def test_get_vertex_coordinates_with_geo_ref(self):
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]], num.int)
domain = General_mesh(nodes, triangles, geo_reference=geo)
verts = domain.get_vertex_coordinates(triangle_id=0) # bac
msg = ("num.array([b,a,c])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([b,a,c])), str(verts)))
self.assertTrue(num.allclose(num.array([b,a,c]), verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0)
msg = ("num.array([b,a,c])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([b,a,c])), str(verts)))
self.assert_(num.allclose(num.array([b,a,c]), verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0, absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([nodes_absolute[1],
nodes_absolute[0],
nodes_absolute[2]])),
str(verts)))
self.assert_(num.allclose(num.array([nodes_absolute[1],
nodes_absolute[0],
nodes_absolute[2]]),
verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0,
absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([nodes_absolute[1],
nodes_absolute[0],
nodes_absolute[2]])),
str(verts)))
self.assert_(num.allclose(num.array([nodes_absolute[1],
nodes_absolute[0],
nodes_absolute[2]]),
verts), msg)
def test_get_vertex_coordinates_with_geo_ref(self):
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1, 0, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]],
num.int)
domain = General_mesh(nodes, triangles, geo_reference=geo)
verts = domain.get_vertex_coordinates(triangle_id=0) # bac
msg = ("num.array([b,a,c])=\n%s\nshould be close to 'verts'=\n%s" %
(str(num.array([b, a, c])), str(verts)))
self.assertTrue(num.allclose(num.array([b, a, c]), verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0)
msg = ("num.array([b,a,c])=\n%s\nshould be close to 'verts'=\n%s" %
(str(num.array([b, a, c])), str(verts)))
self.assertTrue(num.allclose(num.array([b, a, c]), verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0, absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s" % (str(
num.array([
nodes_absolute[1], nodes_absolute[0], nodes_absolute[2]
])), str(verts)))
self.assertTrue(
num.allclose(
num.array(
[nodes_absolute[1], nodes_absolute[0], nodes_absolute[2]]),
verts), msg)
verts = domain.get_vertex_coordinates(triangle_id=0, absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s" % (str(
num.array([
nodes_absolute[1], nodes_absolute[0], nodes_absolute[2]
])), str(verts)))
self.assertTrue(
num.allclose(
num.array(
[nodes_absolute[1], nodes_absolute[0], nodes_absolute[2]]),
verts), msg)
def test_assert_index_in_nodes(self):
"""test_assert_index_in_nodes -
Test that node indices in triangles are within nodes array.
"""
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# max index is 5, use 5, expect success
triangles = num.array([[1, 0, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]])
General_mesh(nodes, triangles, geo_reference=geo)
# should fail with negative area
triangles = num.array([[0, 1, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]])
self.assertRaises(AssertionError,
General_mesh,
nodes,
triangles,
geo_reference=geo)
# max index is 5, use 6, expect assert failure
triangles = num.array([[1, 6, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]])
self.assertRaises(AssertionError,
General_mesh,
nodes,
triangles,
geo_reference=geo)
# max index is 5, use 10, expect assert failure
triangles = num.array([[1, 10, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]])
self.assertRaises(AssertionError,
General_mesh,
nodes,
triangles,
geo_reference=geo)
def test_get_node(self):
"""test_get_triangles_and_vertices_per_node -
Test that tuples of triangle, vertex can be extracted
from inverted triangles structure
"""
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1, 0, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]])
domain = General_mesh(nodes, triangles, geo_reference=geo)
node = domain.get_node(2)
msg = ('\nc=%s\nnode=%s' % (str(c), str(node)))
self.assertTrue(num.alltrue(c == node), msg)
# repeat get_node(), see if result same
node = domain.get_node(2)
msg = ('\nc=%s\nnode=%s' % (str(c), str(node)))
self.assertTrue(num.alltrue(c == node), msg)
node = domain.get_node(2, absolute=True)
msg = ('\nnodes_absolute[2]=%s\nnode=%s' %
(str(nodes_absolute[2]), str(node)))
self.assertTrue(num.alltrue(nodes_absolute[2] == node), msg)
# repeat get_node(2, absolute=True), see if result same
node = domain.get_node(2, absolute=True)
msg = ('\nnodes_absolute[2]=%s\nnode=%s' %
(str(nodes_absolute[2]), str(node)))
self.assertTrue(num.alltrue(nodes_absolute[2] == node), msg)
def test_get_node(self):
"""test_get_triangles_and_vertices_per_node -
Test that tuples of triangle, vertex can be extracted
from inverted triangles structure
"""
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]])
domain = General_mesh(nodes, triangles, geo_reference = geo)
node = domain.get_node(2)
msg = ('\nc=%s\nnode=%s' % (str(c), str(node)))
self.assertTrue(num.alltrue(c == node), msg)
# repeat get_node(), see if result same
node = domain.get_node(2)
msg = ('\nc=%s\nnode=%s' % (str(c), str(node)))
self.assertTrue(num.alltrue(c == node), msg)
node = domain.get_node(2, absolute=True)
msg = ('\nnodes_absolute[2]=%s\nnode=%s'
% (str(nodes_absolute[2]), str(node)))
self.assertTrue(num.alltrue(nodes_absolute[2] == node), msg)
# repeat get_node(2, absolute=True), see if result same
node = domain.get_node(2, absolute=True)
msg = ('\nnodes_absolute[2]=%s\nnode=%s'
% (str(nodes_absolute[2]), str(node)))
self.assertTrue(num.alltrue(nodes_absolute[2] == node), msg)
def test_get_edge_midpoint_coordinates_with_geo_ref(self):
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = num.array([0.0, 0.0])
b = num.array([0.0, 2.0])
c = num.array([2.0, 0.0])
d = num.array([0.0, 4.0])
e = num.array([2.0, 2.0])
f = num.array([4.0, 0.0])
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1, 0, 2], [1, 2, 4], [4, 2, 5], [3, 1, 4]],
num.int)
domain = General_mesh(nodes, triangles, geo_reference=geo)
verts = domain.get_edge_midpoint_coordinates(triangle_id=0) # bac
msg = (
"num.array(1/2[a+c,b+c,a+b])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([0.5 * (a + c), 0.5 * (b + c), 0.5 *
(a + b)])), str(verts)))
self.assertTrue(
num.allclose(
num.array([0.5 * (a + c), 0.5 * (b + c), 0.5 * (a + b)]),
verts), msg)
verts = domain.get_edge_midpoint_coordinates(triangle_id=0,
absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s" %
(str(0.5 * num.array([
nodes_absolute[0] + nodes_absolute[2], nodes_absolute[1] +
nodes_absolute[2], nodes_absolute[1] + nodes_absolute[0]
])), str(verts)))
self.assertTrue(
num.allclose(
0.5 * num.array([
nodes_absolute[0] + nodes_absolute[2], nodes_absolute[1] +
nodes_absolute[2], nodes_absolute[1] + nodes_absolute[0]
]), verts), msg)
def test_assert_index_in_nodes(self):
"""test_assert_index_in_nodes -
Test that node indices in triangles are within nodes array.
