def unstructure_mesh(h):
mesh_info = MeshInfo()
# Set the vertices of the domain [0, 1]^3
mesh_info.set_points([
(0,0,0), (1,0,0), (1,1,0), (0,1,0),
(0,0,1), (1,0,1), (1,1,1), (0,1,1),
])
# Set the facets of the domain [0, 1]^3
mesh_info.set_facets([
[0,1,2,3],
[4,5,6,7],
[0,4,5,1],
[1,5,6,2],
[2,6,7,3],
[3,7,4,0],
])
# Generate the tet mesh
mesh = build(mesh_info, max_volume=(h)**3)
point = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
return TetrahedronMesh(point, cell)
def init_mesh(self, n=1, meshtype='tet'):
node = np.array([
[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 1],
[1, 1, 1],
[0, 1, 1]], dtype=np.float)
cell = np.array([
[0, 1, 2, 6],
[0, 5, 1, 6],
[0, 4, 5, 6],
[0, 7, 4, 6],
[0, 3, 7, 6],
[0, 2, 3, 6]], dtype=np.int)
mesh = TetrahedronMesh(node, cell)
mesh.uniform_bisect(n)
mesh.delete_cell(lambda bc: (bc[:, 0] < 0.5) & (bc[:, 1] < 0.5))
return mesh
def init_mesh(self, n=2, meshtype='tet'):
node = 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]],
dtype=np.float64)
cell = np.array([[0, 1, 2, 6], [0, 5, 1, 6], [0, 4, 5, 6],
[0, 7, 4, 6], [0, 3, 7, 6], [0, 2, 3, 6]],
dtype=np.int_)
mesh = TetrahedronMesh(node, cell)
for i in range(n):
mesh.bisect()
NN = mesh.number_of_nodes()
node = mesh.entity('node')
cell = mesh.entity('cell')
bc = mesh.entity_barycenter('cell')
isDelCell = ((bc[:, 0] > 0) & (bc[:, 1] < 0))
cell = cell[~isDelCell]
isValidNode = np.zeros(NN, dtype=np.bool)
isValidNode[cell] = True
node = node[isValidNode]
idxMap = np.zeros(NN, dtype=mesh.itype)
idxMap[isValidNode] = range(isValidNode.sum())
cell = idxMap[cell]
mesh = TetrahedronMesh(node, cell)
mesh.label() # 标记最长边
return mesh
mesh_info.set_facets([
[0, 1, 2, 3],
[4, 5, 6, 7],
[0, 4, 5, 1],
[1, 5, 6, 2],
[2, 6, 7, 3],
[3, 7, 4, 0],
])
# Generate the tet mesh
mesh = build(mesh_info, max_volume=(h)**3)
point = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
tmesh = TetrahedronMesh(point, cell)
# Partition the mesh cells into n parts
edgecuts, parts = metis.part_mesh(tmesh, nparts=n, entity='cell')
point = tmesh.point
edge = tmesh.ds.edge
face = tmesh.ds.face
cell = tmesh.ds.cell
face2cell = tmesh.ds.face2cell
cell2edge = tmesh.ds.cell_to_edge()
face2edge = tmesh.ds.face_to_edge()
isBdPoint = tmesh.ds.boundary_point_flag()
data = {
'Point': point,
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d as a3
from scipy.spatial import Delaunay
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
from fealpy.mesh.TriangleMesh import TriangleMesh
degree = 4
point = np.array(
[[0, 0, 0], [1, 0, 0], [1 / 2, np.sqrt(3) / 2, 0],
[1 / 2, np.sqrt(3) / 6, np.sqrt(6) / 3]],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = TetrahedronMesh(point, cell)
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.set_aspect('equal')
axes.set_axis_off()
edge0 = np.array([(0, 1), (0, 3), (1, 2), (1, 3), (2, 3)], dtype=np.int)
lines = a3.art3d.Line3DCollection(point[edge0], color='k', linewidths=2)
axes.add_collection3d(lines)
edge1 = np.array([(0, 2)], dtype=np.int)
lines = a3.art3d.Line3DCollection(point[edge1],
color='gray',
linewidths=2,
alpha=0.5)
axes.add_collection3d(lines)
#mesh.add_plot(axes, alpha=0.3)
import numpy as np
import mpl_toolkits.mplot3d as a3
import matplotlib.colors as colors
import pylab as pl
import sys
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
from fealpy.functionspace.tools import function_space
degree = int(sys.argv[1])
ax0 = a3.Axes3D(pl.figure())
point = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, -1]],
dtype=np.float)
cell = np.array([[0, 1, 2, 3], [2, 1, 0, 4]], dtype=np.int)
mesh = TetrahedronMesh(point, cell)
V = function_space(mesh, 'Lagrange', degree)
cell2dof = V.cell_to_dof()
ipoints = V.interpolation_points()
mesh.add_plot(ax0)
mesh.find_point(ax0, point=ipoints, showindex=True)
mesh.print()
print('cell2dof:\n', cell2dof)
pl.show()
import numpy as np
import mpl_toolkits.mplot3d as a3
import pylab as pl
