def setSurface(self):
# Crea i valori immagine per la superficie, calcolando su ogni punto della plotTriangulation il valore della superficie di Bezier triangolare sul triangolo PS al quale il punto appartiene.
# Raffinamento uniforme della triangolazione Powell_Sabin ai fini del plottaggio.
refiner = UniformTriRefiner(self.domain.PowellSabinTr)
self.plotTriangulation, self.TrIndex = refiner.refine_triangulation(
return_tri_index=True, subdiv=4)
# Salvo i punti della triangolazione iniziale in un solo array.
self.plotPoints = np.array(
list(zip(self.plotTriangulation.x, self.plotTriangulation.y)))
# Inizializzo l'array delle ordinate.
plotHeights = []
for point_index in range(len(self.plotPoints)):
point = self.plotPoints[point_index]
# Ricerco il triangolo PS al quale appartiene il punto.
m = self.TrIndex[point_index]
triangle = self.domain.PS_triangles[m]
tr_vertexes = np.array(
[self.domain.PS_points[i] for i in triangle])
# Ricavo le coordinate baricentriche bc del punto rispetto al triangolo PS.
bc = self.getBarycentricCoords(tr_vertexes, point)
# Calcolo l'ordinata associata al punto.
plotHeights.append(self.triDeCasteljau(m, (0, 0, 0), bc, 3))
# Salvo array delle ordinate.
self.plotHeights = np.array(plotHeights)
def plot_simplex(self, num_contours: int = 100, num_sub_div: int = 8,
color_map: str = 'viridis', border: bool = True,
ax: Optional[Axes] = None,
**kwargs) -> Axes:
"""
Plot a 3-dimensional functions as a simplex heat-map.
:param num_contours: The number of levels of contours to plot.
:param num_sub_div: Number of recursive subdivisions to create.
:param color_map: Optional colormap for the plot.
:param border: Whether to plot a border around the simplex heat-map.
:param ax: Optional matplotlib axes to plot on.
:param kwargs: Additional arguments for tricontourf method.
"""
corners = array([[0, 0], [1, 0], [0.5, 0.75 ** 0.5]])
triangle = Triangulation(corners[:, 0], corners[:, 1])
mid_points = [
(corners[(i + 1) % 3] + corners[(i + 2) % 3]) / 2
for i in range(3)
]
def to_barycentric(cartesian):
"""
Converts 2D Cartesian to barycentric coordinates.
:param cartesian: A length-2 sequence containing the x and y value.
"""
s = [(corners[i] - mid_points[i]).dot(
cartesian - mid_points[i]
) / 0.75
for i in range(3)]
s_clipped = clip(a=s, a_min=0, a_max=1)
return s_clipped / norm(s_clipped, ord=1)
refiner = UniformTriRefiner(triangle)
tri_mesh = refiner.refine_triangulation(subdiv=num_sub_div)
f = [self._method(to_barycentric(xy))
for xy in zip(tri_mesh.x, tri_mesh.y)]
ax = ax or new_axes()
ax.tricontourf(tri_mesh, f, num_contours, cmap=color_map, **kwargs)
ax.set_aspect('equal')
ax.set_xlim(0, 1)
ax.set_ylim(0, 0.75 ** 0.5)
ax.set_axis_off()
if border:
ax.triplot(triangle, linewidth=1)
return ax
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
try:
from matplotlib.tri import Triangulation, UniformTriRefiner
except ImportError:
raise RuntimeError("Matplotlib not importable, is it installed?")
if function.function_space().mesh().ufl_cell() == Cell('triangle'):
x = np.array([0, 0, 1])
y = np.array([0, 1, 0])
elif function.function_space().mesh().ufl_cell() == Cell('quadrilateral'):
x = np.array([0, 0, 1, 1])
y = np.array([0, 1, 0, 1])
else:
raise RuntimeError("Unsupported Functionality")
base_tri = Triangulation(x, y)
refiner = UniformTriRefiner(base_tri)
sub_triangles = int(log(num_sample_points, 4))
tri = refiner.refine_triangulation(False, sub_triangles)
triangles = tri.get_masked_triangles()
x_ref = tri.x
y_ref = tri.y
num_verts = triangles.max() + 1
num_cells = function.function_space().cell_node_list.shape[0]
ref_points = np.dstack([x_ref, y_ref]).reshape(-1, 2)
z_vals = _calculate_values(function, ref_points, 2)
coords_vals = _calculate_values(function.function_space().
mesh().coordinates,
ref_points, 2)
Z = z_vals.reshape(-1)
X = coords_vals.reshape(-1, 2).T[0]
Y = coords_vals.reshape(-1, 2).T[1]
add_idx = np.arange(num_cells).reshape(-1, 1, 1) * num_verts
all_triangles = (triangles + add_idx).reshape(-1, 3)
triangulation = Triangulation(X, Y, triangles=all_triangles)
return triangulation, Z
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
try:
from matplotlib.tri import Triangulation, UniformTriRefiner
except ImportError:
raise RuntimeError("Matplotlib not importable, is it installed?")
if function.function_space().mesh().ufl_cell() == Cell('triangle'):
x = np.array([0, 0, 1])
y = np.array([0, 1, 0])
elif function.function_space().mesh().ufl_cell() == Cell('quadrilateral'):
x = np.array([0, 0, 1, 1])
y = np.array([0, 1, 0, 1])
else:
raise RuntimeError("Unsupported Functionality")
base_tri = Triangulation(x, y)
refiner = UniformTriRefiner(base_tri)
sub_triangles = int(log(num_sample_points, 4))
tri = refiner.refine_triangulation(False, sub_triangles)
triangles = tri.get_masked_triangles()
x_ref = tri.x
y_ref = tri.y
num_verts = triangles.max() + 1
num_cells = function.function_space().cell_node_list.shape[0]
ref_points = np.dstack([x_ref, y_ref]).reshape(-1, 2)
z_vals = _calculate_values(function, ref_points, 2)
coords_vals = _calculate_values(function.function_space().
mesh().coordinates,
ref_points, 2)
Z = z_vals.reshape(-1)
X = coords_vals.reshape(-1, 2).T[0]
Y = coords_vals.reshape(-1, 2).T[1]
add_idx = np.arange(num_cells).reshape(-1, 1, 1) * num_verts
all_triangles = (triangles + add_idx).reshape(-1, 3)
triangulation = Triangulation(X, Y, triangles=all_triangles)
return triangulation, Z