"""
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
d = [0.0, 4.0]
e = [2.0, 2.0]
f = [4.0, 0.0]
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# max index is 5, use 5, expect success
triangles = num.array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]])
General_mesh(nodes, triangles, geo_reference=geo)
# should fail with negative area
triangles = num.array([[0,1,2], [1,2,4], [4,2,5], [3,1,4]])
self.assertRaises(AssertionError, General_mesh,
nodes, triangles, geo_reference=geo)
# max index is 5, use 6, expect assert failure
triangles = num.array([[1,6,2], [1,2,4], [4,2,5], [3,1,4]])
self.assertRaises(AssertionError, General_mesh,
nodes, triangles, geo_reference=geo)
# max index is 5, use 10, expect assert failure
triangles = num.array([[1,10,2], [1,2,4], [4,2,5], [3,1,4]])
self.assertRaises(AssertionError, General_mesh,
nodes, triangles, geo_reference=geo)
def test_urs_ungridded2sww_mint_maxtII(self):
#Zone: 50
#Easting: 240992.578 Northing: 7620442.472
#Latitude: -21 30 ' 0.00000 '' Longitude: 114 30 ' 0.00000 ''
lat_long = [[-21.5, 114.5], [-21, 114.5], [-21, 115]]
time_step_count = 6
time_step = 100
tide = 9000000
base_name, files = self.write_mux(lat_long, time_step_count, time_step)
urs_ungridded2sww(base_name,
mean_stage=tide,
origin=(50, 23432, 4343),
mint=0,
maxt=100000)
# now I want to check the sww file ...
sww_file = base_name + '.sww'
#Let's interigate the sww file
# Note, the sww info is not gridded. It is point data.
fid = NetCDFFile(sww_file)
# Make x and y absolute
geo_reference = Geo_reference(NetCDFObject=fid)
points = geo_reference.get_absolute(
list(zip(fid.variables['x'][:], fid.variables['y'][:])))
points = ensure_numeric(points)
x = points[:, 0]
#Check the time vector
times = fid.variables['time'][:]
times_actual = [0, 100, 200, 300, 400, 500]
assert num.allclose(ensure_numeric(times),
ensure_numeric(times_actual))
#Check first value
stage = fid.variables['stage'][:]
assert num.allclose(stage[0], x + tide)
fid.close()
self.delete_mux(files)
os.remove(sww_file)
def test_urs_ungridded2sww_mint_maxtII (self):
#Zone: 50
#Easting: 240992.578 Northing: 7620442.472
#Latitude: -21 30 ' 0.00000 '' Longitude: 114 30 ' 0.00000 ''
lat_long = [[-21.5,114.5],[-21,114.5],[-21,115]]
time_step_count = 6
time_step = 100
tide = 9000000
base_name, files = self.write_mux(lat_long,
time_step_count, time_step)
urs_ungridded2sww(base_name, mean_stage=tide, origin =(50,23432,4343),
mint=0, maxt=100000)
# now I want to check the sww file ...
sww_file = base_name + '.sww'
#Let's interigate the sww file
# Note, the sww info is not gridded. It is point data.
fid = NetCDFFile(sww_file)
# Make x and y absolute
geo_reference = Geo_reference(NetCDFObject=fid)
points = geo_reference.get_absolute(map(None, fid.variables['x'][:],
fid.variables['y'][:]))
points = ensure_numeric(points)
x = points[:,0]
#Check the time vector
times = fid.variables['time'][:]
times_actual = [0,100,200,300,400,500]
assert num.allclose(ensure_numeric(times),
ensure_numeric(times_actual))
#Check first value
stage = fid.variables['stage'][:]
assert num.allclose(stage[0], x +tide)
fid.close()
self.delete_mux(files)
os.remove(sww_file)
def test_get_edge_midpoint_coordinates_with_geo_ref(self):
x0 = 314036.58727982
y0 = 6224951.2960092
geo = Geo_reference(56, x0, y0)
a = num.array([0.0, 0.0])
b = num.array([0.0, 2.0])
c = num.array([2.0, 0.0])
d = num.array([0.0, 4.0])
e = num.array([2.0, 2.0])
f = num.array([4.0, 0.0])
nodes = num.array([a, b, c, d, e, f])
nodes_absolute = geo.get_absolute(nodes)
# bac, bce, ecf, dbe
triangles = num.array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]], num.int)
domain = General_mesh(nodes, triangles, geo_reference=geo)
verts = domain.get_edge_midpoint_coordinates(triangle_id=0) # bac
msg = ("num.array(1/2[a+c,b+c,a+b])=\n%s\nshould be close to 'verts'=\n%s"
% (str(num.array([0.5*(a+c),0.5*(b+c),0.5*(a+b)])), str(verts)))
self.assertTrue(num.allclose(num.array([0.5*(a+c),0.5*(b+c),0.5*(a+b)]), verts), msg)
verts = domain.get_edge_midpoint_coordinates(triangle_id=0, absolute=True)
msg = ("num.array([...])=\n%s\nshould be close to 'verts'=\n%s"
% (str(0.5*num.array([nodes_absolute[0]+nodes_absolute[2],
nodes_absolute[1]+nodes_absolute[2],
nodes_absolute[1]+nodes_absolute[0]])),
str(verts)))
self.assert_(num.allclose(0.5*num.array([nodes_absolute[0]+nodes_absolute[2],
nodes_absolute[1]+nodes_absolute[2],
nodes_absolute[1]+nodes_absolute[0]]),
verts), msg)
class General_mesh:
"""Collection of 2D triangular elements
A triangular element is defined in terms of three vertex ids,
ordered counter clock-wise, each corresponding to a given node
which is represented as a coordinate set (x,y).
Vertices from different triangles can point to the same node.
The nodes are implemented as an Nx2 numeric array containing the
x and y coordinates.
To instantiate:
Mesh(nodes, triangles)
where
nodes is either a list of 2-tuples or an Nx2 numeric array of
floats representing all x, y coordinates in the mesh.
triangles is either a list of 3-tuples or an Mx3 numeric array of
integers representing indices of all vertices in the mesh.
Each vertex is identified by its index i in [0, N-1].
Example:
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0, 0.0]
e = [2.0, 2.0]
nodes = [a, b, c, e]
triangles = [ [1,0,2], [1,2,3] ] # bac, bce
# Create mesh with two triangles: bac and bce
mesh = Mesh(nodes, triangles)
Other:
In addition mesh computes an Mx6 array called vertex_coordinates.
This structure is derived from coordinates and contains for each
triangle the three x,y coordinates at the vertices.
See neighbourmesh.py for a specialisation of the general mesh class
which includes information about neighbours and the mesh boundary.
The mesh object is purely geometrical and contains no information
about quantities defined on the mesh.
"""
# FIXME: It would be a good idea to use geospatial data as an alternative
# input
def __init__(self,
nodes,
triangles,
geo_reference=None,
use_inscribed_circle=False,
verbose=False):
"""Build triangular 2d mesh from nodes and triangle information
Input:
nodes: x,y coordinates represented as a sequence of 2-tuples or
a Nx2 numeric array of floats.
triangles: sequence of 3-tuples or Mx3 numeric array of
non-negative integers representing indices into
the nodes array.
georeference (optional): If specified coordinates are
assumed to be relative to this origin.
"""
self.verbose = verbose
if verbose: log.critical('General_mesh: Building basic mesh structure')
self.use_inscribed_circle = use_inscribed_circle
self.triangles = num.array(triangles, num.int)
if verbose:
log.timingInfo("numTriangles, " + str(self.triangles.shape[0]))
self.nodes = num.array(nodes, num.float)
# Register number of elements and nodes
self.number_of_triangles = N = int(self.triangles.shape[0])
self.number_of_nodes = self.nodes.shape[0]
# FIXME: this stores a geo_reference, but when coords are returned
# This geo_ref is not taken into account!
if geo_reference is None:
self.geo_reference = Geo_reference() # Use defaults
else:
self.geo_reference = geo_reference
# Input checks
msg = (
'Triangles must an Mx3 numeric array or a sequence of 3-tuples. '
'The supplied array has the shape: %s' % str(self.triangles.shape))
assert len(self.triangles.shape) == 2, msg
msg = ('Nodes must an Nx2 numeric array or a sequence of 2-tuples'
'The supplied array has the shape: %s' % str(self.nodes.shape))
assert len(self.nodes.shape) == 2, msg
msg = 'Vertex indices reference non-existing coordinate sets'
