Tbifurcation Struct Reference

Detailed Description

A bifurcation is the connection between two aspects (or branches) of the same manifold. Bifucation occurs at the singular points.

We detect singularities analysing pairs of consecutive charts (see DetermineChartNeighbours). If there is a change in the degree between the couple of charts (see GetChartDegree) we know for sure there is a singularity between the centers of the two charts. Then we trigger a process to isolate the singular point and then to generate a point (and a chart) in the other aspect (or branch) of the manifold.

Note that the new chart is not neighbour of the two charts used to detect the singularity (their tangent spaces are two different). Thus, in some sense this structure is used to store the neighbouring relations not directly stored in the charts.

Definition at line 159 of file atlas.h.

Data Fields

unsigned int mID1
 
unsigned int d1
 
unsigned int mID2
 
unsigned int d2
 
double * p
 

Field Documentation

unsigned int Tbifurcation::mID1

Identifier of the first chart used to detect the singularity.

Definition at line 160 of file atlas.h.

Referenced by DefineChartsAtBifurcation(), DetectBifurcation(), FindRightNullVector(), FindSingularPoint(), LoadBifurcations(), PlotBifurcations(), RefineSingularPoint(), and SaveBifurcations().

unsigned int Tbifurcation::d1

Degree for the center of the first chart

Definition at line 161 of file atlas.h.

Referenced by DetectBifurcation(), FindSingularPoint(), LoadBifurcations(), and SaveBifurcations().

unsigned int Tbifurcation::mID2

Identifier of the second chart used to detect the singularity.

Definition at line 162 of file atlas.h.

Referenced by DetectBifurcation(), FindSingularPoint(), LoadBifurcations(), PlotBifurcations(), and SaveBifurcations().

unsigned int Tbifurcation::d2

Degree for the center of the second chart

Definition at line 163 of file atlas.h.

Referenced by DetectBifurcation(), FindSingularPoint(), LoadBifurcations(), and SaveBifurcations().

double* Tbifurcation::p