def test_refinement():
points_ori = np.array([
[0, 0, 0],
[1, 1, 0],
[2, 0, 0],
# [1,0,0]
])
knot = np.array([0, 0, 0, 1, 1, 1]) # D1
resolution = 500
reso = np.linspace(0, 1, resolution)
nr = gn.NURB(points_ori, [knot])
points = nr.cpoints
B = nr.B
weight = nr.weight
x, y, z = gn.engine.NURB_construction([knot], points, resolution, weight)
basis_fun, derivatives = gn.NURB_engine.basis_function_array_nurbs(
knot, 2, resolution, weight)
fig = make_plot(B, basis_fun, reso, np.asarray([x, y]).T)
knot_ins1 = np.asarray([0.5])
points1, knot1 = gn.nurb.knot_insertion(B, [2], [knot], knot_ins1)
basis_fun1, derivatives1 = gn.NURB_engine.basis_function_array_nurbs(
knot1[0], 2, resolution, weight)
x1, y1, z1 = gn.engine.NURB_construction(knot1, points1, resolution,
weight)
fig1 = make_plot(points1, basis_fun1, reso, np.asarray([x1, y1]).T)
nr2 = gn.NURB(points1, knot1)
points2 = nr2.cpoints
B2 = nr2.B
weight = nr.weight
knot_ins2 = np.asarray([0.3])
points2, knot2 = gn.nurb.knot_insertion(B2, [2], knot1, knot_ins2)
basis_fun2, derivatives2 = gn.NURB_engine.basis_function_array_nurbs(
knot2[0], 2, resolution, weight)
x2, y2, z2 = gn.engine.NURB_construction(knot2, points2, resolution,
weight)
fig2 = make_plot(points2, basis_fun2, reso, np.asarray([x2, y2]).T)
knot_ins3 = np.asarray([0.3, 0.5, 0.7])
points3, knot3 = gn.nurb.knot_insertion(B, [2], [knot], knot_ins3)
basis_fun3, derivatives3 = gn.NURB_engine.basis_function_array_nurbs(
knot3[0], 2, resolution, weight)
x3, y3, z3 = gn.engine.NURB_construction(knot3, points3, resolution,
weight)
fig3 = make_plot(points3, basis_fun3, reso, np.asarray([x3, y3]).T)
save = True
if save or save_all:
fig.savefig(fig_folder + "h_refine_ori.pdf", **kwargs_savefig)
fig1.savefig(fig_folder + "h_refine_1.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "h_refine_2.pdf", **kwargs_savefig)
fig3.savefig(fig_folder + "h_refine_3.pdf", **kwargs_savefig)
def test_knot_refinement():
points_ori = np.array([[0, 0, 0 ], # , 0],
[2, 0.2, 0], # 0],
[0, 1, 0], # , 0],
[2, 1, 0],
[4, 2, 0],
[5, 1, 0],
[3, 0, 0]]) # , 0]])
knot = np.array([0, 0, 0, 0.4, 0.6, 0.8, 0.8, 1, 1, 1])
resolution = 500
reso = np.linspace(0, 1, resolution)
nr = gn.NURB(points_ori, [knot])
points = nr.cpoints
B=nr.B
weight=nr.weight
x, y, z = gn.engine.NURB_construction([knot],points, resolution, weight)
basis_fun, derivatives = gn.NURB_engine.basis_function_array_nurbs(knot, 2, resolution, weight)
fig = make_plot(B, [knot], basis_fun, reso, np.asarray([x, y]).T)
knot_ins1 = np.asarray([0.5])
points1, knot1 = gn.nurb.knot_insertion(B, [2], [knot], knot_ins1)
basis_fun1, derivatives1 = gn.NURB_engine.basis_function_array_nurbs(knot1[0], 2, resolution, weight)
x1, y1, z = gn.engine.NURB_construction(knot1, points1, resolution, weight)
fig1 = make_plot(points1, knot1, basis_fun1, reso, np.asarray([x1, y1]).T)