assert num.max(self.triangles) < self.nodes.shape[0], msg
# FIXME: Maybe move to statistics?
# Or use with get_extent
xy_extent = [
min(self.nodes[:, 0]),
min(self.nodes[:, 1]),
max(self.nodes[:, 0]),
max(self.nodes[:, 1])
]
self.xy_extent = num.array(xy_extent, num.float)
# Allocate space for geometric quantities
self.normals = num.zeros((N, 6), num.float)
self.areas = num.zeros(N, num.float)
self.edgelengths = num.zeros((N, 3), num.float)
# Get x,y coordinates for all triangle vertices and store
self.centroid_coordinates = num.zeros((N, 2), num.float)
#Allocate space for geometric quantities
self.radii = num.zeros(N, num.float)
# Get x,y coordinates for all triangle vertices and store
self.vertex_coordinates = V = self.compute_vertex_coordinates()
# Get x,y coordinates for all triangle edge midpoints and store
self.edge_midpoint_coordinates = self.compute_edge_midpoint_coordinates(
)
# Initialise each triangle
if verbose:
log.critical('General_mesh: Computing areas, normals, '
'edgelengths, centroids and radii')
# Calculate Areas
V0 = V[0:3 * N:3, :]
V1 = V[1:3 * N:3, :]
V2 = V[2:3 * N:3, :]
# Area
x0 = V0[:, 0]
y0 = V0[:, 1]
x1 = V1[:, 0]
y1 = V1[:, 1]
x2 = V2[:, 0]
y2 = V2[:, 1]
self.areas[:] = -((x1 * y0 - x0 * y1) + (x2 * y1 - x1 * y2) +
(x0 * y2 - x2 * y0)) / 2.0
#areas = -((x0-x1)*(y2-y1) - (y0-y1)*(x2-x1))/2.0
#assert num.allclose(self.areas, areas)
ind = num.where(self.areas <= 0.0)
msg = 'Degenerate Triangle(s) ' + str(ind[0])
assert num.all(self.areas > 0.0), msg
#print V.shape, V0.shape, V1.shape, V2.shape
# #print E.shape, E[0:3*M:3, :].shape, E[1:3*M:3, :].shape, E[2:3*M:3, :].shape
# E[0:3*M:3, :] = 0.5*(V1+V2)
# E[1:3*M:3, :] = 0.5*(V2+V0)
# E[2:3*M:3, :] = 0.5*(V0+V1)
i0 = self.triangles[:, 0]
i1 = self.triangles[:, 1]
i2 = self.triangles[:, 2]
assert num.allclose(x0, self.nodes[i0, 0])
assert num.allclose(y0, self.nodes[i0, 1])
assert num.allclose(x1, self.nodes[i1, 0])
assert num.allclose(y1, self.nodes[i1, 1])
assert num.allclose(x2, self.nodes[i2, 0])
assert num.allclose(y2, self.nodes[i2, 1])
xn0 = x2 - x1
yn0 = y2 - y1
l0 = num.sqrt(xn0**2 + yn0**2)
xn0 /= l0
yn0 /= l0
xn1 = x0 - x2
yn1 = y0 - y2
l1 = num.sqrt(xn1**2 + yn1**2)
xn1 /= l1
yn1 /= l1
xn2 = x1 - x0
yn2 = y1 - y0
l2 = num.sqrt(xn2**2 + yn2**2)
xn2 /= l2
yn2 /= l2
# Compute and store
self.normals[:, 0] = yn0
self.normals[:, 1] = -xn0
self.normals[:, 2] = yn1
self.normals[:, 3] = -xn1
self.normals[:, 4] = yn2
self.normals[:, 5] = -xn2
self.edgelengths[:, 0] = l0
self.edgelengths[:, 1] = l1
self.edgelengths[:, 2] = l2
self.centroid_coordinates[:, 0] = old_div((x0 + x1 + x2), 3)
self.centroid_coordinates[:, 1] = old_div((y0 + y1 + y2), 3)
if self.use_inscribed_circle == False:
#OLD code. Computed radii may exceed that of an
#inscribed circle
#Midpoints
xm0 = old_div((x1 + x2), 2)
ym0 = old_div((y1 + y2), 2)
xm1 = old_div((x2 + x0), 2)
ym1 = old_div((y2 + y0), 2)
xm2 = old_div((x0 + x1), 2)
ym2 = old_div((y0 + y1), 2)
#The radius is the distance from the centroid of
#a triangle to the midpoint of the side of the triangle
#closest to the centroid
d0 = num.sqrt((self.centroid_coordinates[:, 0] - xm0)**2 +
(self.centroid_coordinates[:, 1] - ym0)**2)
d1 = num.sqrt((self.centroid_coordinates[:, 0] - xm1)**2 +
(self.centroid_coordinates[:, 1] - ym1)**2)
d2 = num.sqrt((self.centroid_coordinates[:, 0] - xm2)**2 +
(self.centroid_coordinates[:, 1] - ym2)**2)
self.radii[:] = num.minimum(num.minimum(d0, d1), d2)
else:
#NEW code added by Peter Row. True radius
#of inscribed circle is computed
a = num.sqrt((x0 - x1)**2 + (y0 - y1)**2)
b = num.sqrt((x1 - x2)**2 + (y1 - y2)**2)
c = num.sqrt((x2 - x0)**2 + (y2 - y0)**2)
self.radii[:] = old_div(2.0 * self.areas, (a + b + c))
# for i in range(N):
# if verbose and i % ((N+10)/10) == 0: log.critical('(%d/%d)' % (i, N))
#
# x0, y0 = V[3*i, :]
# x1, y1 = V[3*i+1, :]
# x2, y2 = V[3*i+2, :]
#
#
# i0 = self.triangles[i][0]
# i1 = self.triangles[i][1]
# i2 = self.triangles[i][2]
#
## assert x0 == self.nodes[i0][0]
## assert y0 == self.nodes[i0][1]
##
## assert x1 == self.nodes[i1][0]
## assert y1 == self.nodes[i1][1]
##
## assert x2 == self.nodes[i2][0]
## assert y2 == self.nodes[i2][1]
#
## # Area
## self.areas[i] = abs((x1*y0-x0*y1) + (x2*y1-x1*y2) + (x0*y2-x2*y0))/2
##
## msg = 'Triangle %g (%f,%f), (%f,%f), (%f, %f)' % (i,x0,y0,x1,y1,x2,y2)
## msg += ' is degenerate: area == %f' % self.areas[i]
## assert self.areas[i] > 0.0, msg
#
# # Normals
# # The normal vectors
# # - point outward from each edge
# # - are orthogonal to the edge
# # - have unit length
# # - Are enumerated according to the opposite corner:
# # (First normal is associated with the edge opposite
# # the first vertex, etc)
# # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle
# n0 = num.array([x2-x1, y2-y1], num.float)
# l0 = num.sqrt(num.sum(n0**2))
#
# n1 = num.array([x0-x2, y0-y2], num.float)
# l1 = num.sqrt(num.sum(n1**2))
#
# n2 = num.array([x1-x0, y1-y0], num.float)
# l2 = num.sqrt(num.sum(n2**2))
#
# # Normalise
# n0 /= l0
# n1 /= l1
# n2 /= l2
#
## # Compute and store
## self.normals[i, :] = [n0[1], -n0[0],
## n1[1], -n1[0],
## n2[1], -n2[0]]
#
# # Edgelengths
# #self.edgelengths[i, :] = [l0, l1, l2]
#
#
#
# #Compute centroid
## centroid = num.array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3], num.float)
### self.centroid_coordinates[i] = centroid
##
##
## if self.use_inscribed_circle == False:
## #OLD code. Computed radii may exceed that of an
## #inscribed circle
##
## #Midpoints
## m0 = num.array([(x1 + x2)/2, (y1 + y2)/2], num.float)
## m1 = num.array([(x0 + x2)/2, (y0 + y2)/2], num.float)
## m2 = num.array([(x1 + x0)/2, (y1 + y0)/2], num.float)
##
## #The radius is the distance from the centroid of
## #a triangle to the midpoint of the side of the triangle
## #closest to the centroid
## d0 = num.sqrt(num.sum( (centroid-m0)**2 ))
## d1 = num.sqrt(num.sum( (centroid-m1)**2 ))
## d2 = num.sqrt(num.sum( (centroid-m2)**2 ))
##
## #self.radii[i] = min(d0, d1, d2)
##
## else:
## #NEW code added by Peter Row. True radius
## #of inscribed circle is computed
##
## a = num.sqrt((x0-x1)**2+(y0-y1)**2)
## b = num.sqrt((x1-x2)**2+(y1-y2)**2)
## c = num.sqrt((x2-x0)**2+(y2-y0)**2)
##
## self.radii[i]=2.0*self.areas[i]/(a+b+c)
# Build structure listing which triangles belong to which node.
if verbose:
log.critical('General Mesh: Building inverted triangle structure')
self.build_inverted_triangle_structure()
if verbose: log.timingInfo("aoi, '%s'" % self.get_area())
def __len__(self):
return self.number_of_triangles
def __repr__(self):
return ('Mesh: %d vertices, %d triangles' %
(self.nodes.shape[0], len(self)))
def get_normals(self):
"""Return all normal vectors.
