I think this is a GEOS bug due to roundoff errors, but the following
assertion (interpolated points should intersect the lines from which
they were interpolated) fails. I'll investigate the issue with the GEOS
people. Also, sorry if I haven't responded to emails; I'll catch up as
soon.
from shapely.wkt import loads
m = loads("""MULTILINESTRING ((336700.9845364579814486
1738886.2085458301007748, 343584.4261802079854533
1738555.8341833299491554), (343584.4261802079854533
1738555.8341833299491554, 350539.0000000000000000
1736135.0000000000000000), (350539.0000000000000000
1736135.0000000000000000, 353532.0000000000000000
1733674.0000000000000000))""")
p = loads("""POINT (344705.7704083333374001 1737219.7509562498889863)""")
assert m.intersects(m.interpolate(m.project(p))) == True
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