nr2 = gn.NURB(points1, knot1)
points2 = nr2.cpoints
B2 = nr2.B
weight = nr2.weight
knot_ins2 = np.asarray([0.3])
points2, knot2 = gn.nurb.knot_insertion(B2, [2], knot1, knot_ins2)
basis_fun2, derivatives2 = gn.NURB_engine.basis_function_array_nurbs(knot2[0], 2, resolution, weight)
x2, y2, z = gn.engine.NURB_construction(knot2, points2, resolution, weight)
fig2 = make_plot(points2,knot2, basis_fun2, reso, np.asarray([x2, y2]).T)
nr3 = gn.NURB(points2, knot2)
points3 = nr3.cpoints
B3 = nr3.B
weight = nr3.weight
knot_ins3 = np.asarray([0.9])
points3, knot3 = gn.nurb.knot_insertion(B3, [2], knot2, knot_ins3)
basis_fun3, derivatives3 = gn.NURB_engine.basis_function_array_nurbs(knot3[0], 2, resolution, weight)
x3, y3, z = gn.engine.NURB_construction(knot3, points3, resolution, weight)
fig3 = make_plot(points3, knot3, basis_fun3, reso, np.asarray([x3, y3]).T)
knot_ins4 = np.arange(0.05,1,0.1)
points4, knot4 = gn.nurb.knot_insertion(B, [2], [knot], knot_ins4)
basis_fun4, derivatives4 = gn.NURB_engine.basis_function_array_nurbs(knot4[0], 2, resolution, weight=None)
x4, y4, z = gn.engine.NURB_construction(knot4, points4, resolution, weight)
fig4 = make_plot(points4, knot4, basis_fun4, reso, np.asarray([x4, y4]).T)
def test_degree_refinement():
points_ori = np.array([[0, 0, 0], # , 0],
[2, 0.2, 0], # 0],
[0, 1, 0], # , 0],
[2, 1, 0],
[4, 2, 0],
[5, 1, 0],
[3, 0, 0]]) # , 0]])
knot = np.array([0, 0, 0, 0.4, 0.6, 0.8, 0.8, 1, 1, 1])
resolution=500
reso = np.linspace(0, 1, resolution)
from pygeoiga.nurb.refinement import degree_elevation
nr = gn.NURB(points_ori, [knot])
B, knots = degree_elevation(nr.B, nr.knots, times=1)
basis_fun, derivatives = gn.NURB_engine.basis_function_array_nurbs(knots[0], 3, resolution, weight=None)
x, y, z = gn.engine.NURB_construction(knots, B, resolution, weight=None)
fig3 = make_plot(B[...,:-1], knots, basis_fun, reso, np.asarray([x, y]).T)
B, knots = degree_elevation(B, knots, times=1)
basis_fun, derivatives = gn.NURB_engine.basis_function_array_nurbs(knots[0], 4, resolution, weight=None)
x, y, z = gn.engine.NURB_construction(knots, B, resolution, weight=None)
fig4 = make_plot(B[..., :-1], knots, basis_fun, reso, np.asarray([x, y]).T)
B, knots = degree_elevation(B, knots, times=1)
basis_fun, derivatives = gn.NURB_engine.basis_function_array_nurbs(knots[0], 5, resolution, weight=None)
x, y, z = gn.engine.NURB_construction(knots, B, resolution, weight=None)
fig5 = make_plot(B[..., :-1], knots, basis_fun, reso, np.asarray([x, y]).T)
print(knots)
#array([0. , 0. , 0. , 0. , 0. , 0. , 0.4, 0.4, 0.4, 0.4, 0.6, 0.6, 0.6,
# 0.6, 0.8, 0.8, 0.8, 0.8, 0.8, 1. , 1. , 1. , 1. , 1. , 1. ]),
save = True
if save:
fig3.savefig("3_degree.png", transparent=True)
fig4.savefig("4_degree.png", transparent=True)
fig5.savefig( "5_degree.png", transparent=True)
def test_create2d():
points2D = np.array([[[150, 0, 50], [150, 25, 50], [150, 50, 50],