Return normal vectors for all triangles as an Nx6 array
(ordered as x0, y0, x1, y1, x2, y2 for each triangle)
"""
return self.normals
def get_normal(self, i, j):
"""Return normal vector j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
return self.normals[i, 2 * j:2 * j + 2]
def get_edgelength(self, i, j):
"""Return length of j'th edge of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
return self.edgelengths[i, j]
def get_number_of_triangles(self):
return self.number_of_triangles
def get_number_of_nodes(self):
return self.number_of_nodes
def get_nodes(self, absolute=False):
"""Return all nodes in mesh.
The nodes are ordered in an Nx2 array where N is the number of nodes.
This is the same format they were provided in the constructor
i.e. without any duplication.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
(To see which, switch to default absolute=True and run tests).
"""
N = self.number_of_nodes
V = self.nodes[:N, :]
if absolute is True:
if not self.geo_reference.is_absolute():
V = self.geo_reference.get_absolute(V)
return V
def get_node(self, i, absolute=False):
"""Return node coordinates for triangle i.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
(To see which, switch to default absolute=True and run tests).
Note: This method returns a modified _copy_ of the nodes slice if
absolute is True. If absolute is False, just return the slice.
This is related to the ensure_numeric() returning a copy problem.
"""
V = self.nodes[i, :]
if absolute is True:
if not self.geo_reference.is_absolute():
# get a copy so as not to modify the internal self.nodes array
V = copy.copy(V)
V += num.array([
self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()
], num.float)
return V
def get_vertex_coordinates(self, triangle_id=None, absolute=False):
"""Return vertex coordinates for all triangles.
Return all vertex coordinates for all triangles as a 3*M x 2 array
where the jth vertex of the ith triangle is located in row 3*i+j and
M the number of triangles in the mesh.
if triangle_id is specified (an integer) the 3 vertex coordinates
for triangle_id are returned.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
"""
V = self.vertex_coordinates
if triangle_id is None:
if absolute is True:
if not self.geo_reference.is_absolute():
V = self.geo_reference.get_absolute(V)
return V
else:
i = triangle_id
msg = 'triangle_id must be an integer'
assert int(i) == i, msg
assert 0 <= i < self.number_of_triangles
i3 = 3 * i
if absolute is True and not self.geo_reference.is_absolute():
offset = num.array([
self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()
], num.float)
return V[i3:i3 + 3, :] + offset
else:
return V[i3:i3 + 3, :]
def get_vertex_coordinate(self, i, j, absolute=False):
"""Return coordinates for vertex j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
msg = 'vertex id j must be an integer in [0,1,2]'
assert j in [0, 1, 2], msg
V = self.get_vertex_coordinates(triangle_id=i, absolute=absolute)
return V[j, :]
def compute_vertex_coordinates(self):
"""Return all vertex coordinates for all triangles as a 3*M x 2 array
where the jth vertex of the ith triangle is located in row 3*i+j.
This function is used to precompute this important structure. Use
get_vertex coordinates to retrieve the points.
"""
M = self.number_of_triangles
vertex_coordinates = num.zeros((3 * M, 2), num.float)
k0 = self.triangles[:, 0]
k1 = self.triangles[:, 1]
k2 = self.triangles[:, 2]
# I = num.arange(M,dtype=num.int)
#
# V0 = V[0:3*M:3, :]
# V1 = V[1:3*M:3, :]
# V2 = V[2:3*M:3, :]
vertex_coordinates[0:3 * M:3, :] = self.nodes[k0, :]
vertex_coordinates[1:3 * M:3, :] = self.nodes[k1, :]
vertex_coordinates[2:3 * M:3, :] = self.nodes[k2, :]
# for i in range(M):
# for j in range(3):
# k = self.triangles[i,j] # Index of vertex j in triangle i
# vertex_coordinates[3*i+j,:] = self.nodes[k]
return vertex_coordinates
def get_edge_midpoint_coordinates(self, triangle_id=None, absolute=False):
"""Return edge midpoint coordinates for all triangles or from particular triangle.
Return all edge midpoint coordinates for all triangles as a 3*M x 2 array
where the jth midpoint of the ith triangle is located in row 3*i+j and
M the number of triangles in the mesh.
if triangle_id is specified (an integer) the 3 midpoint coordinates
for triangle_id are returned.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
"""
E = self.edge_midpoint_coordinates
if triangle_id is None:
if absolute is True:
if not self.geo_reference.is_absolute():
E = self.geo_reference.get_absolute(E)
return E
else:
i = triangle_id
msg = 'triangle_id must be an integer'
assert int(i) == i, msg
assert 0 <= i < self.number_of_triangles
i3 = 3 * i
if absolute is True and not self.geo_reference.is_absolute():
offset = num.array([
self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()
], num.float)
return E[i3:i3 + 3, :] + offset
else:
return E[i3:i3 + 3, :]
def get_edge_midpoint_coordinate(self, i, j, absolute=False):
"""Return coordinates for edge midpoint j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
msg = 'edge midpoint id j must be an integer in [0,1,2]'
assert j in [0, 1, 2], msg
E = self.get_edge_midpoint_coordinates(triangle_id=i,
absolute=absolute)
return E[j, :] # Return (x, y) for edge mid point
def compute_edge_midpoint_coordinates(self):
"""Return all edge midpoint coordinates for all triangles as a 3*M x 2 array
where the jth edge midpoint of the ith triangle is located in row 3*i+j.
This function is used to precompute this important structure. Use
get_edge_midpoint_coordinates to retrieve the points.
Assumes that vertex_coordinates have been computed
"""
M = self.number_of_triangles
E = num.zeros((3 * M, 2), num.float)
V = self.vertex_coordinates
V0 = V[0:3 * M:3, :]
V1 = V[1:3 * M:3, :]
V2 = V[2:3 * M:3, :]
#print V.shape, V0.shape, V1.shape, V2.shape
#print E.shape, E[0:3*M:3, :].shape, E[1:3*M:3, :].shape, E[2:3*M:3, :].shape
E[0:3 * M:3, :] = 0.5 * (V1 + V2)
E[1:3 * M:3, :] = 0.5 * (V2 + V0)
E[2:3 * M:3, :] = 0.5 * (V0 + V1)
return E
def get_triangles(self, indices=None):
"""Get mesh triangles.
Return Mx3 integer array where M is the number of triangles.
Each row corresponds to one triangle and the three entries are
indices into the mesh nodes which can be obtained using the method
get_nodes()
Optional argument, indices is the set of triangle ids of interest.
"""
if indices is None:
return self.triangles
return num.take(self.triangles, indices, axis=0)
def get_disconnected_triangles(self):
"""Get mesh based on nodes obtained from get_vertex_coordinates.
