def figure_10c(**kwargs):
fig = utils.get_figure(.425, aspect_ratio=1 / utils.golden_ratio)
# ax_upper = fig.add_subplot(211)
# ax_lower = fig.add_subplot(212)
ax_upper = fig.add_axes([.2, .6, .75, .25])
ax_lower = fig.add_axes([.2, .1, .75, .25])
axes = (ax_upper, ax_lower)
basis_upper = BSplineBasis([0, 0, 0, 1, 1, 1], polynomial_order=2)
basis_lower = BSplineBasis([0, 0, 0, 1 / 3, 2 / 3, 1, 1, 1],
polynomial_order=2)
bases = (basis_upper, basis_lower)
titles = (
r"$\Xi' = \left\lbrace 0, 0, 0, 1, 1, 1 \right\rbrace, \, p = 2$",
r"$\Xi'' = \left\lbrace 0, 0, 0, \frac{1}{3}, \frac{2}{3}, 1, 1, 1 \right\rbrace, \, p = 2$"
)
method = (r'$p$-refinement \\ (order elevation)',
r'$h$-refinement \\ (knot insertion)')
for ax, basis, title, method in zip(axes, bases, titles, method):
basis.attach_basis_functions(ax)
title_size = 10
ax.set_ylabel(r'$N_{i, \,p}\left(\xi\right)$', fontsize=title_size)
ax.set_xlabel(r'$\xi$', fontsize=title_size)
ax.set_title(title, fontsize=title_size)
ax.set_xlim(0, 1.0)
ax.set_ylim(0, 1.0)
ax.grid(True, **GRID_KWARGS)
ax.annotate(
s=method,
xy=(0.5, 1.275),
xycoords='axes fraction',
xytext=(10, 8),
textcoords='offset points',
fontsize=title_size,
)
ax.annotate(s='',
xy=(0.5, 1.275),
xycoords='axes fraction',
xytext=(0, 25),
textcoords='offset points',
arrowprops=dict(
width=1,
facecolor='black',
headlength=10,
))
# plt.tight_layout()
utils.save_current_figure('fig_10c', tight=False, **kwargs)
plt.close()
def plot_curve_2D(self, fig_scale='full', **kwargs):
"""Only works in 2D..."""
fig = utils.get_figure(fig_scale)
ax = fig.add_subplot(111)
self.attach_curve_2D(ax)
utils.save_current_figure(**kwargs)
plt.close()
def figure_10a(**kwargs):
fig = utils.get_figure('half')
ax = fig.add_subplot(111)
basis = BSplineBasis([0, 0, 1, 1], polynomial_order=1)
basis.attach_basis_functions(ax)
title_size = 10
ax.set_xlabel(r'$\xi$', fontsize=title_size)
ax.set_ylabel(r'$N_{i, \,p}\left(\xi\right)$', fontsize=title_size)
ax.set_title(r'$\Xi = \left\lbrace 0, 0, 1, 1 \right\rbrace, \, p = 1$',
fontsize=title_size)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
ax.grid(True, **GRID_KWARGS)
utils.save_current_figure('fig_10a', **kwargs)
plt.close()
def plot_basis_functions(self,
fig_scale='full',
title=True,
legend_on_right=True,
**kwargs):
fig = utils.get_figure(fig_scale)
ax = fig.add_subplot(111)
self.attach_basis_functions(ax)
ax.set_xlim(self.xi_min, self.xi_max)
ax.set_ylim(0, 1.01)
ax.set_xlabel(r'$\xi$', fontsize=12)
ax.set_ylabel(r'$N_{i,p}(\xi)$', fontsize=12)
if title:
ax.set_title(
fr'Basis Functions for $\Xi = \left\lbrace {",".join(str(s) for s in self.knot_vector)} \right\rbrace$, $p = {self.polynomial_order}$'
)
if legend_on_right:
ax.legend(bbox_to_anchor=(1.02, 1),
loc='upper left',
borderaxespad=0.,
fontsize=12,
handlelength=1,
ncol=1 + (len(self.basis_function_indices) // 15))
else:
ax.legend(loc='upper right', handlelength=1)
ax.grid(True, **GRID_KWARGS)
utils.save_current_figure(name=self.name + '__basis', **kwargs)
plt.close()
def figure_9(**kwargs):
fig = utils.get_figure('full', aspect_ratio=.8)
ax_original_curve = fig.add_subplot(221)
ax_original_basis = fig.add_subplot(223)
ax_new_curve = fig.add_subplot(222)
ax_new_basis = fig.add_subplot(224)
original_basis = BSplineBasis([0, 0, 0, 1, 1, 1], polynomial_order=2)
original_curve = BSplineCurve(original_basis, [(0, 0), (.5, 1), (1, 0)])
title_size = 10
ax_original_curve.set_title(
r'Original Curve: $\Xi = \left\lbrace0, 0, 0, 1, 1, 1\right\rbrace, \; p = 2$',
fontsize=title_size)
ax_original_basis.set_title(r'Original Basis Functions',
fontsize=title_size)
ax_new_curve.set_title(
r"$p$-Refined Curve: $\Xi' = \left\lbrace0, 0, 0, 0, 1, 1, 1, 1\right\rbrace, \; p = 3$",
fontsize=title_size)
ax_new_basis.set_title(r'$p$-Refined Basis Functions', fontsize=title_size)
