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https://github.com/wassname/simpeg.git
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rowanc1
961 lines
39 KiB
Python
961 lines
39 KiB
Python
from SimPEG import np, sp, Utils, Solver
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from BaseMesh import BaseMesh
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from InnerProducts import InnerProducts
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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import matplotlib.colors as colors
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import matplotlib.cm as cmx
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def SortByX0():
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eps = 1e-7
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def mycmp(c1,c2):
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if c1.x0.size == 2:
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if np.abs(c1.x0[1] - c2.x0[1]) < eps:
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return c1.x0[0] - c2.x0[0]
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return c1.x0[1] - c2.x0[1]
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elif c1.x0.size == 3:
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if np.abs(c1.x0[2] - c2.x0[2]) < eps:
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if np.abs(c1.x0[1] - c2.x0[1]) < eps:
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return c1.x0[0] - c2.x0[0]
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return c1.x0[1] - c2.x0[1]
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return c1.x0[2] - c2.x0[2]
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class K(object):
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def __init__(self, obj, *args):
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self.obj = obj
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def __lt__(self, other):
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return mycmp(self.obj, other.obj) < 0
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def __gt__(self, other):
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return mycmp(self.obj, other.obj) > 0
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def __eq__(self, other):
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return mycmp(self.obj, other.obj) == 0
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def __le__(self, other):
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return mycmp(self.obj, other.obj) <= 0
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def __ge__(self, other):
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return mycmp(self.obj, other.obj) >= 0
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def __ne__(self, other):
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return mycmp(self.obj, other.obj) != 0
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return K
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class TreeObject(object):
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"""docstring for TreeObject"""
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children = None #: children of the tree object
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num = None
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depth = 0
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def __init__(self, mesh, parent, depth):
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self.mesh = mesh
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self._parent = parent
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self.depth = depth
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@property
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def parent(self): return self._parent
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@property
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def dim(self): return self.mesh.dim
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@property
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def isleaf(self): return self.children is None
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@property
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def branchdepth(self):
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if self.isleaf:
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return self.depth
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else:
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return np.max([node.branchdepth for node in self.children.flatten('F')])
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class TreeNode(TreeObject):
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"""docstring for TreeNode"""
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def __init__(self, mesh, x0=[0,0], parent=None):
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TreeObject.__init__(self, mesh, parent, 0)
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self.x0 = np.array(x0, dtype=float)
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self.mesh.nodes.add(self)
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@property
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def center(self): return self.x0
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class TreeEdge(TreeObject):
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"""docstring for TreeEdge"""
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def __init__(self, mesh, x0=[0,0], edgeType=None, sz=[1,], depth=0,
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node0=None, node1=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent, depth)
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self.x0 = np.array(x0, dtype=float)
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self.edgeType = edgeType
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self.sz = np.array(sz, dtype=float)
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mesh.edges.add(self)
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if edgeType is 'x': mesh.edgesX.add(self)
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elif edgeType is 'y': mesh.edgesY.add(self)
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elif edgeType is 'z': mesh.edgesZ.add(self)
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self.node0 = node0 if isinstance(node0,TreeNode) else TreeNode(mesh, x0=self.x0)
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self.node1 = node1 if isinstance(node1,TreeNode) else TreeNode(mesh, x0=self.x0 + self.tangent*self.sz[0])
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def refine(self):
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if not self.isleaf: return
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self.mesh.isNumbered = False
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self.children = np.empty(2,dtype=TreeFace)
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# Create refined x0's
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x0r_0 = self.x0
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x0r_1 = self.x0+0.5*self.tangent*self.sz
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self.children[0] = TreeEdge(self.mesh, x0=x0r_0, edgeType=self.edgeType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.node0)
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self.children[1] = TreeEdge(self.mesh, x0=x0r_1, edgeType=self.edgeType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.children[0].node1, node1=self.node1)
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self.mesh.edges.remove(self)
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if self.edgeType is 'x':
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self.mesh.edgesX.remove(self)
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elif self.edgeType is 'y':
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self.mesh.edgesY.remove(self)
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elif self.edgeType is 'z':
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self.mesh.edgesZ.remove(self)
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@property
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def tangent(self):
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if self.edgeType is 'x': return np.r_[1.,0,0]
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elif self.edgeType is 'y': return np.r_[0,1.,0]
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elif self.edgeType is 'z': return np.r_[0,0,1.]