Return array Mx3 array of integers where each row corresponds to
a triangle. A triangle is a triplet of indices into
point coordinates obtained from get_vertex_coordinates and each
index appears only once
This provides a mesh where no triangles share nodes
(hence the name disconnected triangles) and different
nodes may have the same coordinates.
This version of the mesh is useful for storing meshes with
discontinuities at each node and is e.g. used for storing
data in sww files.
The triangles created will have the format
[[0,1,2],
[3,4,5],
[6,7,8],
...
[3*M-3 3*M-2 3*M-1]]
"""
M = len(self) # Number of triangles
K = 3 * M # Total number of unique vertices
return num.reshape(num.arange(K, dtype=num.int), (M, 3))
def get_unique_vertices(self, indices=None):
"""Return indices to vertices as a sorted list.
FIXME (Ole): It may not be needed anymore
"""
triangles = self.get_triangles(indices=indices)
unique_verts = {}
for triangle in triangles:
unique_verts[triangle[0]] = 0
unique_verts[triangle[1]] = 0
unique_verts[triangle[2]] = 0
res = list(unique_verts.keys())
res.sort() # Ensure uniqueness
return res
# Note Padarn 27/11/12:
# This function was modified, but then it was deicded it was not
# needed. It should be restored if it is used elsewhere in the code
# (it was being used in quantity.py in the _set_vertex_values function).
# Note however, the function in the head of the code is very slow and
# could be easily sped up many fold.
#
# Have we profiled it? (Ole 31/5/2020)
def get_triangles_and_vertices_per_node(self, node=None):
"""Get triangles associated with given node.
Return list of triangle_ids, vertex_ids for specified node.
If node in None or absent, this information will be returned
for all nodes in a list L where L[v] is the triangle
list for node v.
"""
triangle_list = []
if node is not None:
# Get index for this node
#first = num.sum(self.number_of_triangles_per_node[:node])
first = self.node_index[node]
# Get number of triangles for this node
count = self.number_of_triangles_per_node[node]
for i in range(count):
index = self.vertex_value_indices[first + i]
volume_id = old_div(index, 3)
vertex_id = index % 3
triangle_list.append((volume_id, vertex_id))
triangle_list = num.array(triangle_list, num.int) #array default#
else:
# Get info for all nodes recursively.
# If need be, we can speed this up by
# working directly with the inverted triangle structure
for i in range(self.number_of_nodes):
L = self.get_triangles_and_vertices_per_node(node=i)
triangle_list.append(L)
return triangle_list
def build_inverted_triangle_structure(self):
"""Build structure listing triangles belonging to each node
Two arrays are created and store as mesh attributes
number_of_triangles_per_node: An integer array of length N
listing for each node how many triangles use it. N is the number of
nodes in mesh.
vertex_value_indices: An array of length M listing indices into
triangles ordered by node number. The (triangle_id, vertex_id)
pairs are obtained from each index as (index/3, index%3) or each
index can be used directly into a flat triangles array. This
is for example the case in the quantity.c where this structure is
used to average vertex values efficiently.
Example:
a = [0.0, 0.0] # node 0
b = [0.0, 2.0] # node 1
c = [2.0, 0.0] # node 2
d = [0.0, 4.0] # node 3
e = [2.0, 2.0] # node 4
f = [4.0, 0.0] # node 5
nodes = array([a, b, c, d, e, f])
# bac, bce, ecf, dbe
triangles = array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]])
For this structure:
number_of_triangles_per_node = [1 3 3 1 3 1]
which means that node a has 1 triangle associated with it, node b
has 3, node has 3 and so on.
vertex_value_indices = [ 1 0 3 10 2 4 7 9 5 6 11 8]
which reflects the fact that
node 0 is used by triangle 0, vertex 1 (index = 1)
node 1 is used by triangle 0, vertex 0 (index = 0)
and by triangle 1, vertex 0 (index = 3)
and by triangle 3, vertex 1 (index = 10)
node 2 is used by triangle 0, vertex 2 (index = 2)
and by triangle 1, vertex 1 (index = 4)
and by triangle 2, vertex 1 (index = 7)
node 3 is used by triangle 3, vertex 0 (index = 9)
node 4 is used by triangle 1, vertex 2 (index = 5)
and by triangle 2, vertex 0 (index = 6)
and by triangle 3, vertex 2 (index = 11)
node 5 is used by triangle 2, vertex 2 (index = 8)
Preconditions:
self.nodes and self.triangles are defined
Postcondition:
self.number_of_triangles_per_node is built
self.vertex_value_indices is built
"""
# Count number of triangles per node
# number_of_triangles_per_node = num.zeros(self.number_of_nodes,
# num.int) #array default#
# for volume_id, triangle in enumerate(self.get_triangles()):
# for vertex_id in triangle:
# number_of_triangles_per_node[vertex_id] += 1
# Need to pad number_of_triangles_per_node in case lone nodes at end of list
#number_of_triangles_per_node = num.zeros(self.number_of_nodes, num.int)
number_of_triangles_per_node = num.bincount(
self.triangles.flat).astype(num.int)
number_of_lone_nodes = self.number_of_nodes - len(
number_of_triangles_per_node)
orphan_nodes = num.argwhere(number_of_triangles_per_node == 0)
number_of_orphan_nodes = len(orphan_nodes)
if number_of_orphan_nodes > 0 and self.verbose:
msg = 'Node(s) %d not associated to a triangle.' % orphan_nodes[0]
print(msg)
if number_of_lone_nodes > 0:
number_of_triangles_per_node = \
num.append(number_of_triangles_per_node,num.zeros(number_of_lone_nodes,num.int))
#assert num.allclose(number_of_triangles_per_node_new, number_of_triangles_per_node)
# Allocate space for inverted structure
number_of_entries = num.sum(number_of_triangles_per_node)
assert number_of_entries == 3 * self.number_of_triangles
#vertex_value_indices = num.zeros(number_of_entries, num.int) #array default#
# Array of vertex_indices (3*vol_id+vertex_id) sorted into contiguous
# order around each node. Use with number_of_triangles_per_node to
# find vertices associated with a node.
# ie There are number_of_triangles_per_node[i] vertices
vertex_value_indices = num.argsort(self.triangles.flat).astype(num.int)
#vertex_value_indices = num.argsort(self.triangles.flatten())
# node_index = num.zeros((self.number_of_nodes)+1, dtype = num.int)
# node_index[0] = 0
# for i in xrange(self.number_of_nodes):
# node_index[i+1] = node_index[i] + number_of_triangles_per_node[i]
node_index = num.zeros((self.number_of_nodes) + 1, dtype=num.int)
node_index[1:] = num.cumsum(number_of_triangles_per_node)
#assert num.allclose(node_index,node_index_new)
# Save structures
self.node_index = node_index
self.number_of_triangles_per_node = number_of_triangles_per_node
self.vertex_value_indices = vertex_value_indices
def get_extent(self, absolute=False):
"""Return min and max of all x and y coordinates
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
"""
C = self.get_vertex_coordinates(absolute=absolute)
X = C[:, 0:6:2].copy()
Y = C[:, 1:6:2].copy()
xmin = num.min(X)
xmax = num.max(X)
ymin = num.min(Y)
ymax = num.max(Y)
return xmin, xmax, ymin, ymax
def get_areas(self):
"""Get areas of all individual triangles."""