new_basis = BSplineBasis([0, 0, 0, 0, 1, 1, 1, 1], polynomial_order=3)
new_curve = BSplineCurve(new_basis, [(0, 0), (1 / 3, 2 / 3),
(2 / 3, 2 / 3), (1, 0)])
for ax, basis in ((ax_original_curve, original_curve), (ax_new_curve,
new_curve)):
basis.attach_curve_2D(ax)
ax.set_xlim(-.05, 1.05)
ax.set_ylim(-.05, 1.05)
ax.grid(True, linewidth=.5)
ax.axis('on')
ax.set_xticks((0, 1 / 3, 2 / 3, 1))
ax.set_xticklabels((
r'$0$',
r'$\frac{1}{3}$',
r'$\frac{2}{3}$',
r'$1$',
))
ax.set_yticks((0, 2 / 3, 1))
ax.set_yticklabels((
r'$0$',
r'$\frac{2}{3}$',
r'$1$',
))
for ax, basis in ((ax_original_basis, original_basis), (ax_new_basis,
new_basis)):
basis.attach_basis_functions(ax)
ax.set_xlim(0, 1.0)
ax.set_ylim(0, 1.0)
ax.set_xlabel(r'$\xi$')
ax.grid(True, **GRID_KWARGS)
ax_original_basis.set_ylabel(r'$N_{i, \,p}\left(\xi\right)$')
plt.tight_layout()
utils.save_current_figure('fig_9', **kwargs)
plt.close()
def plot_surface_3D(self, length=30, fps=30, **kwargs):
"""Only works in 3D..."""
fig = utils.get_figure(scale=3)
ax = fig.add_subplot(111, projection='3d')
# surface_x = self.xi_1_mesh
# surface_y = self.xi_2_mesh
# surface_x, surface_y, surface_z = self.surface()
xyz = self.surface()
# surface_x, surface_y = np.meshgrid(surface_x, surface_y)
# print(np.shape(surface_x))
# print(np.shape(surface_y))
# print(np.shape(surface_z))
control_points_x = np.array(
[control_point[0] for control_point in self.control_net.values()])
control_points_y = np.array(
[control_point[1] for control_point in self.control_net.values()])
control_points_z = np.array(
[control_point[2] for control_point in self.control_net.values()])
# x_min = min(np.min(surface_x), np.min(control_points_x))
# x_max = max(np.max(surface_x), np.max(control_points_x))
# x_range = np.abs(x_max - x_min)
#
# y_min = min(np.min(surface_y), np.min(control_points_y))
# y_max = max(np.max(surface_y), np.max(control_points_y))
# y_range = np.abs(y_max - y_min)
#
# z_min = min(np.min(surface_z), np.min(control_points_z))
# z_max = max(np.max(surface_z), np.max(control_points_z))
# z_range = np.abs(z_max - z_min)
#
# ax.set_xlim(x_min - 0.05 * x_range, x_max + 0.05 * x_range)
# ax.set_ylim(y_min - 0.05 * y_range, y_max + 0.05 * y_range)
# ax.set_zlim(z_min - 0.05 * z_range, z_max + 0.05 * z_range)
ax.scatter(control_points_x,
control_points_y,
control_points_z,
depthshade=False,
**CONTROL_POLYGON_KWARGS)
# print(np.max(surface_x), np.max(surface_y), np.max(surface_z))
# print(np.min(surface_x), np.min(surface_y), np.min(surface_z))
# print(surface_x)
# print(surface_y)
# print(surface_z)
xyz = np.reshape(xyz, (-1, 3))
print(xyz.shape)
x, y, z = xyz[:, 0], xyz[:, 1], xyz[:, 2]
ax.scatter(x, y, z)
# ax.plot_trisurf(
# x, y, z,
# cmap = plt.get_cmap('viridis'),
# linewidth = 0,
# antialiased = True,
# )
# ax.plot_surface(surface_x, surface_y, surface_z, rstride = 1, cstride = 1)
# ax.plot_trisurf(surface_x, surface_y, surface_z)
# ax.plot_trisurf(surface_x, surface_y, surface_z, **CURVE_KWARGS)
ax.axis('off')
ax.view_init(
elev=45, azim=0
) # note that this resets ax.dist to 10, so we can't use it below
ax.dist = 7.5 # default is 10, so zoom in a little because there's no axis to take up the rest of the space
plt.show()
utils.save_current_figure(**kwargs)
### ANIMATION ###
frames = length * fps
writer = anim.writers['ffmpeg'](
fps=fps, bitrate=2000) # don't need a very high bitrate
def animate(frame):
print(frame, frames, frame / frames)
ax.azim = 360 * frame / frames # one full rotation
return [
] # must return the list of artists we modified (i.e., nothing, since all we did is rotate the view)
ani = anim.FuncAnimation(fig, animate, frames=frames, blit=True)
ani.save(f"{os.path.join(kwargs['target_dir'], kwargs['name'])}.mp4",
writer=writer)
plt.close()