PyVista visualization capabilities.

This demo is implemented in demo_plot.py and it illustrates:

  • How to create an unfitted implicit domain using the library of available implicit functions.

  • The available PyVista based visualization tools.

This demo requires the FEniCSx and PyVista capabilities of QUGaR.

Geometry definition

First we check that FEniCSx and PyVista installations are available.

import qugar.utils

if not qugar.utils.has_FEniCSx:
    raise ValueError("FEniCSx installation not found is required.")

if not qugar.utils.has_PyVista:
    raise ValueError("PyVista installation not found is required.")

Then the modules and functions to be used are imported:

from typing import cast

from mpi4py import MPI

import numpy as np
import pyvista as pv

import qugar
import qugar.impl
import qugar.mesh
import qugar.plot
import qugar.reparam

Domain definition

We create an unfitted domain using a 3D cylinder defined by a point on the axis, the direction of the revolution axis, and the radius.

func = qugar.impl.create_cylinder(
    radius=0.4, origin=np.array([0.55, 0.45, 0.47]), axis=np.array([1.0, 0.9, -0.95]), use_bzr=True
)

and then generate the unfitted domain using a Cartesian mesh over a hypercube \([0,1]^3\) with 5 cells per direction.

dim = func.dim
n_cells = [5] * dim

mesh = qugar.mesh.create_Cartesian_mesh(
    comm=MPI.COMM_WORLD, n_cells=n_cells, xmin=np.zeros(dim), xmax=np.ones(dim)
)
unf_domain = qugar.impl.create_unfitted_impl_domain(func, mesh)

Visualization

We are going to visualize the quadrature for the unfitted domain, separating the quadrature for the cut cells, unfitted boundaries, and cut facets.

First we create PyVista objects for the quadrature,

quad = qugar.plot.quadrature_to_PyVista(unf_domain, n_pts_dir=3)

quad_cells = cast(pv.UnstructuredGrid, quad.get("Cut cells quadrature"))
quad_unf_bdry = cast(pv.UnstructuredGrid, quad.get("Unfitted boundary quadrature"))
quad_facets = cast(pv.UnstructuredGrid, quad.get("Cut facets quadrature"))

cut and full cells and cut facets of the unfitted domain,

cut_cells = qugar.plot.unfitted_domain_to_PyVista(unf_domain, cut=True, full=False, empty=False)
full_cells = qugar.plot.unfitted_domain_to_PyVista(unf_domain, cut=False, full=True, empty=False)

cut_facets = qugar.plot.unfitted_domain_facets_to_PyVista(
    unf_domain, cut=True, full=False, empty=False
)

and for the reparameterization of the domain’s interior and its levelset boundary

reparam = qugar.reparam.create_reparam_mesh(unf_domain, n_pts_dir=4, levelset=False)
reparam_pv = qugar.plot.reparam_mesh_to_PyVista(reparam)

reparam_srf = qugar.reparam.create_reparam_mesh(unf_domain, n_pts_dir=4, levelset=True)
reparam_srf_pv = qugar.plot.reparam_mesh_to_PyVista(reparam_srf)

We are going to plot the different quadrature points and the reparameterization of the domain’s in different subplots.

  • First, we plot the reparameterization of the domain, splitting the interior and the wirebasket (the lines separating the reparameterization of each cell). We superimpose the cut and full cells.

pl = pv.Plotter(shape=(2, 2))
pl.subplot(0, 0)
pl.add_title("Reparemeterization", font_size=12)
pl.add_mesh(reparam_pv.get("reparam"), color="white")
pl.add_mesh(reparam_pv.get("wirebasket"), color="red", line_width=2)
pl.add_mesh(cut_cells, color="blue", style="wireframe")
pl.add_mesh(full_cells, color="blue", style="wireframe")

  • Second, we plot the quadrature of the cut cells, together with the cut and full cells, and a translucent reparameterization of the domain.

pl.subplot(0, 1)
pl.add_title("Cut cells quadrature", font_size=12)
pl.add_mesh(reparam_pv, opacity=0.25, color="white")
pl.add_mesh(quad_cells, point_size=4, render_points_as_spheres=True)
pl.add_mesh(cut_cells, color="blue", style="wireframe")

  • Third, we plot the quadrature for the unfitted boundary as well as the normal vectors at those points, together with the cut cells, and a translucent reparameterization of the domains unfitted boundary.

pl.subplot(1, 0)
pl.add_title("Unfitted boundary quadrature", font_size=12)
pl.add_mesh(quad_unf_bdry, point_size=4, render_points_as_spheres=True)
pl.add_mesh(cut_cells, color="blue", style="wireframe")
glyphs = quad_unf_bdry.glyph(
    orient="Normals", scale=False, factor=0.05, geom=pv.Arrow(), color_mode="scalar"
)
pl.add_mesh(glyphs)
pl.add_mesh(reparam_srf_pv.get("reparam"), color="white")
pl.add_mesh(reparam_srf_pv.get("wirebasket"), color="blue", line_width=2)

  • Finally, we plot the quadrature for the cut facets together with the cut facets themselves.

pl.subplot(1, 1)
pl.add_title("Cut facets quadrature", font_size=12)
pl.add_mesh(quad_facets, point_size=4, render_points_as_spheres=True)
pl.add_mesh(cut_facets, color="gray", opacity=0.1)
pl.add_mesh(cut_cells, color="blue", style="wireframe")
pl.show()