return self.areas
def get_area(self):
"""Return total area of mesh"""
return num.sum(self.areas)
def set_georeference(self, g):
self.geo_reference = g
def get_georeference(self):
return self.geo_reference
def test_urs_ungridded2sww (self):
#Zone: 50
#Easting: 240992.578 Northing: 7620442.472
#Latitude: -21 30 ' 0.00000 '' Longitude: 114 30 ' 0.00000 ''
lat_long = [[-21.5,114.5],[-21,114.5],[-21,115]]
time_step_count = 2
time_step = 400
tide = 9000000
base_name, files = self.write_mux(lat_long,
time_step_count, time_step)
urs_ungridded2sww(base_name, mean_stage=tide,
verbose=self.verbose)
# now I want to check the sww file ...
sww_file = base_name + '.sww'
#Let's interigate the sww file
# Note, the sww info is not gridded. It is point data.
fid = NetCDFFile(sww_file)
# Make x and y absolute
x = fid.variables['x'][:]
y = fid.variables['y'][:]
geo_reference = Geo_reference(NetCDFObject=fid)
points = geo_reference.get_absolute(map(None, x, y))
points = ensure_numeric(points)
x = points[:,0]
y = points[:,1]
#Check that first coordinate is correctly represented
#Work out the UTM coordinates for first point
zone, e, n = redfearn(lat_long[0][0], lat_long[0][1])
assert num.allclose([x[0],y[0]], [e,n])
#Check the time vector
times = fid.variables['time'][:]
times_actual = []
for i in range(time_step_count):
times_actual.append(time_step * i)
assert num.allclose(ensure_numeric(times),
ensure_numeric(times_actual))
#Check first value
stage = fid.variables['stage'][:]
xmomentum = fid.variables['xmomentum'][:]
ymomentum = fid.variables['ymomentum'][:]
elevation = fid.variables['elevation'][:]
assert num.allclose(stage[0,0], e +tide) #Meters
#Check the momentums - ua
#momentum = velocity*(stage-elevation)
# elevation = - depth
#momentum = velocity_ua *(stage+depth)
# = n*(e+tide+n) based on how I'm writing these files
#
answer_x = n*(e+tide+n)
actual_x = xmomentum[0,0]
#print "answer_x",answer_x
#print "actual_x",actual_x
assert num.allclose(answer_x, actual_x) #Meters
#Check the momentums - va
#momentum = velocity*(stage-elevation)
# elevation = - depth
#momentum = velocity_va *(stage+depth)
# = e*(e+tide+n) based on how I'm writing these files
#
answer_y = -1*e*(e+tide+n)
actual_y = ymomentum[0,0]
#print "answer_y",answer_y
#print "actual_y",actual_y
assert num.allclose(answer_y, actual_y) #Meters
# check the stage values, first time step.
# These arrays are equal since the Easting values were used as
# the stage
assert num.allclose(stage[0], x +tide) #Meters
# check the elevation values.
# -ve since urs measures depth, sww meshers height,
# these arrays are equal since the northing values were used as
# the elevation
assert num.allclose(-elevation, y) #Meters
fid.close()
self.delete_mux(files)
os.remove(sww_file)
class General_mesh:
"""Collection of 2D triangular elements
A triangular element is defined in terms of three vertex ids,
ordered counter clock-wise, each corresponding to a given node
which is represented as a coordinate set (x,y).
Vertices from different triangles can point to the same node.
The nodes are implemented as an Nx2 numeric array containing the
x and y coordinates.
To instantiate:
Mesh(nodes, triangles)
where
nodes is either a list of 2-tuples or an Nx2 numeric array of
floats representing all x, y coordinates in the mesh.
triangles is either a list of 3-tuples or an Mx3 numeric array of
integers representing indices of all vertices in the mesh.
Each vertex is identified by its index i in [0, N-1].
Example:
a = [0.0, 0.0]
b = [0.0, 2.0]
c = [2.0,0.0]
e = [2.0, 2.0]
nodes = [a, b, c, e]
triangles = [ [1,0,2], [1,2,3] ] # bac, bce
# Create mesh with two triangles: bac and bce
mesh = Mesh(nodes, triangles)
Other:
In addition mesh computes an Mx6 array called vertex_coordinates.
This structure is derived from coordinates and contains for each
triangle the three x,y coordinates at the vertices.
See neighbourmesh.py for a specialisation of the general mesh class
which includes information about neighbours and the mesh boundary.
The mesh object is purely geometrical and contains no information
about quantities defined on the mesh.
"""
# FIXME: It would be a good idea to use geospatial data as an alternative
# input
def __init__(self,
nodes,
triangles,
geo_reference=None,
use_inscribed_circle=False,
verbose=False):
"""Build triangular 2d mesh from nodes and triangle information
Input:
nodes: x,y coordinates represented as a sequence of 2-tuples or
a Nx2 numeric array of floats.
triangles: sequence of 3-tuples or Mx3 numeric array of
non-negative integers representing indices into
the nodes array.
georeference (optional): If specified coordinates are
assumed to be relative to this origin.
"""
if verbose: log.critical('General_mesh: Building basic mesh structure')
self.use_inscribed_circle = use_inscribed_circle
self.triangles = num.array(triangles, num.int)
if verbose:
log.timingInfo("numTriangles, " + str(self.triangles.shape[0]))
self.nodes = num.array(nodes, num.float)
# Register number of elements and nodes
self.number_of_triangles = N = self.triangles.shape[0]
self.number_of_nodes = self.nodes.shape[0]
# FIXME: this stores a geo_reference, but when coords are returned
# This geo_ref is not taken into account!
if geo_reference is None:
self.geo_reference = Geo_reference() # Use defaults
else:
self.geo_reference = geo_reference
# Input checks
msg = ('Triangles must an Mx3 numeric array or a sequence of 3-tuples. '
'The supplied array has the shape: %s'
% str(self.triangles.shape))
assert len(self.triangles.shape) == 2, msg
msg = ('Nodes must an Nx2 numeric array or a sequence of 2-tuples'
'The supplied array has the shape: %s' % str(self.nodes.shape))
assert len(self.nodes.shape) == 2, msg
msg = 'Vertex indices reference non-existing coordinate sets'
