Tolerances

In this example, we demonstrate how geometry tolerances can affect meshing.

from qtcad.builder import Builder
from qtcad.builder import Mask, Polygon

First we create a mask with three shapes: a large base rectangle and two smaller rectangles that touch each other.

base = Polygon.box(10, 10).centered()
insert_left = Polygon.box(4, 4).centered().translated(-2, 0)
insert_right = insert_left.translated(4, 0).auto_name()

mask = Mask("shapes", shapes=[base, insert_left, insert_right])

[15:24:17] INFO     Auto-named Polygon instance to 'base'              masks.py:231
           INFO     Auto-named Polygon instance to 'insert_left'       masks.py:231
           INFO     Auto-named Polygon instance to 'insert_right'      masks.py:231

Next we define a function that creates a mesh with a given geometry tolerance and a gap between the two smaller rectangles.

def test_tolerances(tol, gap):
    builder = (
        Builder()
        .set_geometry_tolerance(tol)
        .add_mask(mask)
        .use_shape("base")
        .add_surface()
        .use_shape("insert_left")
        .add_surface()
        .use_shape("insert_right")
        .copy_shape("insert_right_gapped", translate=(gap, 0))
        .add_surface()
        .mesh(2, show_gmsh_output=True)
    )

    entities = set(builder.get_all_entities(0))

    print("Points:", entities)
    return builder, entities

We can now create two meshes, one with tight tolerances and one with loose tolerances. We visualize the meshes and print the points in each case.

In the case where the tolerance is smaller than the gap between the two smaller rectangles, the two rectangles are treated as separate entities and the mesh reflects that.

builder, tight_points = test_tolerances(tol=1e-4, gap=1e-2)
builder.view(
    surface_labels=True,
    save="figs/tolerances_tight.svg",  # caption: With tight tolerances the two touching lines are separated by an invisible gap;
)

Fig. 7 With tight tolerances the two touching lines are separated by an invisible gap

           INFO     Selected shapes: [Polygon 0 'base']              builder.py:854
           INFO     Creating a surface from shape 0 with name       builder.py:2500
                    'base' from mask 'shapes' at z=0
           INFO     Creating new physical group with name 'base'    builder.py:2580
           INFO     Selected shapes: [Polygon 1 'insert_left']       builder.py:854
           INFO     Creating a surface from shape 1 with name       builder.py:2500
                    'insert_left' from mask 'shapes' at z=0
           INFO     Fragmenting...                                fragmenter.py:218
           INFO     Creating new physical group with name           builder.py:2580
                    'insert_left'
           INFO     Selected shapes: [Polygon 2 'insert_right']      builder.py:854
           INFO     Creating a surface from shape 3 with name       builder.py:2500
                    'insert_right_gapped' from mask 'shapes' at z=0
           INFO     Fragmenting...                                fragmenter.py:218
           INFO     Creating new physical group with name           builder.py:2580
                    'insert_right_gapped'
           INFO     Preparing to mesh                               builder.py:1561
           INFO     Detecting appropriate random factor             builder.py:3681
           INFO     Increased random factor from 1e-09 to           builder.py:3699
                    1.4802974253785605e-08
           INFO     Random factor is now appropriate                builder.py:3705
           INFO     Meshing                                         builder.py:1577
Points: {(0, 1), (0, 7), (0, 4), (0, 10), (0, 3), (0, 9), (0, 6), (0, 12), (0, 2), (0, 5), (0, 8), (0, 11)}
           INFO     Saving figure                                   builder.py:1926

<qtcad.builder.builder.Builder object at 0x75dd41c3c2d0>

In the case where the tolerance is larger than the gap, the two rectangles are merged into a single entity and again the mesh reflects that.

builder, loose_points = test_tolerances(tol=1e-1, gap=1e-2)
builder.view(
    surface_labels=True,
    save="figs/tolerances_loose.svg",  # caption: With loose tolerances the two touching lines are merged into one.;
)

Fig. 8 With loose tolerances the two touching lines are merged into one.

           INFO     Selected shapes: [Polygon 0 'base']              builder.py:854
           INFO     Creating a surface from shape 0 with name       builder.py:2500
                    'base' from mask 'shapes' at z=0
           INFO     Creating new physical group with name 'base'    builder.py:2580
           INFO     Selected shapes: [Polygon 1 'insert_left']       builder.py:854
           INFO     Creating a surface from shape 1 with name       builder.py:2500
                    'insert_left' from mask 'shapes' at z=0
           INFO     Fragmenting...                                fragmenter.py:218
           INFO     Creating new physical group with name           builder.py:2580
                    'insert_left'
           INFO     Selected shapes: [Polygon 2 'insert_right']      builder.py:854
           INFO     Creating a surface from shape 3 with name       builder.py:2500
                    'insert_right_gapped' from mask 'shapes' at z=0
           INFO     Fragmenting...                                fragmenter.py:218
           INFO     Creating new physical group with name           builder.py:2580
                    'insert_right_gapped'
           INFO     Preparing to mesh                               builder.py:1561
           INFO     Detecting appropriate random factor             builder.py:3681
           INFO     Random factor is now appropriate                builder.py:3705
           INFO     Meshing                                         builder.py:1577
Points: {(0, 1), (0, 7), (0, 4), (0, 10), (0, 3), (0, 9), (0, 6), (0, 2), (0, 5), (0, 8)}
           INFO     Saving figure                                   builder.py:1926

<qtcad.builder.builder.Builder object at 0x75dd41c3cb90>

Finally, we can see the difference in points between the two meshes. The tighter mesh has two extra points:

print(tight_points - loose_points)

{(0, 12), (0, 11)}