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def plotGrid(self, ax, text=False, lineOpts={'color':'r', 'ls': '-'}):
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line = np.c_[self.node0.x0, self.node1.x0].T
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ax.plot(line[:,0], line[:,1], zs=line[:,2], **lineOpts)
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@property
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def center(self):
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return 0.5*(self.node0.x0 + self.node1.x0)
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class TreeFace(TreeObject):
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"""docstring for TreeFace"""
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def __init__(self, mesh, x0=[0,0], faceType=None, sz=[1,], depth=0,
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node0=None, node1=None,
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edge0=None, edge1=None, edge2=None, edge3=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent, depth)
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self.x0 = np.array(x0, dtype=float)
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self.faceType = faceType
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self.sz = np.array(sz, dtype=float)
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mesh.faces.add(self)
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if faceType is 'x': mesh.facesX.add(self)
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elif faceType is 'y': mesh.facesY.add(self)
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elif faceType is 'z': mesh.facesZ.add(self)
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if self.dim == 2:
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# Add the nodes:
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self.node0 = node0 if isinstance(node0,TreeNode) else TreeNode(mesh, x0=self.x0)
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self.node1 = node1 if isinstance(node1,TreeNode) else TreeNode(mesh, x0=self.x0 + self.tangent0*self.sz[0])
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if self.dim == 3:
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#TODO: Change this to edges
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#
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# 2___________3
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# | e1 |
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# | |
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# e2| x |e3 t1
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# | | ^
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# |___________| |___> t0
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# 0 e0 1
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#
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N = {}
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N["n0"] = getattr(edge0, 'node0', None) or getattr(edge2, 'node0', None)
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N["n1"] = getattr(edge0, 'node1', None) or getattr(edge3, 'node0', None)
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N["n2"] = getattr(edge1, 'node0', None) or getattr(edge2, 'node1', None)
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N["n3"] = getattr(edge1, 'node1', None) or getattr(edge3, 'node1', None)
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eType = ['x', 'y'] if self.faceType == 'z' else ['x', 'z'] if self.faceType == 'y' else ['y', 'z']
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e0 = edge0 if isinstance(edge0,TreeEdge) else TreeEdge(mesh, x0=self.x0, edgeType=eType[0], sz=np.r_[sz[0]], depth=depth, parent=parent, node0=N['n0'], node1=N['n1'])
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N["n0"], N["n1"] = e0.node0, e0.node1
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e1 = edge1 if isinstance(edge1,TreeEdge) else TreeEdge(mesh, x0=self.x0 + self.tangent1*self.sz[1], edgeType=eType[0], sz=np.r_[sz[0]], depth=depth, parent=parent, node0=N['n2'], node1=N['n3'])
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N["n2"], N["n3"] = e1.node0, e1.node1
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e2 = edge2 if isinstance(edge2,TreeEdge) else TreeEdge(mesh, x0=self.x0, edgeType=eType[1], sz=np.r_[sz[1]], depth=depth, parent=parent, node0=N['n0'], node1=N['n2'])
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N["n0"], N["n2"] = e2.node0, e2.node1
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e3 = edge3 if isinstance(edge3,TreeEdge) else TreeEdge(mesh, x0=self.x0 + self.tangent0*self.sz[0], edgeType=eType[1], sz=np.r_[sz[1]], depth=depth, parent=parent, node0=N['n1'], node1=N['n3'])
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N["n1"], N["n3"] = e3.node0, e3.node1
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self.nodes = N
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self.edges = {'e0':e0, 'e1':e1, 'e2':e2, 'e3':e3}
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@property
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def tangent0(self):
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if self.faceType is 'x': t = np.r_[0,1.,0]
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elif self.faceType is 'y': t = np.r_[1.,0,0]
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elif self.faceType is 'z': t = np.r_[1.,0,0]
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return t[:self.dim]
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@property
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def tangent1(self):
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if self.dim == 2: return
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if self.faceType is 'x': t = np.r_[0,0,1.]
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elif self.faceType is 'y': t = np.r_[0,0,1.]
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elif self.faceType is 'z': t = np.r_[0,1.,0]
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return t[:self.dim]
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@property
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def normal(self):
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if self.faceType is 'x': n = np.r_[1.,0,0]
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elif self.faceType is 'y': n = np.r_[0,1.,0]
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elif self.faceType is 'z': n = np.r_[0,0,1.]
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return n[:self.dim]
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@property
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def index(self):
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if self.isleaf: return [self.num]
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l = [face.index for face in self.children.flatten(order='F')]
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# Flatten the list
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# e.g.
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# [[1,3],[4]] --> [1, 3, 4]
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return [item for sublist in l for item in sublist]
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@property
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def area(self):
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"""area of the face"""
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return self.sz.prod()
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def refine(self):
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if not self.isleaf: return
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self.mesh.isNumbered = False
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if self.dim == 2:
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self._refine2D()
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elif self.dim == 3:
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self._refine3D()
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def _refine2D(self):
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self.children = np.empty(2,dtype=TreeFace)
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# Create refined x0's
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x0r_0 = self.x0
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x0r_1 = self.x0+0.5*self.tangent0*self.sz
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self.children[0] = TreeFace(self.mesh, x0=x0r_0, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.node0)
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self.children[1] = TreeFace(self.mesh, x0=x0r_1, faceType=self.faceType, sz=0.5*self.sz, depth=self.depth+1, parent=self, node0=self.children[0].node1, node1=self.node1)
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self.mesh.faces.remove(self)
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if self.faceType is 'x':
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self.mesh.facesX.remove(self)
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elif self.faceType is 'y':
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self.mesh.facesY.remove(self)
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def _refine3D(self):
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#
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# 2_______________3 _______________
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# | e1--> | | | |
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# ^ | | ^ | (0,1) | (1,1) |
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# | | | | | | |
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# | | x | | ---> |-------+-------|
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# e2 | | e3 | | |
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# | | | (0,0) | (1,0) |
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# |_______________| |_______|_______|
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# 0 e0--> 1
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order = [{'c':[0,0],
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'e0': ('p', 'e0', [0]), 'e1': 'new' ,
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'e2': ('p', 'e2', [0]), 'e3': 'new' },
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{'c':[1,0],
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'e0': ('p', 'e0', [1]), 'e1': 'new' ,
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'e2': ('c', 'e3', [0,0]), 'e3': ('p', 'e3', [0])},
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{'c':[0,1],
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'e0': ('c', 'e1', [0,0]), 'e1': ('p', 'e1', [0]),
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'e2': ('p', 'e2', [1]), 'e3': 'new' },
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{'c':[1,1],
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'e0': ('c', 'e1', [1,0]), 'e1': ('p', 'e1', [1]),
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'e2': ('c', 'e3', [0,1]), 'e3': ('p', 'e3', [1])}]
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def getEdge(pointer):
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if pointer is 'new': return
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if pointer[0] == 'p':
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return self.edges[pointer[1]].children[pointer[2][0]]
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if pointer[0] == 'c':
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return self.children[pointer[2][0],pointer[2][1]].edges[pointer[1]]
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self.children = np.empty((2,2), dtype=TreeFace)
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for edgeName in self.edges:
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self.edges[edgeName].refine()
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for O in order:
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i, j = O['c']
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x0r = self.x0 + 0.5*i*self.tangent0*self.sz[0] + 0.5*j*self.tangent1*self.sz[1]
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e0, e1, e2, e3 = getEdge(O['e0']), getEdge(O['e1']), getEdge(O['e2']), getEdge(O['e3'])
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self.children[i,j] = TreeFace(self.mesh, x0=x0r, faceType=self.faceType, depth=self.depth+1, sz=0.5*self.sz, parent=self, edge0=e0, edge1=e1, edge2=e2, edge3=e3)
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self.mesh.faces.remove(self)
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if self.faceType is 'x':
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self.mesh.facesX.remove(self)
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elif self.faceType is 'y':
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self.mesh.facesY.remove(self)
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elif self.faceType is 'z':
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self.mesh.facesZ.remove(self)
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def plotGrid(self, ax, text=True):
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if not self.isleaf: return
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if self.dim == 2:
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line = np.c_[self.node0.x0, self.node1.x0].T
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ax.plot(line[:,0], line[:,1],'r-')
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if text: ax.text(self.center[0], self.center[1],self.num)
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elif self.dim == 3:
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if text: ax.text(self.center[0], self.center[1], self.center[2], self.num)
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@property
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def center(self):
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if self.dim == 2:
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return self.x0 + 0.5*self.tangent0*self.sz[0]
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elif self.dim == 3:
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return self.x0 + 0.5*self.tangent0*self.sz[0] + 0.5*self.tangent1*self.sz[1]
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class TreeCell(TreeObject):
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"""docstring for TreeCell"""
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children = None #:
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def __init__(self, mesh, x0=[0,0], depth=0, sz=[1,1],
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fXm=None, fXp=None,
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fYm=None, fYp=None,
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fZm=None, fZp=None,
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parent=None):
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TreeObject.__init__(self, mesh, parent, depth)
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self.x0 = np.array(x0, dtype=float)
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self.sz = np.array(sz, dtype=float)
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if self.dim == 2:
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#
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# 2___________3
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# | fYp |
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# | |
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# fXm| x |fXp y
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# | | ^
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# |___________| |___> x
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# 0 fYm 1
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#
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N = {}
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N["n0"] = getattr(fXm, 'node0', None) or getattr(fYm, 'node0', None)
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N["n1"] = getattr(fXp, 'node0', None) or getattr(fYm, 'node1', None)
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N["n2"] = getattr(fXm, 'node1', None) or getattr(fYp, 'node0', None)
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N["n3"] = getattr(fXp, 'node1', None) or getattr(fYp, 'node1', None)
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fXm = fXm if isinstance(fXm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='x', sz=np.r_[sz[1]], depth=depth, parent=parent, node0=N['n0'], node1=N['n2'])
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N["n0"], N["n2"] = fXm.node0, fXm.node1
