Tbifurcation Struct Reference Detailed DescriptionA 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.
Field Documentation
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().
Degree for the center of the first chart Definition at line 161 of file atlas.h. Referenced by DetectBifurcation(), FindSingularPoint(), LoadBifurcations(), and SaveBifurcations().
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().
Degree for the center of the second chart Definition at line 163 of file atlas.h. Referenced by DetectBifurcation(), FindSingularPoint(), LoadBifurcations(), and SaveBifurcations().
Representative point for this bifurcation. Definition at line 164 of file atlas.h. Referenced by DefineChartsAtBifurcation(), DeleteBifurcations(), DetectBifurcation(), FindPointInOtherBranch(), FindRightNullVector(), FindSingularPoint(), LoadBifurcations(), RefineSingularPoint(), and SaveBifurcations(). |
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