition at line 110 of file chart.h.

Referenced by Chart2Manifold(), CompareTangentSpaces(), ComputeJacobianKernelBasis(), CopyChart(), DeleteChart(), GetChartDegree(), GetChartTangentSpace(), InitChartInt(), LoadChart(), Local2Global(), Manifold2Chart(), MinCosinusBetweenCharts(), and SaveChart().

◆ BJ

boolean* Tchart::BJ

TRUE for the rows of the Jacobian that form a basis. This is used to compute the degree of the chart and, thus it is only defined for non-singular charts.

Definition at line 112 of file chart.h.

Referenced by Chart2Manifold(), ComputeJacobianKernelBasis(), CopyChart(), DeleteChart(), GetChartDegree(), GetChartJacobianBasis(), InitChartInt(), LoadChart(), and SaveChart().