def _two_dimension_triangle_func_val(function, num_sample_points):
"""Calculate the triangulation and function values for a given 2D function
:arg function: 2D function
:arg num_sample_points: Number of sampling points. This is not
obeyed exactly, but a linear triangulation is created which
matches it reasonably well.
"""
from math import log
mesh = function.function_space().mesh()
cell = mesh.ufl_cell()
if cell.cellname() == "triangle":
x = np.array([0, 0, 1])
y = np.array([0, 1, 0])
elif cell.cellname() == "quadrilateral":
x = np.array([0, 0, 1, 1])
y = np.array([0, 1, 0, 1])
else:
raise ValueError("Unsupported cell type %s" % cell)
base_tri = matplotlib.tri.Triangulation(x, y)
refiner = matplotlib.tri.UniformTriRefiner(base_tri)
sub_triangles = int(log(num_sample_points, 4))
tri = refiner.refine_triangulation(False, sub_triangles)
triangles = tri.get_masked_triangles()
ref_points = np.dstack([tri.x, tri.y]).reshape(-1, 2)
z_vals = _calculate_values(function, ref_points, 2)
coords_vals = _calculate_values(mesh.coordinates, ref_points, 2)
num_verts = ref_points.shape[0]
num_cells = function.function_space().cell_node_list.shape[0]
add_idx = np.arange(num_cells).reshape(-1, 1, 1) * num_verts
all_triangles = (triangles + add_idx).reshape(-1, 3)
Z = z_vals.reshape(-1)
X = coords_vals.reshape(-1, mesh.geometric_dimension())
return X, Z, all_triangles
def _setup_nd(self, mesh, num_sample_points):
cell_name = mesh.ufl_cell().cellname()
if cell_name == "triangle":
x = np.array([0, 0, 1])
y = np.array([0, 1, 0])
elif cell_name in ["quadrilateral", "interval * interval"]:
x = np.array([0, 0, 1, 1])
y = np.array([0, 1, 0, 1])
else:
raise ValueError(f"Unsupported cell type {cell_name}")
# First, create the *reference points* -- a triangulation and points in
# a single reference cell of the mesh, which will be coarser or denser
# depending on how many sample points were specified.
base_tri = matplotlib.tri.Triangulation(x, y)
refiner = matplotlib.tri.UniformTriRefiner(base_tri)
sub_triangles = int(math.log(num_sample_points, 4))
tri = refiner.refine_triangulation(False, sub_triangles)
triangles = tri.get_masked_triangles()
self._reference_points = np.column_stack((tri.x, tri.y))
# Now create a matching triangulation of the whole domain.
num_vertices = self._reference_points.shape[0]
num_cells = mesh.coordinates.function_space().cell_node_list.shape[0]
add_idx = np.arange(num_cells).reshape(-1, 1, 1) * num_vertices
all_triangles = (triangles + add_idx).reshape(-1, 3)
coordinate_values = self(mesh.coordinates)
X = coordinate_values.reshape(-1, mesh.geometric_dimension())
coords = toreal(X, "real")
if mesh.geometric_dimension() == 2:
x, y = coords[:, 0], coords[:, 1]
self.triangulation = matplotlib.tri.Triangulation(
x, y, triangles=all_triangles)
elif mesh.geometric_dimension() == 3:
self.coordinates = coords
self.triangles = all_triangles