UniformOverMesh iso-probabilistic transformation issue

[jschueller]

What happened?

A colleague tried combining UniformOverMesh with LHS, and that should probably not be allowed;
in practice yield points outside of the mesh (from levelset x+y<171):
I doubt we can map the standard space into a mesh yet, even when the mesh is convex
maybe getStandardDistribution should return something else, if that exists :)
what do you think @regislebrun ?

How to reproduce the issue?

import openturns as ot
import openturns.viewer as otv

ot.Log.Show(ot.Log.INFO)
f = ot.SymbolicFunction(['x', 'y'], ['x+y'])
levelSet = ot.LevelSet(f, ot.Less(), 171)
box=ot.Interval([10, 20], [151, 161])
mesh = ot.LevelSetMesher([10]*2).build(levelSet, box, False)
mesh.draw()
distribution = ot.UniformOverMesh(mesh)
sample_mc=distribution.getSample(30)
lhs = ot.LHSExperiment(distribution, 30)
sample_lhs = lhs.generate()
graph_h = distribution.drawPDF()
cloud_h = ot.Cloud(sample_mc, 'MCs')
cloud_lhs = ot.Cloud(sample_lhs, 'lhs')
graph_h.add(cloud_h)
graph_h.add(cloud_lhs)
otv.View(graph_h).save("/tmp/unimesh_lhs.png")

Additional Context

the use-case was to generate a DOE that has low discrepancy properties, but on a weird mesh domain
I advised to generate a larger Sobol/LHS sample inside the mesh box bounds then prune points outside the mesh

[regislebrun]

@jschueller The main problem is the computation of CDF and marginal distributions, mandatory an accurate and efficient Rosenblatt transformation. Unfortunately the two are currently missing 😞

Note that with the new version of MarginalDistribution, it looks like we are progressing. Your script gives: