/usr/share/pyshared/sfc/geometry/UFCCell.py is in sfc 1.0.0.dfsg-1.
This file is owned by root:root, with mode 0o644.
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# -*- coding: utf-8 -*-
"""
This module contains a class UFCCell to represent the properties of a cell in a easily accessible way.
"""
# Copyright (C) 2008 Martin Sandve Alnes and Simula Resarch Laboratory
#
# This file is part of SyFi.
#
# SyFi is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# SyFi is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with SyFi. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2008-08-12
# Last changed: 2008-08-12
import swiginac
from swiginac import matrix, exp, sqrt
import SyFi
from sfc.symbolic_utils import cross, inner, symbols
from sfc.common.output import sfc_debug
# TODO: this code could do with some tests!
class UFCCell:
def __init__(self, polygon):
sfc_debug("Entering UFCCell.__init__")
assert isinstance(polygon, SyFi.Polygon)
self.polygon = polygon
name = polygon.str()
x, y, z = symbols("xyz")
if isinstance(polygon, SyFi.ReferenceLine) or name == "ReferenceLine":
self.shape = "interval"
self.facet_shape = "point"
# ... dimensions:
self.nsd = 1
self.num_vertices = 2
self.num_edges = 1
self.num_faces = 0
self.num_facets = self.num_vertices
self.num_entities = (self.num_vertices, self.num_edges)
# ... connectivity:
self.facet_vertices = [
(0,),
(1,)
]
# ... geometry:
self.vertices = [matrix(self.nsd, 1, polygon.vertex(i)) for i in range(self.num_vertices)]
self.facet_polygons = self.vertices
# ... normal vector:
n = matrix(1, 1, [1])
self.facet_n = [-n, +n] # TODO: is this what we want to do for the interval "normal"?
# ... implicit equations:
self.facet_equations = [x, x-1]
elif isinstance(polygon, SyFi.ReferenceTriangle) or name == "ReferenceTriangle":
self.shape = "triangle"
self.facet_shape = "interval"
# ... dimensions:
self.nsd = 2
self.num_vertices = 3
self.num_edges = 3
self.num_faces = 1
self.num_facets = self.num_edges
self.num_entities = (self.num_vertices, self.num_edges, self.num_faces)
# ... connectivity:
# facet vertices in counterclockwise direction around reference cell:
self.facet_vertices = [
(1, 2),
(2, 0),
(0, 1)
]
# ... geometry:
self.vertices = [matrix(self.nsd, 1, polygon.vertex(i)) for i in range(self.num_vertices)]
self.facet_polygons = [polygon.line(i) for i in range(self.num_facets)]
# ... normal vector:
self.facet_n = []
for facet in range(self.num_facets):
fromvert, tovert = self.facet_vertices[facet]
# FIXME: finish facet stuff
t = self.vertices[fromvert] - self.vertices[tovert]
n = matrix(2, 1, [t[1], -t[0]])
n = n / sqrt(inner(n,n)) # TODO: Is this approach efficient? FIXME: Is this correct? Scaling to unit normal on reference domain, but this isn't necessarily unit length on global domain...
self.facet_n.append(n)
# ... implicit equations:
self.edge_equations = [x+y-1, x, y]
self.facet_equations = self.edge_equations
elif isinstance(polygon, SyFi.ReferenceTetrahedron) or name == "ReferenceTetrahedron":
self.shape = "tetrahedron"
self.facet_shape = "triangle"
# ... dimensions:
self.nsd = 3
self.num_vertices = 4
self.num_edges = 6
self.num_faces = 4
self.num_facets = self.num_faces
self.num_entities = (self.num_vertices, self.num_edges, self.num_faces, 1)
# ... connectivity:
# facet vertices in counterclockwise direction around reference cell:
self.facet_vertices = [
(1, 2, 3),
(0, 3, 2), # (0, 2, 3)
(0, 1, 3),
(0, 2, 1) # (0, 1, 2)
]
# ... geometry:
self.vertices = [matrix(self.nsd, 1, polygon.vertex(i)) for i in range(self.num_vertices)]
self.facet_polygons = [polygon.triangle(i) for i in range(self.num_facets)]
# ... normal vector:
self.facet_n = []
for facet in range(self.num_facets):
vert = self.facet_vertices[facet]
t01 = self.vertices[vert[1]] - self.vertices[vert[0]]
t02 = self.vertices[vert[2]] - self.vertices[vert[0]]
n = cross(t01, t02)
n = n / sqrt(inner(n,n)) # TODO: is this approach efficient? FIXME: Is this correct? Scaling to unit normal on reference domain...