assert num.max(self.triangles) < self.nodes.shape[0], msg
# FIXME: Maybe move to statistics?
# Or use with get_extent
xy_extent = [min(self.nodes[:,0]), min(self.nodes[:,1]),
max(self.nodes[:,0]), max(self.nodes[:,1])]
self.xy_extent = num.array(xy_extent, num.float)
# Allocate space for geometric quantities
self.normals = num.zeros((N, 6), num.float)
self.areas = num.zeros(N, num.float)
self.edgelengths = num.zeros((N, 3), num.float)
# Get x,y coordinates for all triangle vertices and store
self.centroid_coordinates = num.zeros((N, 2), num.float)
#Allocate space for geometric quantities
self.radii = num.zeros(N, num.float)
# Get x,y coordinates for all triangle vertices and store
self.vertex_coordinates = V = self.compute_vertex_coordinates()
# Get x,y coordinates for all triangle edge midpoints and store
self.edge_midpoint_coordinates = self.compute_edge_midpoint_coordinates()
# Initialise each triangle
if verbose:
log.critical('General_mesh: Computing areas, normals, '
'edgelengths, centroids and radii')
# Calculate Areas
V0 = V[0:3*N:3, :]
V1 = V[1:3*N:3, :]
V2 = V[2:3*N:3, :]
# Area
x0 = V0[:,0]
y0 = V0[:,1]
x1 = V1[:,0]
y1 = V1[:,1]
x2 = V2[:,0]
y2 = V2[:,1]
self.areas[:] = -((x1*y0-x0*y1) + (x2*y1-x1*y2) + (x0*y2-x2*y0))/2.0
#areas = -((x0-x1)*(y2-y1) - (y0-y1)*(x2-x1))/2.0
#assert num.allclose(self.areas, areas)
ind = num.where(self.areas <= 0.0)
msg = 'Degenerate Triangle(s) '+str(ind[0])
assert num.all(self.areas > 0.0), msg
#print V.shape, V0.shape, V1.shape, V2.shape
# #print E.shape, E[0:3*M:3, :].shape, E[1:3*M:3, :].shape, E[2:3*M:3, :].shape
# E[0:3*M:3, :] = 0.5*(V1+V2)
# E[1:3*M:3, :] = 0.5*(V2+V0)
# E[2:3*M:3, :] = 0.5*(V0+V1)
i0 = self.triangles[:,0]
i1 = self.triangles[:,1]
i2 = self.triangles[:,2]
assert num.allclose( x0, self.nodes[i0,0] )
assert num.allclose( y0, self.nodes[i0,1] )
assert num.allclose( x1, self.nodes[i1,0] )
assert num.allclose( y1, self.nodes[i1,1] )
assert num.allclose( x2, self.nodes[i2,0] )
assert num.allclose( y2, self.nodes[i2,1] )
xn0 = x2-x1
yn0 = y2-y1
l0 = num.sqrt(xn0**2 + yn0**2)
xn0 /= l0
yn0 /= l0
xn1 = x0-x2
yn1 = y0-y2
l1 = num.sqrt(xn1**2 + yn1**2)
xn1 /= l1
yn1 /= l1
xn2 = x1-x0
yn2 = y1-y0
l2 = num.sqrt(xn2**2 + yn2**2)
xn2 /= l2
yn2 /= l2
# Compute and store
self.normals[:,0] = yn0
self.normals[:,1] = -xn0
self.normals[:,2] = yn1
self.normals[:,3] = -xn1
self.normals[:,4] = yn2
self.normals[:,5] = -xn2
self.edgelengths[:,0] = l0
self.edgelengths[:,1] = l1
self.edgelengths[:,2] = l2
self.centroid_coordinates[:,0] = (x0 + x1 + x2)/3
self.centroid_coordinates[:,1] = (y0 + y1 + y2)/3
if self.use_inscribed_circle == False:
#OLD code. Computed radii may exceed that of an
#inscribed circle
#Midpoints
xm0 = (x1 + x2)/2
ym0 = (y1 + y2)/2
xm1 = (x2 + x0)/2
ym1 = (y2 + y0)/2
xm2 = (x0 + x1)/2
ym2 = (y0 + y1)/2
#The radius is the distance from the centroid of
#a triangle to the midpoint of the side of the triangle
#closest to the centroid
d0 = num.sqrt((self.centroid_coordinates[:,0] - xm0)**2 + (self.centroid_coordinates[:,1] - ym0)**2)
d1 = num.sqrt((self.centroid_coordinates[:,0] - xm1)**2 + (self.centroid_coordinates[:,1] - ym1)**2)
d2 = num.sqrt((self.centroid_coordinates[:,0] - xm2)**2 + (self.centroid_coordinates[:,1] - ym2)**2)
self.radii[:] = num.minimum(num.minimum(d0, d1), d2)
else:
#NEW code added by Peter Row. True radius
#of inscribed circle is computed
a = num.sqrt((x0-x1)**2+(y0-y1)**2)
b = num.sqrt((x1-x2)**2+(y1-y2)**2)
c = num.sqrt((x2-x0)**2+(y2-y0)**2)
self.radii[:]=2.0*self.areas/(a+b+c)
# for i in range(N):
# if verbose and i % ((N+10)/10) == 0: log.critical('(%d/%d)' % (i, N))
#
# x0, y0 = V[3*i, :]
# x1, y1 = V[3*i+1, :]
# x2, y2 = V[3*i+2, :]
#
#
# i0 = self.triangles[i][0]
# i1 = self.triangles[i][1]
# i2 = self.triangles[i][2]
#
## assert x0 == self.nodes[i0][0]
## assert y0 == self.nodes[i0][1]
##
## assert x1 == self.nodes[i1][0]
## assert y1 == self.nodes[i1][1]
##
## assert x2 == self.nodes[i2][0]
## assert y2 == self.nodes[i2][1]
#
## # Area
## self.areas[i] = abs((x1*y0-x0*y1) + (x2*y1-x1*y2) + (x0*y2-x2*y0))/2
##
## msg = 'Triangle %g (%f,%f), (%f,%f), (%f, %f)' % (i,x0,y0,x1,y1,x2,y2)
## msg += ' is degenerate: area == %f' % self.areas[i]
## assert self.areas[i] > 0.0, msg
#
# # Normals
# # The normal vectors
# # - point outward from each edge
# # - are orthogonal to the edge
# # - have unit length
# # - Are enumerated according to the opposite corner:
# # (First normal is associated with the edge opposite
# # the first vertex, etc)
# # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle
# n0 = num.array([x2-x1, y2-y1], num.float)
# l0 = num.sqrt(num.sum(n0**2))
#
# n1 = num.array([x0-x2, y0-y2], num.float)
# l1 = num.sqrt(num.sum(n1**2))
#
# n2 = num.array([x1-x0, y1-y0], num.float)
# l2 = num.sqrt(num.sum(n2**2))
#
# # Normalise
# n0 /= l0
# n1 /= l1
# n2 /= l2
#
## # Compute and store
## self.normals[i, :] = [n0[1], -n0[0],
## n1[1], -n1[0],
## n2[1], -n2[0]]
#
# # Edgelengths
# #self.edgelengths[i, :] = [l0, l1, l2]
#
#
#
# #Compute centroid
## centroid = num.array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3], num.float)
### self.centroid_coordinates[i] = centroid
##
##
## if self.use_inscribed_circle == False:
## #OLD code. Computed radii may exceed that of an
## #inscribed circle
##
## #Midpoints
## m0 = num.array([(x1 + x2)/2, (y1 + y2)/2], num.float)
## m1 = num.array([(x0 + x2)/2, (y0 + y2)/2], num.float)
## m2 = num.array([(x1 + x0)/2, (y1 + y0)/2], num.float)
##
## #The radius is the distance from the centroid of
## #a triangle to the midpoint of the side of the triangle
## #closest to the centroid
## d0 = num.sqrt(num.sum( (centroid-m0)**2 ))
## d1 = num.sqrt(num.sum( (centroid-m1)**2 ))
## d2 = num.sqrt(num.sum( (centroid-m2)**2 ))
##
## #self.radii[i] = min(d0, d1, d2)
##
## else:
## #NEW code added by Peter Row. True radius
## #of inscribed circle is computed
##
## a = num.sqrt((x0-x1)**2+(y0-y1)**2)
## b = num.sqrt((x1-x2)**2+(y1-y2)**2)
## c = num.sqrt((x2-x0)**2+(y2-y0)**2)
##
## self.radii[i]=2.0*self.areas[i]/(a+b+c)
# Build structure listing which triangles belong to which node.
if verbose: log.critical('General Mesh: Building inverted triangle structure')
self.build_inverted_triangle_structure()
if verbose: log.timingInfo("aoi, '%s'" % self.get_area())
def __len__(self):
return self.number_of_triangles
def __repr__(self):
return ('Mesh: %d vertices, %d triangles'
% (self.nodes.shape[0], len(self)))
def get_normals(self):
"""Return all normal vectors.
Return normal vectors for all triangles as an Nx6 array
(ordered as x0, y0, x1, y1, x2, y2 for each triangle)
"""
return self.normals
def get_normal(self, i, j):
"""Return normal vector j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
return self.normals[i, 2*j:2*j+2]
def get_edgelength(self, i, j):
"""Return length of j'th edge of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
return self.edgelengths[i, j]
def get_number_of_triangles(self):
return self.number_of_triangles
def get_number_of_nodes(self):
return self.number_of_nodes
def get_nodes(self, absolute=False):
"""Return all nodes in mesh.
The nodes are ordered in an Nx2 array where N is the number of nodes.
This is the same format they were provided in the constructor
i.e. without any duplication.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
(To see which, switch to default absolute=True and run tests).
"""
N = self.number_of_nodes
V = self.nodes[:N,:]
if absolute is True:
if not self.geo_reference.is_absolute():
V = self.geo_reference.get_absolute(V)
return V
def get_node(self, i, absolute=False):
"""Return node coordinates for triangle i.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
(To see which, switch to default absolute=True and run tests).
Note: This method returns a modified _copy_ of the nodes slice if
absolute is True. If absolute is False, just return the slice.
This is related to the ensure_numeric() returning a copy problem.
