[Python] Having trouble setting mesh size fields so that the mesh has a good transition from...

In my gmsh Python code, which consists of several stacked cylinders and one cylinder inside, I would like to set the meshsize field(s) so that the transitions from fine mesh to coarse mesh is more gradual. I am using the distance and threshold fields in my example code, I can see the effect of DistMin, but DistMax does not seem to change the mesh.

Here is my Python program:

import gmsh
import sys

gmsh.initialize()
gmsh.model.add("converted_geo")

gmsh.model.occ.addCylinder(0.0, 0.0, 35.0, 0.0, 0.0, 30.0, 9.0, tag=1)
gmsh.model.occ.addCylinder(0.0, 0.0, 0.0, 0.0, 0.0, 20.0, 120.0, tag=2)
gmsh.model.occ.addCylinder(0.0, 0.0, 20.0, 0.0, 0.0, 15.0, 120.0, tag=3)
gmsh.model.occ.addCylinder(0.0, 0.0, 35.0, 0.0, 0.0, 15.0, 120.0, tag=4)
gmsh.model.occ.addCylinder(0.0, 0.0, -20.0, 0.0, 0.0, 20.0, 120.0, tag=5)

gmsh.model.occ.synchronize()

# Boolean Fragments
v1 = gmsh.model.occ.fragment([(3, 2)], [(3, 5)])
v2 = gmsh.model.occ.fragment([(3, 3)], [(3, 1), (3, 4)])
v3 = gmsh.model.occ.fragment([(3, 5)], [(3, 2)])
v4 = gmsh.model.occ.fragment([(3, 8)], [(3, 6), (3, 7), (3, 3)])

# Add final large cylinder
gmsh.model.occ.addCylinder(0.0, 0.0, 50.0, 0.0, 0.0, 120.0, 120.0, tag=9)
gmsh.model.occ.synchronize()

# Final Boolean Fragment
v5 = gmsh.model.occ.fragment([(3, 9)], [(3, 2), (3, 3), (3, 5), (3, 6), (3, 7), (3, 8)])
gmsh.model.occ.synchronize()

# Mesh size settings
gmsh.option.setNumber("Mesh.MeshSizeFromPoints", 0)
gmsh.option.setNumber("Mesh.MeshSizeFromCurvature", 25)
gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary", 0)
gmsh.option.setNumber("Mesh.MeshSizeMax", 20.0)
gmsh.option.setNumber("Mesh.MeshSizeMin", 1.0)

# Mesh fields
gmsh.model.mesh.field.add("Distance", 1)
gmsh.model.mesh.field.setNumbers(1, "FacesList", [3,18,19,20,21])
gmsh.model.mesh.field.setNumber(1, "Sampling", 20)


gmsh.model.mesh.field.add("Threshold", 2)
gmsh.model.mesh.field.setNumber(2, "InField", 1)
gmsh.model.mesh.field.setNumber(2, "SizeMin", 1)
gmsh.model.mesh.field.setNumber(2, "SizeMax", 20)
gmsh.model.mesh.field.setNumber(2, "DistMin", 10)
gmsh.model.mesh.field.setNumber(2, "DistMax", 50)


gmsh.model.mesh.field.add("Min", 5)
gmsh.model.mesh.field.setNumbers(5, "FieldsList", [1, 2])
gmsh.model.mesh.field.setAsBackgroundMesh(5)

# Generate mesh
gmsh.model.occ.synchronize()
gmsh.model.mesh.generate(3)

# Optional: Save
gmsh.write("converted_mesh.msh")

# Finalize
if '-nopopup' not in sys.argv:
gmsh.fltk.run()

gmsh.finalize()


I've also tried an extend meshsize field, but I don't think I can combine it with distance, it did not seem to help and seemed to make the mesh generation take longer. Perhaps I am using the wrong meshsize fields or some setting incorrectly. The mesh size change from min to max with my code seems too abrupt, but I do not know how to fix that.

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