FindShortestCurve¶

Finds the shortest curve (minimizing geodesic) between two points on a region. On a circle this is the shorter arc, returned as a Circle arc with exact angles.

$ wo 'FindShortestCurve[Circle[], {1, 0}, {0, 1}]'
Circle[{0, 0}, 1, {0, Pi/2}]

ArcLength of the result is the geodesic distance:

$ wo 'ArcLength[FindShortestCurve[Circle[], {1, 0}, {0, 1}]]'
Pi/2

In a convex solid the shortest curve is the straight segment between the points:

$ wo 'FindShortestCurve[Disk[], {1/10, 4/5}, {-1/2, 0}]'
Line[{{1/10, 4/5}, {-1/2, 0}}]

Curve regions are treated as meshes: interior mesh vertices are returned at machine precision, while the two query points are kept verbatim.

$ wo 'FindShortestCurve[Line[{{1, 0}, {2, 1}, {3, 0}, {4, 1}}], {1, 0}, {3, 0}]'
Line[{{1, 0}, {2., 1.}, {3, 0}}]