[140, 50, 50], [140, 25, 50], [140, 0, 50]],
[[150, 0, 30], [150, 25, 30], [150, 50, 30],
[140, 50, 30], [140, 25, 30], [140, 0, 30]],
[[150, 0, 15], [150, 25, 15], [150, 50, 15],
[140, 50, 15], [140, 25, 15], [140, 0, 15]],
[[150, 0, 0], [150, 25, 0], [150, 50, 0],
[140, 50, 0], [140, 25, 0], [140, 0, 0]]])
knot1 = np.array([0, 0, 0, 0, 1, 1, 1, 1]) # D1
knot2 = np.array([0, 0, 0, 0.3, 0.5, 0.7, 1, 1, 1]) #D2
#knot = np.asarray((knot1, knot2))
weight2D = np.array([[[1], [1], [1], [1], [1], [1]],
[[1], [1], [1], [1], [1], [1]],
[[1], [1], [1], [1], [1], [1]],
[[1], [1], [1], [1], [1], [1]]])
resolution = 30
#nurb2 = gn.NURB(points2D,[knot1, knot2],weight2D, resolution=resolution, engine = "c++")
#print(nurb2.model)
#print(nurb2.degree, nurb2.dim)
nurb3 = gn.NURB(points2D, [knot1, knot2],
weight2D,
resolution=resolution,
engine="python")
print(nurb3.model)
print(nurb3.degree, nurb3.dim)
def test_create1d():
points1D = np.array([[30, 0, 15], [30, 5, 15], [30, 10, 15], [25, 10, 15],
[25, 5, 15], [25, 0, 15]])
knot10 = np.array([0, 0, 0, 0.3, 0.5, 0.7, 1, 1, 1]) #D1
weight1D = np.array([[[1], [1], [1], [1], [1], [1]]])
resolution = 30
#nurb1 = gn.NURB(points1D, [knot10], weight1D, resolution=resolution, engine="c++")
#print(nurb1.degree, nurb1.dim)
nurb2 = gn.NURB(points1D, [knot10],
weight1D,
resolution=resolution,
engine="python")
print(nurb2.degree, nurb2.dim)
def test_create3d():
points3D = np.array([
[[[100, 0, 50], [100, 50, 50], [50, 50, 50], [45, 20, 50],
[15, 20, 50], [15, 50, 50]],
[[100, 0, 30], [100, 50, 30], [50, 50, 30], [45, 20, 30],
[15, 20, 30], [15, 50, 30]],
[[100, 0, 15], [100, 50, 15], [50, 50, 15], [45, 20, 15],
[15, 20, 15], [15, 50, 15]],
[[100, 0, 0], [100, 50, 0], [50, 50, 0], [45, 20, 0], [15, 20, 0],
[15, 50, 0]]],
[[[95, 0, 50], [95, 45, 50], [55, 45, 50], [50, 15, 50], [10, 15, 50],
[10, 50, 50]],
[[95, 0, 30], [95, 45, 30], [55, 45, 30], [50, 15, 30], [10, 15, 30],
[10, 50, 30]],
[[95, 0, 15], [95, 45, 15], [55, 45, 15], [50, 15, 15], [10, 15, 15],
[10, 50, 15]],
[[95, 0, 0], [95, 45, 0], [55, 45, 0], [50, 15, 0], [10, 15, 0],
[10, 50, 0]]],
[[[90, 0, 50], [90, 40, 50], [60, 40, 50], [55, 10, 50], [5, 10, 50],
[5, 50, 50]],
[[90, 0, 30], [90, 40, 30], [60, 40, 30], [55, 10, 30], [5, 10, 30],
[5, 50, 30]],
[[90, 0, 15], [90, 40, 15], [60, 40, 15], [55, 10, 15], [5, 10, 15],
[5, 50, 15]],
[[90, 0, 0], [90, 40, 0], [60, 40, 0], [55, 10, 0], [5, 10, 0],
[5, 50, 0]]],
[[[85, 0, 50], [85, 35, 50], [65, 35, 50], [60, 5, 50], [0, 5, 50],
[0, 50, 50]],
[[85, 0, 30], [85, 35, 30], [65, 35, 30], [60, 5, 30], [0, 5, 30],
[0, 50, 30]],
[[85, 0, 15], [85, 35, 15], [65, 35, 15], [60, 5, 15], [0, 5, 15],
[0, 50, 15]],
[[85, 0, 0], [85, 35, 0], [65, 35, 0], [60, 5, 0], [0, 5, 0],
[0, 50, 0]]],
])
knot11 = np.array([0, 0, 0, 0, 1, 1, 1, 1]) # D1
