def coarsen_poly(self, plot=True):
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
isMarkedCell = np.array([0, 0, 0, 1, 0], dtype=np.bool_)
mesh.refine_poly(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 3, 4, 5, 6]] = True
mesh.coarsen_poly(isMarkedCell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh.add_halfedge_plot(axes, showindex=True)
plt.show()
def coarsen_tri(self, maxit=2, method='rg', plot=True, rb=True):
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
mesh.hedgecolor = color
mesh.refine_triangle_rg(isMarkedCell)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if method == 'rg':
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 5, 6, 7, 9]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[0, 1, 2, 3, 4, 5, 6, 7]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.ones(NC, dtype=np.bool_)
print('*************lll*********')
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def data_structure(self, plot=True):
node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float)
cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def refine_halfedge(self, plot=True):
node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float)
cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
isMarkedCell = np.array([0, 1, 0, 0, 0], dtype=np.bool_)
isMarkedHEdge = mesh.mark_halfedge(isMarkedCell)
mesh.refine_halfedge(isMarkedHEdge)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
plt.show()
def coarsen_poly(self, plot=True):
node = np.array([[0,0],[1,0],[1,1],[0,1],[2,0],[2,1]], dtype = np.float)
cell = np.array([[0,1,2],[0,2,3],[1,4,5],[2,1,5]],dtype = np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
isMarkedCell = np.array([0,0,0,1,0], dtype=np.bool_)
mesh.refine_poly(isMarkedCell)
isMarkedCell = np.array([0,0,0,0,1,1,1], dtype=np.bool_)
mesh.coarsen_poly(isMarkedCell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
edge = totalEdge[i0] # 最终的边数组
print('edge:\n', edge)
E = 3 # 每个三角形有 3 条边
NE = edge.shape[0] # 获得网格中边的个数, 即 `edge` 的行数
i1 = np.zeros(NE, dtype=np.int32) # 分配空间
i1[j] = range(3 * NC) # totalEdge0 的行数是 3*NC, j 的长度也是 3*NC
print('i0:\n', i0)
print('i1:\n', i1)
edge2cell = np.zeros((NE, 4), dtype=np.int32)
edge2cell[:, 0] = i0 // E # 得到每条边的左边单元
edge2cell[:, 1] = i1 // E # 得到每条边的右边单元
edge2cell[:, 2] = i0 % E # 得到每条边的在左边单元中的局部编号
edge2cell[:, 3] = i1 % E # 得到每条边在其右边单元中的局部编号
print('edge2cell:\n', edge2cell)
mesh = TriangleMesh(node, cell)
mesh.print()
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
plt.savefig('numpy-mesh-edge.png')
plt.show()
node = mesh.entity('node')
cell = mesh.entity('cell')
tmesh = Tritree(node, cell)
femspace = LagrangeFiniteElementSpace(mesh, p=1)
uI = femspace.interpolation(peak)
estimator = Estimator(uI[:], mesh, 0.2, 0.5)
isExtremeNode = estimator.is_extreme_node()
print(isExtremeNode.sum())
tmesh.adaptive_refine(estimator)
mesh = estimator.mesh
isExtremeNode = estimator.is_extreme_node()
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, index=isExtremeNode)
fig2 = plt.figure()
fig2.set_facecolor('white')
axes = fig2.gca(projection='3d')
x = mesh.node[:, 0]
y = mesh.node[:, 1]
cell = mesh.ds.cell
femspace = LagrangeFiniteElementSpace(mesh, p=1)
uI = femspace.interpolation(peak)
axes.plot_trisurf(x, y, cell, estimator.rho, cmap=plt.cm.jet, lw=0.0)
plt.show()
def refine_triangle_rbTest(self, l, plot=True, rb=True):
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
mesh = TriangleMesh(node, cell)
#mesh.uniform_refine()
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
c = np.array([0.2, 0.2])
r = 1.2
h = 1e-2
k = 0
NB = 0
start = time.time()
while k < l:
halfedge = mesh.ds.halfedge
halfedge1 = halfedge[:, 3]
node = mesh.node
flag = node - c
flag = flag[:, 0]**2 + flag[:, 1]**2
flag = flag <= r**2
flag1 = flag[halfedge[:, 0]].astype(int)
flag2 = flag[halfedge[halfedge1, 0]].astype(int)
markedge = flag1 + flag2 == 1
markedcell = halfedge[markedge, 1]
markedcell = np.unique(markedcell)
cell = np.unique(halfedge[:, 1])
nc = cell.shape[0]
markedcell1 = np.zeros(nc)
markedcell1[markedcell] = 1
if rb:
mesh.refine_triangle_rb(markedcell1)
else:
mesh.refine_triangle_rbg(markedcell1)
k += 1
print('循环', k, '次***************************')
#print('node', node)
#print('cell',cell)
end = time.time()
print(end - start)
if plot:
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
plt.show()
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
cindex = np.arange(mesh.number_of_cells() - 1) + 1
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
NN = mesh.number_of_nodes()
nindex = np.zeros(NN, dtype=np.int)
halfedge = mesh.ds.halfedge
nindex = mesh.nodedata['level']
cindex = mesh.get_data('cell', 'level')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, multiindex=nindex)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
plt.show()
def refine_tri(self, maxit=2, method='rg', plot=True, rb=True):
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
