def test_plot_basis_function():
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
U = np.array([0, 0, 0, 0, 1,1,1, 2, 3, 4, 4, 4, 4])
resolution = 1000
degree = len(np.where(U == 0.)[0]) - 1
N, der = basis_function_array_nurbs(U,
degree,
resolution,
None)
fig = plt.figure()
ax = plt.gca()
ax.plot(N)
fig.show()
def get_basis_function(self, direction: int = 0, resolution=None):
"""
Obtain the basis functions and derivatives of the knot vector at desired direction
Args:
direction: parametric direction of knot vector
resolution: amount of points to form the basis function
Returns:
"""
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
N, dN = basis_function_array_nurbs(
self.knots[direction], self.degree[direction],
resolution if resolution is not None else self.resolution,
self.weight)
return N, dN
def test_make_NURB_biquadratic():
from pygeoiga.nurb.cad import make_surface_biquadratic
knots, B = make_surface_biquadratic()
from pygeoiga.plot.nrbplotting_mpl import create_figure, p_cpoints, p_knots, p_curve, p_surface
fig, [ax2, ax] = plt.subplots(1, 2, sharey=True, figsize=(7, 3))
ax = p_knots(knots, B, ax=ax, dim=2, point=False, line=True, color="k")
ax = p_surface(knots,
B,
ax=ax,
dim=2,
color="blue",
border=False,
alpha=0.5)
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("x")
#ax.annotate("1", (-1, 1), fontsize=20)
#ax.annotate("2", (1.6, 3), fontsize=20)
ax.set_aspect(0.8)
ax2 = p_cpoints(B,
ax=ax2,
dim=2,
color="blue",
linestyle="-",
point=False,
line=True)
ax2 = p_cpoints(B,
ax=ax2,
dim=2,
color="red",
marker="s",
point=True,
line=False)
n, m = B.shape[0], B.shape[1]
P = np.asarray([(B[x, y, 0], B[x, y, 1]) for x in range(n)
for y in range(m)])
for count, point in enumerate(P):
ax2.annotate("$P_{%s}$" % str(count),
point,
fontsize=8,
xytext=(3, 7),
textcoords="offset points")
ax2.spines["right"].set_visible(False)
ax2.spines["top"].set_visible(False)
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.set_aspect(0.8)
fig.show()
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
fig3 = plt.figure(constrained_layout=True)
gs = fig3.add_gridspec(2,
2,
hspace=0,
wspace=0,
width_ratios=[0.2, 1],
height_ratios=[1, 0.2])
(ax_v, ax3), (no, ax_u) = gs.subplots(sharex=True, sharey=True)
no.remove()
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_u.plot(resol, N_spline_u)
ax_u.spines["top"].set_visible(False)
ax_u.spines["right"].set_visible(False)
ax_u.set_xlim(0, 1)
ax_u.set_ylim(0, 1)
ax_v.plot(N_spline_v, resol)
ax_v.spines["top"].set_visible(False)
ax_v.spines["right"].set_visible(False)
ax_v.set_yticks(knots[2:-2])
ax_v.set_xlim(1, 0)
ax_v.set_ylim(0, 1)
for i in knots[0]:
ax3.vlines(i, 0, 1, 'k')
for j in knots[1]:
ax3.hlines(j, 0, 1, 'k')
ax3.set_xlim(0, 1)
ax3.set_ylim(0, 1)
ax3.set_axis_off()
ax_u.set_xlabel("$u$")
ax_v.set_ylabel("$v$")
ax_v.set_yticks(knots[1][2:-2])
ax_u.set_xticks(knots[0][2:-2])
for ax in ax_u, ax_v, ax3, no:
ax.label_outer()
fig3.show()
save = True
if save or save_all:
fig.savefig(fig_folder + "B-spline_biquadratic.pdf", **kwargs_savefig)
fig3.savefig(fig_folder + "B-spline_biquadratic_parameter.pdf",
**kwargs_savefig)
def plot(B, knots, file_name):
from pygeoiga.plot.nrbplotting_mpl import create_figure, p_cpoints, p_knots, p_curve, p_surface
fig, ax = plt.subplots(constrained_layout=True)
ax = p_knots(knots, B, ax=ax, dim=2, point=False, line=True, color="k")
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
ax.plot(0.7, 3, "r*", markersize=10)
fig.tight_layout(pad=0, h_pad=0, w_pad=0)
fig.show()
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
fig2 = plt.figure(constrained_layout=True)
gs = fig2.add_gridspec(2,
2,
hspace=0,
wspace=0,
width_ratios=[0.2, 1],
height_ratios=[1, 0.2])
(ax_v, ax2), (no, ax_u) = gs.subplots(sharex=True, sharey=True)
no.remove()
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_u.plot(resol, N_spline_u)
ax_u.spines["top"].set_visible(False)
ax_u.spines["right"].set_visible(False)
ax_u.set_xlim(0, 1)
ax_u.set_ylim(0, 1)
ax_v.plot(N_spline_v, resol)
ax_v.spines["top"].set_visible(False)
ax_v.spines["right"].set_visible(False)
ax_v.set_yticks(knots[2:-2])
ax_v.set_xlim(1, 0)
ax_v.set_ylim(0, 1)
for i in knots[0]:
ax2.vlines(i, 0, 1, 'k')
for j in knots[1]:
ax2.hlines(j, 0, 1, 'k')
ax2.set_xlim(0, 1)
ax2.set_ylim(0, 1)
ax2.set_axis_off()
ax2.plot(0.65, 0.45, "r*", markersize=10)
ax_u.set_xlabel("$u$")
ax_v.set_ylabel("$v$")
ax_v.set_yticks(knots[1][2:-2])
ax_u.set_xticks(knots[0][2:-2])
for ax in ax_u, ax_v, ax2, no:
ax.label_outer()
fig2.show()
fig3, ax3 = plt.subplots()
ax3.vlines(-1, -1, 1, 'k')
ax3.vlines(1, -1, 1, 'k')
ax3.hlines(-1, -1, 1, 'k')
ax3.hlines(1, -1, 1, 'k')
ax3.spines['left'].set_position('center')
ax3.spines['bottom'].set_position('center')
# Eliminate upper and right axes
ax3.spines['right'].set_visible(False)
ax3.spines['top'].set_visible(False)
# Show ticks in the left and lower axes only
ax3.xaxis.set_ticks_position('bottom')
ax3.yaxis.set_ticks_position('left')
ax3.set_xlabel(r"$\xi $", fontsize=15)
ax3.set_ylabel(r"$\eta$", rotation=0, fontsize=15)
ax3.xaxis.set_label_coords(1.05, 0.475)
ax3.yaxis.set_label_coords(0.475, 1.05)
ax3.set_yticks([-1, -0.5, 0.5, 1])
ax3.set_xticks([-1, -0.5, 0.5, 1])
ax3.set_aspect("equal")
fig3.show()
save = True
if save or save_all:
fig.savefig(fig_folder + file_name, **kwargs_savefig)
fig2.savefig(
fig_folder + file_name.split(".")[0] + "_parameter.pdf",
**kwargs_savefig)
fig3.savefig(fig_folder + file_name.split(".")[0] + "_element.pdf",
**kwargs_savefig)
def plot(B, knots, file_name):
from pygeoiga.plot.nrbplotting_mpl import create_figure, p_cpoints, p_knots, p_curve, p_surface
fig, [ax2, ax] = plt.subplots(1,
2,
figsize=(10, 5),
constrained_layout=True)
ax = p_knots(knots, B, ax=ax, dim=2, point=False, line=True, color="k")
ax = p_surface(knots,
B,
ax=ax,
dim=2,
color="blue",
border=False,
alpha=0.5)
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
ax2 = p_cpoints(B,
ax=ax2,
dim=2,
color="blue",
linestyle="-",
point=False,
line=True)
ax2 = p_cpoints(B,
ax=ax2,
dim=2,
color="red",
marker="o",
point=True,
line=False)
n, m = B.shape[0], B.shape[1]
ax2.spines["right"].set_visible(False)
ax2.spines["top"].set_visible(False)
ax2.set_xlabel("$x$")
ax2.set_ylabel("$y$", rotation=90)
ax2.set_aspect(0.8)
ax.set_title("Physical space ($x,y$)", fontsize=20)
ax2.set_title("Control net", fontsize=20)
fig.tight_layout(pad=0, h_pad=0, w_pad=0)
fig.show()
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
fig3 = plt.figure(constrained_layout=True)
gs = fig3.add_gridspec(2,
2,
hspace=0,
wspace=0,
width_ratios=[0.2, 1],
height_ratios=[1, 0.2])
(ax_v, ax3), (no, ax_u) = gs.subplots(sharex=True, sharey=True)
no.remove()
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_u.plot(resol, N_spline_u)
ax_u.spines["top"].set_visible(False)
ax_u.spines["right"].set_visible(False)
ax_u.set_xlim(0, 1)
ax_u.set_ylim(0, 1)
ax_v.plot(N_spline_v, resol)
ax_v.spines["top"].set_visible(False)
ax_v.spines["right"].set_visible(False)
ax_v.set_yticks(knots[2:-2])
ax_v.set_xlim(1, 0)
ax_v.set_ylim(0, 1)
for i in knots[0]:
ax3.vlines(i, 0, 1, 'k')
for j in knots[1]:
ax3.hlines(j, 0, 1, 'k')
ax3.set_xlim(0, 1)
ax3.set_ylim(0, 1)
ax3.set_axis_off()
ax3.set_title("Parametric space ($u,v$)", fontsize=20)
ax_u.set_xlabel("$u$")
ax_v.set_ylabel("$v$")
ax_v.set_yticks(knots[1][2:-2])
ax_u.set_xticks(knots[0][2:-2])
for ax in ax_u, ax_v, ax3, no:
ax.label_outer()
fig3.show()
save = False
if save or save_all:
fig.savefig(fig_folder + file_name, **kwargs_savefig)
fig3.savefig(
fig_folder + file_name.split(".")[0] + "_parameter.pdf",
**kwargs_savefig)
def test_image_example2():
from pygeoiga.nurb.cad import make_surface_biquadratic
knots, B = make_surface_biquadratic()
from pygeoiga.nurb.refinement import knot_insertion
knot_ins_1 = [0.3, 0.6]
knot_ins_0 = [0.25, 0.75]
B, knots = knot_insertion(B, (2, 2), knots, knot_ins_0, direction=0)
B, knots = knot_insertion(B, (2, 2), knots, knot_ins_1, direction=1)
before = B
from pygeoiga.plot.nrbplotting_mpl import create_figure, p_cpoints, p_knots, p_curve, p_surface
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
fig = plt.figure(constrained_layout=True)
gs = fig.add_gridspec(3,
3,
hspace=0,
wspace=0,
width_ratios=[0.2, 0.2, 1],
height_ratios=[1, 0.2, 0.2])
(ax_bv, ax_v, ax2), (no1, no2, ax_u), (no3, no4,
ax_bu) = gs.subplots(sharex=True,
sharey=True)
for no in no1, no2, no3, no4:
no.remove()
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_u.plot(resol, N_spline_u)
ax_u.spines["top"].set_visible(False)
ax_u.spines["right"].set_visible(False)
ax_u.set_xlim(0, 1)
ax_u.set_ylim(0, 1)
ax_v.plot(N_spline_v, resol)
ax_v.spines["top"].set_visible(False)
ax_v.spines["right"].set_visible(False)
ax_v.set_yticks(knots[2:-2])
ax_v.set_xlim(0, 1)
ax_v.set_ylim(0, 1)
ax_u.set_xlabel("$u$")
ax_v.set_ylabel("$v$")
ax_v.set_xlabel("$N(v)$")
ax_u.set_ylabel("$N(u)$")
ax_v.set_yticks(knots[1][2:-2])
ax_u.set_xticks(knots[0][2:-2])
for i in knots[0]:
ax2.vlines(i, 0, 1, 'k')
for j in knots[1]:
ax2.hlines(j, 0, 1, 'k')
ax2.set_xlim(0, 1)
ax2.set_ylim(0, 1)
ax2.set_axis_off()
fig2, ax = plt.subplots(constrained_layout=True)
ax = p_cpoints(B,
ax=ax,
dim=2,
point=False,
line=True,
color="black",
linestyle="-")
ax = p_cpoints(B, ax=ax, dim=2, point=True, line=False, color="red")
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
fig2.tight_layout(pad=0, h_pad=0, w_pad=0)
fig2.show()
from pygeoiga.nurb.refinement import knot_insertion
knot_ins_1 = [0.3, 0.6]
knot_ins_0 = [0.25, 0.5, 0.75]
B, knots = knot_insertion(B, (2, 2), knots, knot_ins_0, direction=0)
B, knots = knot_insertion(B, (2, 2), knots, knot_ins_1, direction=1)
new = B
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_bu.plot(resol, N_spline_u)
ax_bu.spines["top"].set_visible(False)
ax_bu.spines["right"].set_visible(False)
ax_bu.set_xlim(0, 1)
ax_bu.set_ylim(0, 1)
ax_bv.plot(N_spline_v, resol)
ax_bv.spines["top"].set_visible(False)
ax_bv.spines["right"].set_visible(False)
ax_bv.set_yticks(knots[2:-2])
ax_bv.set_xlim(0, 1)
ax_bv.set_ylim(0, 1)
ax_bu.set_xlabel("$u$")
ax_bv.set_ylabel("$v$")
ax_bv.set_xlabel("$B(v)$")
ax_bu.set_ylabel("$B(u)$")
ax_bv.set_yticks(knots[1][2:-2])
ax_bu.set_xticks(knots[0][2:-2])
#for ax in ax_u, ax_v, ax2, no, ax_bu, ax_bv:
# ax.label_outer()
fig2.show()
degree_u = len(np.where(knots[0] == 0.)[0]) - 1
degree_v = len(np.where(knots[1] == 0.)[0]) - 1
n_xi = len(knots[0]) - degree_u - 3
n_eta = len(knots[1]) - degree_v - 3
from pygeoiga.analysis.common import IEN_element_topology, transform_matrix_B
IEN = IEN_element_topology(n_xi, n_eta, degree_u)
P, W = transform_matrix_B(B)
fig3, ax = plt.subplots(constrained_layout=True)
for i in range(0, n_xi, 2):
pos = IEN[i::n_xi]
for e in pos[::2]:
# cont = np.hstack([IEN[0][:degree_u+1], IEN[0][degree_u+3], np.flip(IEN[0][-degree_u-1:]), IEN[0][degree_u+1], IEN[0][0]])
cont = np.hstack([
e[:degree_u + 1], e[degree_u + 3],
np.flip(e[-degree_u - 1:]), e[degree_u + 1], e[0]
])
ax.plot(P[cont][:, 0],
P[cont][:, 1],
linestyle="-",
color="black",
marker=None)
ax = p_cpoints(B, ax=ax, dim=2, point=True, line=False, color="red")
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
fig3.tight_layout(pad=0, h_pad=0, w_pad=0)
fig.show()
fig2.show()
fig3.show()
fig_0, ax = plt.subplots(constrained_layout=True)
ax = p_knots(knots, B, ax=ax, dim=2, point=False, line=True, color="k")
ax = p_surface(knots,
B,
ax=ax,
dim=2,
fill=True,
border=False,
color="gray",
alpha=0.5)
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
fig_0.tight_layout(pad=0, h_pad=0, w_pad=0)
fig_0.show()
save = False
if save or save_all:
fig.savefig(fig_folder + "bezier_extraction.pdf", **kwargs_savefig)
fig_0.savefig(fig_folder + "curve_original.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "control_original.pdf", **kwargs_savefig)
fig3.savefig(fig_folder + "control_bezier.pdf", **kwargs_savefig)
def plot(B, knots, file_name):
from pygeoiga.plot.nrbplotting_mpl import create_figure, p_cpoints, p_knots, p_curve, p_surface
fig, ax = plt.subplots(constrained_layout=True)
ax = p_knots(knots, B, ax=ax, dim=2, point=False, line=True, color="k")
ax = p_cpoints(B, ax=ax, dim=2, point=True, line=True, color="red")
ax.spines["right"].set_visible(False)
ax.spines["top"].set_visible(False)
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_aspect(0.8)
fig.tight_layout(pad=0, h_pad=0, w_pad=0)
fig.show()
from pygeoiga.engine.NURB_engine import basis_function_array_nurbs
fig2 = plt.figure(constrained_layout=True)
gs = fig2.add_gridspec(2,
2,
hspace=0,
wspace=0,
width_ratios=[0.2, 1],
height_ratios=[1, 0.2])
(ax_v, ax2), (no, ax_u) = gs.subplots(sharex=True, sharey=True)
no.remove()
N_spline_u, _ = basis_function_array_nurbs(knot_vector=knots[0],
degree=2,
resolution=100)
N_spline_v, _ = basis_function_array_nurbs(knot_vector=knots[1],
degree=2,
resolution=100)
resol = np.linspace(0, 1, 100)
ax_u.plot(resol, N_spline_u)
ax_u.spines["top"].set_visible(False)
ax_u.spines["right"].set_visible(False)
ax_u.set_xlim(0, 1)
ax_u.set_ylim(0, 1)
ax_v.plot(N_spline_v, resol)
ax_v.spines["top"].set_visible(False)
ax_v.spines["right"].set_visible(False)
ax_v.set_yticks(knots[2:-2])
ax_v.set_xlim(1, 0)
ax_v.set_ylim(0, 1)
for i in knots[0]:
ax2.vlines(i, 0, 1, 'k')
for j in knots[1]:
ax2.hlines(j, 0, 1, 'k')
ax2.set_xlim(0, 1)
ax2.set_ylim(0, 1)
ax2.set_axis_off()
ax_u.set_xlabel("$u$")
ax_v.set_ylabel("$v$")
ax_v.set_yticks(knots[1][2:-2])
ax_u.set_xticks(knots[0][2:-2])
for ax in ax_u, ax_v, ax2, no:
ax.label_outer()
fig2.show()
save = False
if save or save_all:
fig2.savefig(fig_folder + file_name, **kwargs_savefig)