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fXp = fXp if isinstance(fXp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] ], faceType='x', sz=np.r_[sz[1]], depth=depth, parent=parent, node0=N['n1'], node1=N['n3'])
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N["n1"], N["n3"] = fXp.node0, fXp.node1
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fYm = fYm if isinstance(fYm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] ], faceType='y', sz=np.r_[sz[0]], depth=depth, parent=parent, node0=N['n0'], node1=N['n1'])
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N["n0"], N["n1"] = fYm.node0, fYm.node1
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fYp = fYp if isinstance(fYp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1]], faceType='y', sz=np.r_[sz[0]], depth=depth, parent=parent, node0=N['n2'], node1=N['n3'])
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N["n2"], N["n3"] = fYp.node0, fYp.node1
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self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp}
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self.nodes = N
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elif self.dim == 3:
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# fZp
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# |
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# 6 ------eX3------ 7
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# /| | / |
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# /eZ2 . / eZ3
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# eY2 | fYp eY3 |
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# / | / fXp|
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# 4 ------eX2----- 5 |
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# |fXm 2 -----eX1--|---- 3 z
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# eZ0 / | eY1 ^ y
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# | eY0 . fYm eZ1 / | /
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# | / | | / | /
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# 0 ------eX0------1 o----> x
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# |
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# fZm
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#
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#
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# fX fY fZ
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# 2___________3 2___________3 2___________3
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# | e1 | | e1 | | e1 |
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# | | | | | |
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# e2 | x | e3 z e2 | x | e3 z e2 | x | e3 y
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# | | ^ | | ^ | | ^
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# |___________| |___> y |___________| |___> x |___________| |___> x
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# 0 e0 1 0 e0 1 0 e0 1
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#
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# Mapping Nodes: numOnFace > numOnCell
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#
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# fXm 0>0, 1>2, 2>4, 3>6 fYm 0>0, 1>1, 2>4, 3>5 fZm 0>0, 1>1, 2>2, 3>3
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# fXp 0>1, 1>3, 2>5, 3>7 fYp 0>2, 1>3, 2>6, 3>7 fZp 0>4, 1>5, 2>6, 3>7
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def getEdge(face, key):
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if face is None: return
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return face.edges[key]
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E = {}
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eX0 = getEdge(fYm, 'e0') or getEdge(fZm, 'e0')
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eX1 = getEdge(fYp, 'e0') or getEdge(fZm, 'e1')
|
|
eX2 = getEdge(fYm, 'e1') or getEdge(fZp, 'e0')
|
|
eX3 = getEdge(fYp, 'e1') or getEdge(fZp, 'e1')
|
|
|
|
eY0 = getEdge(fXm, 'e0') or getEdge(fZm, 'e2')
|
|
eY1 = getEdge(fXp, 'e0') or getEdge(fZm, 'e3')
|
|
eY2 = getEdge(fXm, 'e1') or getEdge(fZp, 'e2')
|
|
eY3 = getEdge(fXp, 'e1') or getEdge(fZp, 'e3')
|
|
|
|
eZ0 = getEdge(fXm, 'e2') or getEdge(fYm, 'e2')
|
|
eZ1 = getEdge(fXp, 'e2') or getEdge(fYm, 'e3')
|
|
eZ2 = getEdge(fXm, 'e3') or getEdge(fYp, 'e2')
|
|
eZ3 = getEdge(fXp, 'e3') or getEdge(fYp, 'e3')
|
|
|
|
|
|
fXm = fXm if isinstance(fXm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='x', sz=np.r_[sz[1], sz[2]], depth=depth, parent=parent, edge0=eY0, edge1=eY2, edge2=eZ0, edge3=eZ2)
|
|
eY0, eY2, eZ0, eZ2 = fXm.edges['e0'], fXm.edges['e1'], fXm.edges['e2'], fXm.edges['e3']
|
|
|
|
fXp = fXp if isinstance(fXp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0]+sz[0], x0[1] , x0[2] ], faceType='x', sz=np.r_[sz[1], sz[2]], depth=depth, parent=parent, edge0=eY1, edge1=eY3, edge2=eZ1, edge3=eZ3)
|
|
eY1, eY3, eZ1, eZ3 = fXp.edges['e0'], fXp.edges['e1'], fXp.edges['e2'], fXp.edges['e3']
|
|
|
|
fYm = fYm if isinstance(fYm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='y', sz=np.r_[sz[0], sz[2]], depth=depth, parent=parent, edge0=eX0, edge1=eX2, edge2=eZ0, edge3=eZ1)
|
|
eX0, eX2, eZ0, eZ1 = fYm.edges['e0'], fYm.edges['e1'], fYm.edges['e2'], fYm.edges['e3']
|
|
|
|
fYp = fYp if isinstance(fYp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1]+sz[1], x0[2] ], faceType='y', sz=np.r_[sz[0], sz[2]], depth=depth, parent=parent, edge0=eX1, edge1=eX3, edge2=eZ2, edge3=eZ3)
|
|
eX1, eX3, eZ2, eZ3 = fYp.edges['e0'], fYp.edges['e1'], fYp.edges['e2'], fYp.edges['e3']
|
|
|
|
fZm = fZm if isinstance(fZm, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2] ], faceType='z', sz=np.r_[sz[0], sz[1]], depth=depth, parent=parent, edge0=eX0, edge1=eX1, edge2=eY0, edge3=eY1)
|
|
eX0, eX1, eY0, eY1 = fZm.edges['e0'], fZm.edges['e1'], fZm.edges['e2'], fZm.edges['e3']
|
|
|
|
fZp = fZp if isinstance(fZp, TreeFace) else TreeFace(mesh, x0=np.r_[x0[0] , x0[1] , x0[2]+sz[2]], faceType='z', sz=np.r_[sz[0], sz[1]], depth=depth, parent=parent, edge0=eX2, edge1=eX3, edge2=eY2, edge3=eY3)
|
|
eX2, eX3, eY2, eY3 = fZp.edges['e0'], fZp.edges['e1'], fZp.edges['e2'], fZp.edges['e3']
|
|
|
|
self.faces = {"fXm":fXm, "fXp":fXp, "fYm":fYm, "fYp":fYp, "fZm":fZm, "fZp":fZp}
|
|
self.edges = {"eX0":eX0, "eX1":eX1, "eX2":eX2, "eX3":eX3, "eY0":eY0, "eY1":eY1, "eY2":eY2, "eY3":eY3, "eZ0":eZ0, "eZ1":eZ1, "eZ2":eZ2, "eZ3":eZ3}
|
|
|
|
mesh.cells.add(self)
|
|
|
|
@property
|
|
def center(self): return self.x0 + 0.5*self.sz
|
|
|
|
def refine(self, function=None):
|
|
if not self.isleaf and function is None: return
|
|
|
|
if function is not None:
|
|
do = function(self.center) > self.depth
|
|
if not do: return
|
|
|
|
if self.dim == 2:
|
|
self._refine2D()
|
|
elif self.dim == 3:
|
|
self._refine3D()
|
|
|
|
# pass the refine function to the children
|
|
if function is not None:
|
|
for child in self.children.flatten():
|
|
child.refine(function)
|
|
|
|
def _refine2D(self):
|
|
|
|
self.mesh.isNumbered = False
|
|
|
|
self.children = np.empty((2,2),dtype=TreeCell)
|
|
x0, sz = self.x0, self.sz
|
|
|
|
for faceName in self.faces:
|
|
self.faces[faceName].refine()
|
|
|
|
order = [{'c':[0,0],
|
|
'fXm': ('p', 'fXm', [0]), 'fXp': 'new' ,
|
|
'fYm': ('p', 'fYm', [0]), 'fYp': 'new' },
|
|
{'c':[1,0],
|
|
'fXm': ('c', 'fXp', [0,0]), 'fXp': ('p', 'fXp', [0]),
|
|
'fYm': ('p', 'fYm', [1]), 'fYp': 'new' },
|
|
{'c':[0,1],
|
|
'fXm': ('p', 'fXm', [1]), 'fXp': 'new' ,
|
|
'fYm': ('c', 'fYp', [0,0]), 'fYp': ('p', 'fYp', [0])},
|
|
{'c':[1,1],
|
|
'fXm': ('c', 'fXp', [0,1]), 'fXp': ('p', 'fXp', [1]),
|
|
'fYm': ('c', 'fYp', [1,0]), 'fYp': ('p', 'fYp', [1])}]
|
|
|
|
def getFace(pointer):
|
|
if pointer is 'new': return None
|
|
if pointer[0] == 'p':
|
|
return self.faces[pointer[1]].children[pointer[2][0],]
|
|
if pointer[0] == 'c':
|
|
return self.children[pointer[2][0],pointer[2][1]].faces[pointer[1]]
|
|
|
|
for O in order:
|
|
i, j = O['c']
|
|
x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1]]
|
|
fXm, fXp, fYm, fYp = getFace(O['fXm']), getFace(O['fXp']), getFace(O['fYm']), getFace(O['fYp'])
|
|
self.children[i,j] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp)
|
|
|
|
self.mesh.cells.remove(self)
|
|
|
|
|
|
def _refine3D(self):