knot22 = np.array([0, 0, 0, 0, 1, 1, 1, 1]) #D2
knot33 = np.array([0, 0, 0, 0.3, 0.5, 0.7, 1, 1, 1]) # D3
weight3D = np.ones(
(points3D.shape[0], points3D.shape[1], points3D.shape[2], 1))
knot = np.asarray((knot11, knot22, knot33))
nurb3 = gn.NURB(points3D, knot, weight3D, engine="c++")
print(nurb3.model)
print(nurb3.degree, nurb3.dim)
def test_NURBS_vs_Bspline():
#control = np.array([[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1], [1, 0]])
#weight = np.array(
# [[1], [1 / np.sqrt(2)], [1], [1 / np.sqrt(2)], [1], [1 / np.sqrt(2)], [1], [1 / np.sqrt(2)], [1]])
#knot = np.array([0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4]) # D1
control = np.array([[0, 0], [1, 0], [1, 1], [2, 1], [2, 0]])
weight = np.array([[1], [0.1], [0.1], [0.1], [1]])
knot = np.array([0, 0, 0, 0.5, 0.5, 1, 1, 1]) # D1
resolution = 500
resol = np.linspace(0, 1, resolution)
spline_curve = gn.NURB(control, [knot], resolution=resolution)
NURB_curve = gn.NURB(control, [knot], weight, resolution)
dpi = 200
figsize = (5, 3)
fig, ax = plt.subplots(dpi=dpi, figsize=figsize)
positions_Spline = np.asarray(spline_curve.model).T
positions_NURBS = np.asarray(NURB_curve.model).T
ax.plot(positions_NURBS[..., 0],
positions_NURBS[..., 1],
'b',
label="NURBS curve")
ax.plot(positions_Spline[..., 0],
positions_Spline[..., 1],
'g',
label="B-spline curve")
ax.plot(control[..., 0],
control[..., 1],
color='red',
marker='s',
linestyle='--')
# ax.set_ylim(top=1)
#ax.axis('off')
#ax.set_aspect(0.5)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
for i in range(len(control)):
#if i==0: xytext=(-5, 0)
#else:
xytext = (5, 0)
ax.annotate("$P_{%i}$" % i,
xy=(control[i, 0], control[i, 1]),
xytext=xytext,
textcoords="offset points",
fontsize=15)
#fig.subplots_adjust(wspace=0, hspace=0)
#fig.tight_layout()
#ax.grid(linestyle="--")
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.legend()
fig.show()
#Basis-functions
basis_fun_spline, derivatives_spline = gn.NURB_engine.basis_function_array_nurbs(
knot, 2, resolution)
basis_fun_NURBS, derivatives_NURBS = gn.NURB_engine.basis_function_array_nurbs(
knot, 2, resolution, weight)
fig2, (bas, bas2) = plt.subplots(1, 2, dpi=dpi, figsize=(15, 5))
bas.plot(resol, basis_fun_spline)
bas.spines["top"].set_visible(False)
bas.spines["right"].set_visible(False)
bas.set_xlim(0, 1)
bas.set_ylim(0, 1)
bas.set_xlabel("B-spline basis functions", fontsize=15)
bas2.plot(resol, basis_fun_NURBS)
bas2.spines["top"].set_visible(False)
bas2.spines["right"].set_visible(False)
#bas2.set_xticks([])
bas2.set_xlim(0, 1)
bas2.set_ylim(0, 1)
bas2.set_xlabel(
"NURBS basis functions, $w_{0} = w_{4} = 1$ and $w_{1} = w_{2} = w_{3}= 0.1$",
fontsize=15)
fig2.show()
save = False
if save or save_all:
fig.savefig(fig_folder + "NURBS_vs_BSpline.pdf", **kwargs_savefig)
fig2.savefig(fig_folder + "NURBS_vs_BSpline_basis_functions.pdf",
**kwargs_savefig)