if False:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
#mesh.refine_triangle_rbg(isMarkedCell)
mesh.ds.NV = 3
cell = mesh.ds.cell_to_node()
node = mesh.entity('node')
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
if False:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'rg':
color[[4, 13, 17, 28]] = 1
color[[23, 27]] = 2
color[[22, 26]] = 3
mesh.hedgecolor = color
isMarkedCell = np.array(
[0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool_)
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'nvb':
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
c = np.array([0.8, 0.8])
r = 0.9
h = 1e-2
k = 0
NB = 0
start = time.time()
while k < maxit:
halfedge = mesh.ds.halfedge
halfedge1 = halfedge[:, 3]
node = mesh.node
flag = node - c
flag = flag[:, 0]**2 + flag[:, 1]**2
flag = flag <= r**2
flag1 = flag[halfedge[:, 0]].astype(int)
flag2 = flag[halfedge[halfedge1, 0]].astype(int)
markedge = flag1 + flag2 == 1
markedcell = halfedge[markedge, 1]
markedcell = np.unique(markedcell)
cell = np.unique(halfedge[:, 1])
nc = cell.shape[0]
markedcell1 = np.zeros(nc)
markedcell1[markedcell] = 1
if method == 'rg':
mesh.refine_triangle_rg(markedcell1.astype(np.bool_))
else:
mesh.refine_triangle_nvb(markedcell1.astype(np.bool_))
k += 1
print('循环', k, '次***************************')
end = time.time()
print('用时', end - start)
if plot:
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
#mesh.find_cell(axes, showindex=True)
#print(np.c_[np.arange(len(mesh.hedgecolor)), mesh.hedgecolor])
plt.show()
def test_interpolation_plane(self):
def u(p):
x = p[..., 0]
y = p[..., 1]
return x * y
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
node = mesh.entity('node')
cell = mesh.entity('cell')
tritree = Tritree(node, cell)
mesh = tritree.to_conformmesh()
space = LagrangeFiniteElementSpace(mesh, p=2)
uI = space.interpolation(u)
error0 = space.integralalg.L2_error(u, uI)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
data = tritree.interpolation(uI)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([1, 0], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes, showindex=True)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
error1 = space.integralalg.L2_error(u, uh)
data = tritree.interpolation(uh)
isLeafCell = tritree.is_leaf_cell()
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes,
node=space.interpolation_points(),
showindex=True)
tritree.find_cell(axes, index=isLeafCell, showindex=True)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
maxcoarsen=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([-1, -1, -1, -1, 0, 1], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
mesh.find_cell(axes, showindex=True)
error2 = space.integralalg.L2_error(u, uh)
print(error0)
print(error1)
print(error2)
plt.show()
import numpy as np
from fealpy.mesh import TriangleMesh
import matplotlib.pyplot as plt
node = np.array([[0.0, 0.0], [1.0, 0.0], [0.5, np.sqrt(3) / 2.0]],
dtype=np.float)
cell = np.array([[0, 1, 2]], dtype=np.int32)
localEdge = np.array([[1, 2], [2, 0], [0, 1]], dtype=np.int32)
bc = (node[localEdge[:, 0]] + node[localEdge[:, 1]]) / 2.0
mesh = TriangleMesh(node, cell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
mesh.find_node(axes,
node=bc,
index=np.array([0, 1, 2], dtype=np.int32),
showindex=True,
markersize=150,
color='g')
plt.savefig('localedge.png')
plt.show()
cell = np.array(mesh.elements, dtype = np.int)
tmesh = TriangleMesh(node, cell)
fig = plt.figure()
axes = fig.gca()
tmesh.add_plot(axes)
cell = tmesh.entity('cell')
node = tmesh.entity('node')
NN = tmesh.number_of_nodes()
isBdNode = tmesh.ds.boundary_node_flag()
newNode = np.zeros((NN, 2), dtype=np.float)
degree = np.zeros(NN, dtype=np.int)
np.add.at(degree, cell, 1)
for i in range(10):
#bc = tmesh.entity_barycenter('cell')
bc, R = tmesh.circumcenter()
np.add.at(newNode, (cell, np.s_[:]), bc[:, np.newaxis, :])
newNode /= degree[:, np.newaxis]
node[~isBdNode] = newNode[~isBdNode]
newNode[:] = 0
fig = plt.figure()
axes = fig.gca()
tmesh.add_plot(axes)
tmesh.find_node(axes, node=newNode, color='r')
tmesh.find_node(axes, node=bc, color='b')
plt.show()
# sedge[j] == stotalEdge
arrayprint("stotalEdge:", stotalEdge)
arrayprint("sedge[j]", sedge[j])
arrayprint("j", j)
arrayprint("cell2edge", cell2edge)
arrayprint("sedge:", sedge)
# sedge == stotalEdge[i0]
arrayprint("stotalEdge[i0]", stotalEdge[i0])
arrayprint("i0", i0)
arrayprint("i1", i1)
arrayprint("node", node) # (NN, 2)
arrayprint("cell", cell) # (NC, 3)
arrayprint("edge", edge) # (NC, 3)
arrayprint("edge2cell", edge2cell) # (NE, 4)
#edge = mesh.entity('edge')
#arrayprint("edge", edge) # (NE, 2)
#cell2edge = mesh.ds.cell_to_edge()
#arrayprint("cell2edge", cell2edge) # (NC, 3)
#edge2cell = mesh.ds.edge_to_cell()
#arrayprint("edge2cell", edge2cell) # (NE, 4)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, fontsize=28)
mesh.find_edge(axes, showindex=True, fontsize=30)
mesh.find_cell(axes, showindex=True, fontsize=32)
plt.show()