|
|
# .----------------.----------------.
|
|
# /| /| /|
|
|
# / | / | / |
|
|
# / | 011 / | 111 / |
|
|
# / | / | / |
|
|
# .----------------.----+-----------. |
|
|
# /| . ---------/|----.----------/|----.
|
|
# / | /| / | /| / | /|
|
|
# / | / | 001 / | / | 101 / | / |
|
|
# / | / | / | / | / | / |
|
|
# . -------------- .----------------. |/ |
|
|
# | . ---+------|----.----+------|----. |
|
|
# | /| .______|___/|____.______|___/|____.
|
|
# | / | / 010 | / | / 110| / | /
|
|
# | / | / | / | / | / | /
|
|
# . ---+---------- . ---+---------- . | /
|
|
# | |/ | |/ | |/ z
|
|
# | . ----------|----.-----------|----. ^ y
|
|
# | / 000 | / 100 | / | /
|
|
# | / | / | / | /
|
|
# | / | / | / o----> x
|
|
# . -------------- . -------------- .
|
|
#
|
|
#
|
|
# Face Refinement:
|
|
#
|
|
# 2_______________3 _______________
|
|
# | | | | |
|
|
# ^ | | | (0,1) | (1,1) |
|
|
# | | | | | |
|
|
# | | x | ---> |-------+-------|
|
|
# t1 | | | | |
|
|
# | | | (0,0) | (1,0) |
|
|
# |_______________| |_______|_______|
|
|
# 0 t0--> 1
|
|
|
|
|
|
order = [{'c':[0,0,0],
|
|
'fXm': ('p', 'fXm', [0,0]), 'fXp': 'new' ,
|
|
'fYm': ('p', 'fYm', [0,0]), 'fYp': 'new' ,
|
|
'fZm': ('p', 'fZm', [0,0]), 'fZp': 'new' ,},
|
|
{'c':[1,0,0],
|
|
'fXm': ('c', 'fXp', [0,0,0]), 'fXp': ('p', 'fXp', [0,0]),
|
|
'fYm': ('p', 'fYm', [1,0]), 'fYp': 'new' ,
|
|
'fZm': ('p', 'fZm', [1,0]), 'fZp': 'new' },
|
|
{'c':[0,1,0],
|
|
'fXm': ('p', 'fXm', [1,0]), 'fXp': 'new' ,
|
|
'fYm': ('c', 'fYp', [0,0,0]), 'fYp': ('p', 'fYp', [0,0]),
|
|
'fZm': ('p', 'fZm', [0,1]), 'fZp': 'new' },
|
|
{'c':[1,1,0],
|
|
'fXm': ('c', 'fXp', [0,1,0]), 'fXp': ('p', 'fXp', [1,0]),
|
|
'fYm': ('c', 'fYp', [1,0,0]), 'fYp': ('p', 'fYp', [1,0]),
|
|
'fZm': ('p', 'fZm', [1,1]), 'fZp': 'new' },
|
|
{'c':[0,0,1],
|
|
'fXm': ('p', 'fXm', [0,1]), 'fXp': 'new' ,
|
|
'fYm': ('p', 'fYm', [0,1]), 'fYp': 'new' ,
|
|
'fZm': ('c', 'fZp', [0,0,0]), 'fZp': ('p', 'fZp', [0,0])},
|
|
{'c':[1,0,1],
|
|
'fXm': ('c', 'fXp', [0,0,1]), 'fXp': ('p', 'fXp', [0,1]),
|
|
'fYm': ('p', 'fYm', [1,1]), 'fYp': 'new' ,
|
|
'fZm': ('c', 'fZp', [1,0,0]), 'fZp': ('p', 'fZp', [1,0])},
|
|
{'c':[0,1,1],
|
|
'fXm': ('p', 'fXm', [1,1]), 'fXp': 'new' ,
|
|
'fYm': ('c', 'fYp', [0,0,1]), 'fYp': ('p', 'fYp', [0,1]),
|
|
'fZm': ('c', 'fZp', [0,1,0]), 'fZp': ('p', 'fZp', [0,1])},
|
|
{'c':[1,1,1],
|
|
'fXm': ('c', 'fXp', [0,1,1]), 'fXp': ('p', 'fXp', [1,1]),
|
|
'fYm': ('c', 'fYp', [1,0,1]), 'fYp': ('p', 'fYp', [1,1]),
|
|
'fZm': ('c', 'fZp', [1,1,0]), 'fZp': ('p', 'fZp', [1,1])}]
|
|
|
|
self.mesh.isNumbered = False
|
|
|
|
self.children = np.empty((2,2,2), dtype=TreeCell)
|
|
x0, sz = self.x0, self.sz
|
|
|
|
for faceName in self.faces:
|
|
self.faces[faceName].refine()
|
|
|
|
def getFace(pointer):
|
|
if pointer is 'new': return None
|
|
if pointer[0] == 'p':
|
|
return self.faces[pointer[1]].children[pointer[2][0],pointer[2][1]]
|
|
if pointer[0] == 'c':
|
|
return self.children[pointer[2][0],pointer[2][1],pointer[2][2]].faces[pointer[1]]
|
|
|
|
for O in order:
|
|
i, j, k = O['c']
|
|
x0r = np.r_[x0[0] + 0.5*i*sz[0], x0[1] + 0.5*j*sz[1], x0[2] + 0.5*k*sz[2]]
|
|
fXm, fXp, fYm, fYp, fZm, fZp = getFace(O['fXm']), getFace(O['fXp']), getFace(O['fYm']), getFace(O['fYp']), getFace(O['fZm']), getFace(O['fZp'])
|
|
self.children[i,j,k] = TreeCell(self.mesh, x0=x0r, depth=self.depth+1, sz=0.5*sz, parent=self, fXm=fXm, fXp=fXp, fYm=fYm, fYp=fYp, fZm=fZm, fZp=fZp)