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
node = 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]],
dtype=np.float)
cell = np.array([[0, 1, 2, 6], [0, 5, 1, 6], [0, 4, 5, 6], [0, 7, 4, 6],
[0, 3, 7, 6], [0, 2, 3, 6]],
dtype=np.int)
mesh = TetrahedronMesh(node, cell)
mesh.uniform_refine(2)
mesh.print()
fig = pl.figure()
axes = a3.Axes3D(fig)
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
pl.show()
point = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
elif example == 2:
point = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [-0.5, -0.5, 0.5],
[-0.5, -0.5, -0.5]],
dtype=np.float)
cell = np.array([[0, 1, 2, 3], [0, 2, 1, 4]], dtype=np.int)
elif example == 3:
point = np.array([(0.0, -np.sqrt(3) / 3, 0.0), (0.5, np.sqrt(3) / 6, 0.0),
(-0.5, np.sqrt(3) / 6, 0.0), (0.0, 0.0, np.sqrt(6) / 3)],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
tmesh = TetrahedronMesh(point, cell)
#isFreePoint = ~tmesh.ds.boundary_point_flag()
#q0 = tmesh.quality()
#for i in range(100):
# q = tmesh.quality()
# maxq0 = np.max(q)
# print(maxq0)
# print('mean:', np.mean(q))
# point0 = tmesh.point.copy()
# grad = tmesh.grad_quality()
# alpha = 1
# tmesh.point[isFreePoint] -= alpha*grad[isFreePoint]
# maxq1 = np.max(tmesh.quality())
# while (~tmesh.is_valid()) or (maxq1 > maxq0):
# alpha /=2
import mpl_toolkits.mplot3d as a3
import matplotlib.colors as colors
import pylab as pl
import sys
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
ax0 = a3.Axes3D(pl.figure())
point = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1], [0, 0, -1]],
dtype=np.float)
cell = np.array([[0, 1, 2, 3], [0, 2, 1, 4]], dtype=np.int)
mesh = TetrahedronMesh(point, cell)
c, _ = mesh.circumcenter()
mesh.add_plot(ax0)
mesh.find_point(ax0, point=c)
mesh.print()
#ax1 = a3.Axes3D(pl.figure())
#
#point = np.array([
# [-1,-1,-1],
# [ 1,-1,-1],
# [ 1, 1,-1],
# [-1, 1,-1],
# [-1,-1, 1],
# [ 1,-1, 1],
# [ 1, 1, 1],
import pylab as pl
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
#point = np.array([
# [0, 0, 0],
# [1, 0, 0],
# [0, 1, 0],
# [0, 0, 1]], dtype=np.float)
#
#cell = np.array([
# [0, 1, 2, 3]], dtype=np.int)
point = 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]],
dtype=np.float)
cell = np.array([[0, 1, 2, 6], [0, 5, 1, 6], [0, 4, 5, 6], [0, 7, 4, 6],
[0, 3, 7, 6], [0, 2, 3, 6]],
dtype=np.int)
mesh = TetrahedronMesh(point, cell)
for i in range(3):
angle = mesh.dihedral_angle()
print("max:", np.max(angle))
print("min:", np.min(angle))
mesh.uniform_refine()
ax0 = a3.Axes3D(pl.figure())
mesh.add_plot(ax0)
pl.show()
from fealpy.mesh.TriangleMesh import TriangleMesh
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
p1 = np.array([0, 1], dtype=np.float)
c1 = np.array([0, 1], dtype=np.int)
p2 = np.array([(0, 0), (1, 0), (0, 1)], dtype=np.float)
c2 = np.array([(0, 1, 2)], dtype=np.int)
mesh2 = TriangleMesh(p2, c2)
mesh2.print()
p3 = np.array([(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1)], dtype=np.float)
c3 = np.array([(0, 1, 2, 3)], dtype=np.int)
mesh3 = TetrahedronMesh(p3, c3)
fig = plt.figure()
a1 = fig.add_subplot(1, 3, 1)
a2 = fig.add_subplot(1, 3, 2)
a3 = fig.add_subplot(1, 3, 3)
a1.set_title('1-simplex')
a2.set_title('2-simplex')
a3.set_title('3-simplex')
mesh2.add_plot(a2)
#mesh2.find_point(a2, showindex=True)
mesh2.add_plot(a3)
#mesh2.find_point(a3, showindex=True)
import numpy as np
from fealpy.mesh.TetrahedronMesh import TetrahedronMesh
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
node = 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]],
dtype=np.float)
cell = np.array([[0, 1, 2, 6], [0, 5, 1, 6], [0, 4, 5, 6], [0, 7, 4, 6],
[0, 3, 7, 6], [0, 2, 3, 6]],
dtype=np.int)
mesh = TetrahedronMesh(node, cell)
mesh.bisect()
mesh.bisect()
mesh.bisect()
mesh.bisect()
fig = plt.figure()
axes = fig.gca(projection='3d')
mesh.add_plot(axes, alpha=0, showedge=True)
mesh.find_node(axes)
mesh.find_edge(axes)
mesh.find_cell(axes)
plt.show()