self.facet_n.append(n)
# ... implicit equations:
self.face_equations = [ (x+y+z-1), x, y, z]
self.facet_equations = self.face_equations
# in a tetrahedron, no two edges are parallel WARNiNG FIXME: this edge code is not verified!
p = matrix(3, 1, [x, y, z])
v0, v1, v2, v3 = self.vertices
self.edge_equations = [ cross( (p - v3), (v2 - v3) ),
cross( (p - v3), (v1 - v3) ),
cross( (p - v2), (v1 - v2) ),
cross( (p - v3), (v0 - v3) ),
cross( (p - v2), (v0 - v2) ),
cross( (p - v1), (v0 - v1) ) ]
elif isinstance(polygon, SyFi.ReferenceRectangle) or name == "ReferenceRectangle":
self.shape = "quadrilateral"
self.facet_shape = "interval"
# ... dimensions:
self.nsd = 2
self.num_vertices = 4
self.num_edges = 4
self.num_faces = 1
self.num_facets = self.num_edges
self.num_entities = (self.num_vertices, self.num_edges, self.num_faces)
# ... connectivity:
# facet vertices in counterclockwise direction around reference cell:
self.facet_vertices = [
(2, 3),
(1, 2),
(3, 0),
(0, 1)
]
# ... geometry:
self.vertices = [matrix(self.nsd, 1, polygon.vertex(i)) for i in range(self.num_vertices)]
self.facet_polygons = [polygon.line(i) for i in range(self.num_facets)]
# ... normal vector:
self.facet_n = []
for facet in range(self.num_facets):
fromvert, tovert = self.facet_vertices[facet]
t = self.vertices[fromvert] - self.vertices[tovert]
n = matrix(2, 1, [t[1], -t[0]])
self.facet_n.append(n)
# ... implicit equations:
self.edge_equations = [x-1, y-1, x, y]
self.facet_equations = self.edge_equations
elif isinstance(polygon, SyFi.ReferenceBox) or name == "ReferenceBox":
self.shape = "hexahedron"
self.facet_shape = "quadrilateral"
# ... dimensions:
self.nsd = 3
self.num_vertices = 8
self.num_edges = 12
self.num_faces = 6
self.num_facets = self.num_faces
self.num_entities = (self.num_vertices, self.num_edges, self.num_faces, 1)
# ... connectivity:
# facet vertices in counterclockwise direction around reference cell:
self.facet_vertices = [
(4, 5, 6, 7),
(2, 3, 7, 6), # (2, 3, 6, 7)
(1, 2, 6, 5), # (1, 2, 5, 6)
(0, 4, 7, 3), # (0, 3, 4, 7)
(0, 1, 5, 4), # (0, 1, 4, 5)
(0, 3, 2, 1) # (0, 1, 2, 3)
]
# Current Lagrange basis function order in SyFi:
#0 [[0, 0, 0], 0]
#1 [[0, 0, 1], 0]
#2 [[1, 0, 0], 0]
#3 [[1, 0, 1], 0]
#4 [[0, 1, 0], 0]
#5 [[0, 1, 1], 0]
#6 [[1, 1, 0], 0]
#7 [[1, 1, 1], 0]