|
|
|
|
self.mesh.cells.remove(self)
|
|
|
|
@property
|
|
def faceIndex(self):
|
|
F = {}
|
|
for face in self.faces:
|
|
F[face] = self.faces[face].index
|
|
return F
|
|
|
|
@property
|
|
def vol(self): return self.sz.prod()
|
|
|
|
def viz(self, ax, color='none', text=False):
|
|
if not self.isleaf: return
|
|
x0, sz = self.x0, self.sz
|
|
ax.add_patch(plt.Rectangle((x0[0], x0[1]), sz[0], sz[1], facecolor=color, edgecolor='k'))
|
|
if text: ax.text(self.center[0],self.center[1],self.num)
|
|
|
|
def plotGrid(self, ax, text=False):
|
|
if not self.isleaf: return
|
|
if self.dim == 2:
|
|
ax.plot(self.center[0],self.center[1],'b.')
|
|
if text: ax.text(self.center[0],self.center[1],self.num)
|
|
elif self.dim == 3:
|
|
ax.plot([self.center[0]],[self.center[1]],'b.', zs=[self.center[2]])
|
|
if text: ax.text(self.center[0], self.center[1], self.center[2], self.num)
|
|
|
|
|
|
class TreeMesh(InnerProducts, BaseMesh):
|
|
"""TreeMesh"""
|
|
|
|
_meshType = 'TREE'
|
|
|
|
def __init__(self, h_in, x0=None):
|
|
assert type(h_in) is list, 'h_in must be a list'
|
|
h = range(len(h_in))
|
|
for i, h_i in enumerate(h_in):
|
|
if type(h_i) in [int, long, float]:
|
|
# This gives you something over the unit cube.
|
|
h_i = np.ones(int(h_i))/int(h_i)
|
|
assert type(h_i) == np.ndarray, ("h[%i] is not a numpy array." % i)
|
|
assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
|
|
h[i] = h_i[:] # make a copy.
|
|
self.h = h
|
|
|
|
if x0 is None:
|
|
x0 = np.zeros(self.dim)
|
|
else:
|
|
assert type(x0) in [list, np.ndarray], 'x0 must be a numpy array or a list'
|
|
x0 = np.array(x0, dtype=float)
|
|
assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh'
|
|
|
|
# TODO: this has a lot of stuff which doesn't work for this style of mesh...
|
|
BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
|
|
|
|
# set the sets for holding the cells, nodes, faces, and edges
|
|
self.cells = set()
|
|
self.nodes = set()
|
|
self.faces = set()
|
|
self.facesX = set()
|
|
self.facesY = set()
|
|
if self.dim == 3:
|
|
self.facesZ = set()
|
|
self.edges = set()
|
|
self.edgesX = set()
|
|
self.edgesY = set()
|
|
self.edgesZ = set()
|
|
|
|
self.children = np.empty([hi.size for hi in h],dtype=TreeCell)
|
|
|
|
if self.dim == 2:
|
|
for i in range(h[0].size):
|
|
for j in range(h[1].size):
|
|
fXm = None if i is 0 else self.children[i-1][j].faces['fXp']
|
|
fYm = None if j is 0 else self.children[i][j-1].faces['fYp']
|
|
x0i = (np.r_[x0[0], h[0][:i]]).sum()
|
|
x0j = (np.r_[x0[1], h[1][:j]]).sum()
|
|
self.children[i][j] = TreeCell(self, x0=[x0i, x0j], depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm)
|
|
|
|
elif self.dim == 3:
|
|
for i in range(h[0].size):
|
|
for j in range(h[1].size):
|
|
for k in range(h[2].size):
|
|
fXm = None if i is 0 else self.children[i-1][j][k].faces['fXp']
|
|
fYm = None if j is 0 else self.children[i][j-1][k].faces['fYp']
|
|
fZm = None if k is 0 else self.children[i][j][k-1].faces['fZp']
|
|
x0i = (np.r_[x0[0], h[0][:i]]).sum()
|
|
x0j = (np.r_[x0[1], h[1][:j]]).sum()
|
|
x0k = (np.r_[x0[2], h[2][:k]]).sum()
|
|
self.children[i][j][k] = TreeCell(self, x0=[x0i, x0j, x0k], depth=0, sz=[h[0][i], h[1][j], h[2][k]], fXm=fXm, fYm=fYm, fZm=fZm)
|
|
|
|
isNumbered = Utils.dependentProperty('_isNumbered', False, ['_faceDiv'], 'Setting this to False will delete all operators.')
