In[]:=
ResourceFunction["InteractiveListSelector"][Table[(SeedRandom[23424+i];With[{g=MeshConnectivityGraph[DiscretizeRegion[Rectangle[],MaxCellMeasure->.008]]},With[{p=FindInfraPoint[g,4,"Distance"->"Max"]},{l1=First@FindInfraPath[g,p[[1]],p[[3]]]},{l2=First@FindInfraPath[g,p[[3]],p[[2]]]},{l3=First@FindInfraPath[g,p[[2]],p[[4]]]},InfraSceneHighlight[g,ConcatenateInfraPath[First@ConcatenateInfraPath[l1,l2],l3]]]])->i,{i,20}]]
Out[]=
In[]:=
ResourceFunction["InteractiveListSelector"][Table[(SeedRandom[23424+i];With[{g=MeshConnectivityGraph[DiscretizeRegion[Rectangle[],MaxCellMeasure->0.02]]},{p=FindInfraPoint[g,2,"Distance"->5]},{l=FindInfraSegment[g,Sequence@@p]},InfraSceneHighlight[g,l]])->i,{i,20}]]
Out[]=
{1,13,19}
In[]:=
Table[With[{g=MeshConnectivityGraph[DiscretizeRegion[Rectangle[],MaxCellMeasure->0.02]]},{p=FindInfraPoint[g,2,"Distance"->5]},{l=(SeedRandom[23424+i];FindInfraSegment[g,Sequence@@p,All])},InfraSceneHighlight[g,l]],{i,{1,13,19}}]
Out[]=
,
,
Here we can replace the “geodesic graph” with a directed graph...
Riemannian manifold
Riemannian manifold
Point equivalence
Point equivalence
Triangles
Triangles
OA = OB = r
AB doesn’t give the angle (except in an infra way)
Embedded in a ball, can compute angle
AOB should be π
Smallest possible angle: 1 edge between A and B
“Continue the circle” that went through A and B [ continue the great circle ]
Can we make a planar continuation of a triangle?
Can we make a planar continuation of a triangle?