# UFC vertex order for hexes requires reordering: TODO: don't need to do this?
#0->0 [[0, 0, 0], 0]
#2->1 [[1, 0, 0], 0]
#6->2 [[1, 1, 0], 0]
#4->3 [[0, 1, 0], 0]
#1->4 [[0, 0, 1], 0]
#3->5 [[1, 0, 1], 0]
#7->6 [[1, 1, 1], 0]
#5->7 [[0, 1, 1], 0]
# ... geometry:
self.vertices = [matrix(self.nsd, 1, polygon.vertex(i)) for i in range(self.num_vertices)]
self.facet_polygons = [polygon.rectangle(i) for i in range(self.num_facets)]
self.facet_n = []
for facet in range(self.num_facets):
# counterclockwise ordering seen from outside of reference cell:
vert = self.facet_vertices[facet]
# computing normal as the cross product of the facet diagonals
t02 = self.vertices[vert[0]] - self.vertices[vert[2]]
t13 = self.vertices[vert[1]] - self.vertices[vert[3]]
n = cross(t02, t13)
#n = n / swiginac.sqrt(inner(n,n)) # TODO: is this approach efficient? FIXME: Is this correct? Scaling to unit normal on reference domain...
self.facet_n.append(n)
# ... implicit equations:
# all faces coincide with a cartesian plane
self.face_equations = [z-1, y-1, x-1, x, y, z]
self.facet_equations = self.face_equations
# points on an edge satisfy the equations of two faces
f = self.face_equations
e = [0]*12
e[0 ] = (f[0], f[1])
e[1 ] = (f[0], f[2])
e[2 ] = (f[0], f[3])
e[3 ] = (f[0], f[4])
e[4 ] = (f[1], f[3])
e[5 ] = (f[1], f[2])
e[6 ] = (f[1], f[5])
e[7 ] = (f[2], f[4])
e[8 ] = (f[2], f[5])
e[9 ] = (f[3], f[4])
e[10] = (f[3], f[5])
e[11] = (f[4], f[5])
self.edge_equations = []
for f1, f2 in e:
self.edge_equations.append( exp(f1)*exp(f2) - 1 ) # TODO: a better equation?
else:
raise RuntimeError("Unknown polygon type %s." % name)
sfc_debug("Leaving UFCCell.__init__")
def find_entity(self, xi):
"Find which cell entity the coordinate xi lies on."
for i in range(self.nsd):
for j in range(self.num_entities[i]):
if self.entity_check(i, j, xi):
return (i, j)
return (self.nsd, 0)
def entity_check(self, d, i, p):
# this is a bit ugly, could benefit from a cleanup
# make p into a list
if isinstance(p, swiginac.matrix):
p = [p[k] for k in range(len(p))]
elif isinstance(p, swiginac.basic):
p = [p]
# check if we match a vertex exactly
if d == 0:
#eq = self.vertex_equations[i]
return bool(self.vertices[i] == matrix(self.nsd, 1, p))
# get implicit equation for this entity
if d == -1:
eq = self.facet_equations[i]
if d == 1:
eq = self.edge_equations[i]
if d == 2:
eq = self.face_equations[i]
# check if implicit equation is zero in this point, which means p is on the entity
x = symbols(["x", "y", "z"])
for j in range(len(p)):
eq = eq.subs(x[j] == p[j])
return inner(eq, eq).expand().is_zero()
def facet_check(self, i, p):
return self.entity_check(-1, i, p)
def vertex_check(self, i, p):
return self.entity_check(0, i, p)
def edge_check(self, i, p):
return self.entity_check(1, i, p)
def face_check(self, i, p):
return self.entity_check(2, i, p)
def __eq__(self, other):
if self.shape == other.shape:
return True
return False
def __ne__(self, other):
if self.shape == other.shape:
return False
return True
def __str__(self):
s = "Cell\n"
s += " shape: %s\n" % self.shape
s += " nsd: %d\n" % self.nsd
s += " num_vertices: %d\n" % self.num_vertices
s += " num_edges: %d\n" % self.num_edges
s += " num_faces: %d\n" % self.num_faces
s += " num_facets: %d\n" % self.num_facets
s += " vertices: %s\n" % str(self.vertices)
s += " facet_equations: %s\n" % str(self.facet_equations)
return s
if __name__ == "__main__":
print ""
polygon = SyFi.ReferenceLine()
cell = UFCCell(polygon)
print cell
print ""
polygon = SyFi.ReferenceTriangle()
cell = UFCCell(polygon)
print cell
print ""
polygon = SyFi.ReferenceTetrahedron()
cell = UFCCell(polygon)
print cell
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