|
|
|
|
@property
|
|
def branchdepth(self):
|
|
return np.max([node.branchdepth for node in self.children.flatten('F')])
|
|
|
|
def refine(self, function):
|
|
for cell in self.children.flatten():
|
|
cell.refine(function)
|
|
|
|
def number(self):
|
|
if self.isNumbered: return
|
|
|
|
self.sortedCells = sorted(self.cells,key=SortByX0())
|
|
for i, sC in enumerate(self.sortedCells): sC.num = i
|
|
|
|
self.sortedNodes = sorted(self.nodes,key=SortByX0())
|
|
for i, sN in enumerate(self.sortedNodes): sN.num = i
|
|
|
|
self.sortedFaceX = sorted(self.facesX,key=SortByX0())
|
|
for i, sFx in enumerate(self.sortedFaceX): sFx.num = i
|
|
|
|
self.sortedFaceY = sorted(self.facesY,key=SortByX0())
|
|
for i, sFy in enumerate(self.sortedFaceY): sFy.num = i + self.nFx
|
|
|
|
if self.dim == 3:
|
|
self.sortedFaceZ = sorted(self.facesZ,key=SortByX0())
|
|
for i, sFz in enumerate(self.sortedFaceZ): sFz.num = i + self.nFx + self.nFy
|
|
|
|
self.sortedEdgeX = sorted(self.edgesX,key=SortByX0())
|
|
for i, sEx in enumerate(self.sortedEdgeX): sEx.num = i
|
|
|
|
self.sortedEdgeY = sorted(self.edgesY,key=SortByX0())
|
|
for i, sEy in enumerate(self.sortedEdgeY): sEy.num = i + self.nEx
|
|
|
|
self.sortedEdgeZ = sorted(self.edgesZ,key=SortByX0())
|
|
for i, sEz in enumerate(self.sortedEdgeZ): sEz.num = i + self.nEx + self.nEy
|
|
|
|
self.isNumbered = True
|
|
|
|
@property
|
|
def dim(self): return len(self.h)
|
|
|
|
@property
|
|
def nC(self): return len(self.cells)
|
|
|
|
@property
|
|
def nN(self): return len(self.nodes)
|
|
|
|
@property
|
|
def nF(self): return len(self.faces)
|
|
|
|
@property
|
|
def nFx(self): return len(self.facesX)
|
|
|
|
@property
|
|
def nFy(self): return len(self.facesY)
|
|
|
|
@property
|
|
def nFz(self): return None if self.dim < 3 else len(self.facesZ)
|
|
|
|
@property
|
|
def nE(self):
|
|
if self.dim == 2:
|
|
return len(self.faces)
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|
elif self.dim == 3:
|
|
return len(self.edges)
|
|
|
|
@property
|
|
def nEx(self):
|
|
if self.dim == 2:
|
|
return len(self.facesY)
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|
elif self.dim == 3:
|
|
return len(self.edgesX)
|
|
|
|
@property
|
|
def nEy(self):
|
|
if self.dim == 2:
|
|
return len(self.facesX)
|
|
elif self.dim == 3:
|
|
return len(self.edgesY)
|
|
|
|
@property
|
|
def nEz(self): return None if self.dim < 3 else len(self.edgesZ)
|
|
|
|
def _grid(self, key):
|
|
self.number()
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|
sObjs = {'CC':self.sortedCells,
|
|
'N':self.sortedNodes,
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|
'Fx': self.sortedFaceX,
|
|
'Fy': self.sortedFaceY,
|
|
'Fz': getattr(self,'sortedFaceZ', None),
|
|
'Ex': getattr(self,'sortedEdgeX', self.sortedFaceY),
|
|
'Ey': getattr(self,'sortedEdgeY', self.sortedFaceX),
|
|
'Ez': getattr(self,'sortedEdgeZ', None)}[key]
|
|
G = np.empty((len(sObjs),self.dim))
|
|
for ii, obj in enumerate(sObjs):
|
|
G[ii,:] = obj.center
|
|
return G
|
|
|
|
@property
|
|
def gridCC(self):
|
|
if getattr(self, '_gridCC', None) is None:
|
|
self._gridCC = self._grid('CC')
|
|
return self._gridCC
|
|
|
|
@property
|
|
def gridN(self):
|
|
if getattr(self, '_gridN', None) is None:
|
|
self._gridN = self._grid('N')
|
|
return self._gridN
|
|
|
|
@property
|
|
def gridFx(self):
|
|
if getattr(self, '_gridFx', None) is None:
|
|
self._gridFx = self._grid('Fx')
|
|
return self._gridFx
|
|
|
|
@property
|
|
def gridFy(self):
|
|
if getattr(self, '_gridFy', None) is None:
|
|
self._gridFy = self._grid('Fy')
|
|
return self._gridFy
|
|
|
|
@property
|
|
def gridFz(self):
|
|
if self.dim == 2: return None
|
|
if getattr(self, '_gridFz', None) is None:
|
|
self._gridFz = self._grid('Fz')
|
|
return self._gridFz
|
|
|
|
@property
|
|
def gridEx(self):
|
|
if self.dim == 2: return self.gridFy
|
|
if getattr(self, '_gridEx', None) is None:
|
|
self._gridEx = self._grid('Ex')
|
|
return self._gridEx
|
|
|
|
@property
|
|
def gridEy(self):
|
|
if self.dim == 2: return self.gridFx
|
|
if getattr(self, '_gridEy', None) is None:
|
|
self._gridEy = self._grid('Ey')
|
|
return self._gridEy
|
|
|
|
@property
|
|
def gridEz(self):
|
|
if self.dim == 2: return None
|
|
if getattr(self, '_gridEz', None) is None:
|
|
self._gridEz = self._grid('Ez')
|
|
return self._gridEz
|
|
|
|
@property
|
|
def vol(self):
|
|
self.number()
|
|
return np.array([cell.vol for cell in self.sortedCells])
|
|
|
|
@property
|
|
def area(self):
|
|
self.number()
|
|
if self.dim == 2:
|
|
faces = self.sortedFaceX + self.sortedFaceY
|
|
elif self.dim == 3:
|
|
faces = self.sortedFaceX + self.sortedFaceY + self.sortedFaceZ
|
|
return np.array([face.area for face in faces], dtype=float)
|
|
|
|
@property
|
|
def faceDiv(self):
|
|
if getattr(self, '_faceDiv', None) is None:
|
|
self.number()
|
|
# TODO: Preallocate!
|
|
I, J, V = [], [], []
|
|
for cell in self.sortedCells:
|
|
for face in cell.faces:
|
|
j = cell.faces[face].index
|
|
I += [cell.num]*len(j)
|
|
J += j
|
|
V += [-1 if 'm' in face else 1]*len(j)
|
|
VOL = self.vol
|
|
D = sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF))
|
|
S = self.area
|
|
self._faceDiv = Utils.sdiag(1/VOL)*D*Utils.sdiag(S)
|
|
return self._faceDiv
|
|
|
|
def _getFaceP(self, face0, face1, face2):
|
|
I, J, V = [], [], []
|
|
for cell in self.sortedCells:
|
|
face = cell.faces[face0]
|
|
if face.isleaf:
|
|
j = face.index
|
|
elif self.dim == 2:
|
|
j = face.children[0 if 'm' in face1 else 1].index
|
|
elif self.dim == 3:
|
|
j = face.children[0 if 'm' in face1 else 1,
|
|
0 if 'm' in face2 else 1].index
|
|
lenj = len(j)
|
|
I += [cell.num]*lenj
|
|
J += j
|
|
V += [1./lenj]*lenj
|
|
return sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF))
|
|
|
|
def _getFacePxx(self, xFace, yFace):
|
|
self.number()
|
|
xP = self._getFaceP(xFace, yFace, None)
|
|
yP = self._getFaceP(yFace, xFace, None)
|
|
return sp.vstack((xP, yP))
|
|
|
|
def _getFacePxxx(self, xFace, yFace, zFace):
|
|
self.number()
|
|
xP = self._getFaceP(xFace, yFace, zFace)
|
|
yP = self._getFaceP(yFace, xFace, zFace)
|
|
zP = self._getFaceP(zFace, xFace, yFace)
|
|
return sp.vstack((xP, yP, zP))
|
|
|
|
def plotGrid(self, ax=None, text=True, plotC=True, plotF=True, plotE=False, plotEx=False, plotEy=False, plotEz=False, showIt=False):
|
|
axOpts = {'projection':'3d'} if self.dim == 3 else {}
|
|
if ax is None: ax = plt.subplot(111, **axOpts)
|
|
|
|
if plotC: [c.plotGrid(ax, text=text) for c in self.cells]
|
|
if plotF: [f.plotGrid(ax, text=text) for f in self.faces]
|
|
if plotE and self.dim==3: [e.plotGrid(ax, text=text) for e in self.edges]
|
|
if plotEx and self.dim==3: [e.plotGrid(ax, text=text) for e in self.edgesX]
|
|
if plotEy and self.dim==3: [e.plotGrid(ax, text=text) for e in self.edgesY]
|
|
if plotEz and self.dim==3: [e.plotGrid(ax, text=text) for e in self.edgesZ]
|
|
|
|
ax.set_xlim((self.x0[0], self.h[0].sum()))
|
|
ax.set_ylim((self.x0[1], self.h[1].sum()))
|
|
if self.dim == 3:
|
|
ax.set_zlim((self.x0[2], self.h[2].sum()))
|
|
if showIt: plt.show()
|
|
|
|
def plotImage(self, I, ax=None, showIt=True):
|
|
if self.dim == 2:
|
|
self._plotImage2D(I, ax=ax, showIt=showIt)
|
|
elif self.dim == 3:
|
|
raise NotImplementedError('3D visualization is not yet implemented.')
|
|
|
|
def _plotImage2D(self, I, ax=None, showIt=True):
|
|
if ax is None: ax = plt.subplot(111)
|
|
jet = cm = plt.get_cmap('jet')
|
|
cNorm = colors.Normalize(vmin=I.min(), vmax=I.max())
|
|
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet)
|
|
ax.set_xlim((self.x0[0], self.h[0].sum()))
|
|
ax.set_ylim((self.x0[1], self.h[1].sum()))
|
|
for ii, node in enumerate(self.sortedCells):
|
|
node.viz(ax=ax, color=scalarMap.to_rgba(I[ii]))
|
|
scalarMap._A = [] # http://stackoverflow.com/questions/8342549/matplotlib-add-colorbar-to-a-sequence-of-line-plots
|
|
plt.colorbar(scalarMap)
|
|
if showIt: plt.show()
|
|
|
|
|
|
|
|
if __name__ == '__main__':
|
|
M = TreeMesh([np.ones(x) for x in [4,10]])
|
|
|
|
def function(xc):
|
|
r = xc - np.r_[2.,6.]
|
|
dist = np.sqrt(r.dot(r))
|
|
if dist < 1.0:
|
|
return 3
|
|
if dist < 1.5:
|
|
return 2
|
|
else:
|
|
return 1
|
|
|
|
M.refine(function)
|
|
|
|
DIV = M.faceDiv
|
|
Mf = M.getFaceInnerProduct()
|
|
# plt.subplot(211)
|
|
# plt.spy(DIV)
|
|
M.plotGrid(ax=plt.subplot(111),text=True,showIt=True)
|
|
|
|
q = np.zeros(M.nC)
|
|
q[208] = -1.0
|
|
q[291] = 1.0
|
|
b = Solver(-DIV*Mf*DIV.T).solve(q)
|
|
plt.figure()
|
|
M.plotImage(b)
|
|
# plt.gca().invert_yaxis()
|
|
print M.vol
|
|
plt.show()
|