"""
V = self.nodes[i,:]
if absolute is True:
if not self.geo_reference.is_absolute():
# get a copy so as not to modify the internal self.nodes array
V = copy.copy(V)
V += num.array([self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()], num.float)
return V
def get_vertex_coordinates(self, triangle_id=None, absolute=False):
"""Return vertex coordinates for all triangles.
Return all vertex coordinates for all triangles as a 3*M x 2 array
where the jth vertex of the ith triangle is located in row 3*i+j and
M the number of triangles in the mesh.
if triangle_id is specified (an integer) the 3 vertex coordinates
for triangle_id are returned.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
"""
V = self.vertex_coordinates
if triangle_id is None:
if absolute is True:
if not self.geo_reference.is_absolute():
V = self.geo_reference.get_absolute(V)
return V
else:
i = triangle_id
msg = 'triangle_id must be an integer'
assert int(i) == i, msg
assert 0 <= i < self.number_of_triangles
i3 = 3*i
if absolute is True and not self.geo_reference.is_absolute():
offset=num.array([self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()], num.float)
return V[i3:i3+3,:] + offset
else:
return V[i3:i3+3,:]
def get_vertex_coordinate(self, i, j, absolute=False):
"""Return coordinates for vertex j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
msg = 'vertex id j must be an integer in [0,1,2]'
assert j in [0,1,2], msg
V = self.get_vertex_coordinates(triangle_id=i, absolute=absolute)
return V[j,:]
def compute_vertex_coordinates(self):
"""Return all vertex coordinates for all triangles as a 3*M x 2 array
where the jth vertex of the ith triangle is located in row 3*i+j.
This function is used to precompute this important structure. Use
get_vertex coordinates to retrieve the points.
"""
M = self.number_of_triangles
vertex_coordinates = num.zeros((3*M, 2), num.float)
k0 = self.triangles[:,0]
k1 = self.triangles[:,1]
k2 = self.triangles[:,2]
# I = num.arange(M,dtype=num.int)
#
# V0 = V[0:3*M:3, :]
# V1 = V[1:3*M:3, :]
# V2 = V[2:3*M:3, :]
vertex_coordinates[0:3*M:3,:] = self.nodes[k0,:]
vertex_coordinates[1:3*M:3,:] = self.nodes[k1,:]
vertex_coordinates[2:3*M:3,:] = self.nodes[k2,:]
# for i in range(M):
# for j in range(3):
# k = self.triangles[i,j] # Index of vertex j in triangle i
# vertex_coordinates[3*i+j,:] = self.nodes[k]
return vertex_coordinates
def get_edge_midpoint_coordinates(self, triangle_id=None, absolute=False):
"""Return edge midpoint coordinates for all triangles or from particular triangle.
Return all edge midpoint coordinates for all triangles as a 3*M x 2 array
where the jth midpoint of the ith triangle is located in row 3*i+j and
M the number of triangles in the mesh.
if triangle_id is specified (an integer) the 3 midpoint coordinates
for triangle_id are returned.
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
Default is False as many parts of ANUGA expects relative coordinates.
"""
E = self.edge_midpoint_coordinates
if triangle_id is None:
if absolute is True:
if not self.geo_reference.is_absolute():
E = self.geo_reference.get_absolute(E)
return E
else:
i = triangle_id
msg = 'triangle_id must be an integer'
assert int(i) == i, msg
assert 0 <= i < self.number_of_triangles
i3 = 3*i
if absolute is True and not self.geo_reference.is_absolute():
offset=num.array([self.geo_reference.get_xllcorner(),
self.geo_reference.get_yllcorner()], num.float)
return E[i3:i3+3,:] + offset
else:
return E[i3:i3+3,:]
def get_edge_midpoint_coordinate(self, i, j, absolute=False):
"""Return coordinates for edge midpoint j of the i'th triangle.
Return value is the numeric array slice [x, y]
"""
msg = 'edge midpoint id j must be an integer in [0,1,2]'
assert j in [0,1,2], msg
E = self.get_edge_midpoint_coordinates(triangle_id=i, absolute=absolute)
return E[j,:] # Return (x, y) for edge mid point
def compute_edge_midpoint_coordinates(self):
"""Return all edge midpoint coordinates for all triangles as a 3*M x 2 array
where the jth edge midpoint of the ith triangle is located in row 3*i+j.
This function is used to precompute this important structure. Use
get_edge_midpoint_coordinates to retrieve the points.
Assumes that vertex_coordinates have been computed
"""
M = self.number_of_triangles
E = num.zeros((3*M, 2), num.float)
V = self.vertex_coordinates
V0 = V[0:3*M:3, :]
V1 = V[1:3*M:3, :]
V2 = V[2:3*M:3, :]
#print V.shape, V0.shape, V1.shape, V2.shape
#print E.shape, E[0:3*M:3, :].shape, E[1:3*M:3, :].shape, E[2:3*M:3, :].shape
E[0:3*M:3, :] = 0.5*(V1+V2)
E[1:3*M:3, :] = 0.5*(V2+V0)
E[2:3*M:3, :] = 0.5*(V0+V1)
return E
def get_triangles(self, indices=None):
"""Get mesh triangles.
Return Mx3 integer array where M is the number of triangles.
Each row corresponds to one triangle and the three entries are
indices into the mesh nodes which can be obtained using the method
get_nodes()
Optional argument, indices is the set of triangle ids of interest.
"""
if indices is None:
return self.triangles
return num.take(self.triangles, indices, axis=0)
def get_disconnected_triangles(self):
"""Get mesh based on nodes obtained from get_vertex_coordinates.
Return array Mx3 array of integers where each row corresponds to
a triangle. A triangle is a triplet of indices into
point coordinates obtained from get_vertex_coordinates and each
index appears only once
This provides a mesh where no triangles share nodes
(hence the name disconnected triangles) and different
nodes may have the same coordinates.
This version of the mesh is useful for storing meshes with
discontinuities at each node and is e.g. used for storing
data in sww files.
The triangles created will have the format
[[0,1,2],
[3,4,5],
[6,7,8],
...
[3*M-3 3*M-2 3*M-1]]
"""
M = len(self) # Number of triangles
K = 3*M # Total number of unique vertices
return num.reshape(num.arange(K, dtype=num.int), (M,3))
def get_unique_vertices(self, indices=None):
"""FIXME(Ole): This function needs a docstring"""
triangles = self.get_triangles(indices=indices)
unique_verts = {}
for triangle in triangles:
unique_verts[triangle[0]] = 0
unique_verts[triangle[1]] = 0
unique_verts[triangle[2]] = 0
return unique_verts.keys()
# Note Padarn 27/11/12:
# This function was modified, but then it was deicded it was not
# needed. It should be restored if it is used elsewhere in the code
# (it was being used in quantity.py in the _set_vertex_values function).
# Note however, the function in the head of the code is very slow and
# could be easily sped up many fold.
def get_triangles_and_vertices_per_node(self, node=None):
"""Get triangles associated with given node.
Return list of triangle_ids, vertex_ids for specified node.
If node in None or absent, this information will be returned
for all nodes in a list L where L[v] is the triangle
list for node v.
"""
triangle_list = []
if node is not None:
# Get index for this node
#first = num.sum(self.number_of_triangles_per_node[:node])
first = self.node_index[node]
# Get number of triangles for this node
count = self.number_of_triangles_per_node[node]
for i in range(count):
index = self.vertex_value_indices[first+i]
volume_id = index / 3
vertex_id = index % 3
triangle_list.append( (volume_id, vertex_id) )
triangle_list = num.array(triangle_list, num.int) #array default#
else:
# Get info for all nodes recursively.
# If need be, we can speed this up by
# working directly with the inverted triangle structure
for i in range(self.number_of_nodes):
L = self.get_triangles_and_vertices_per_node(node=i)
triangle_list.append(L)
return triangle_list
def build_inverted_triangle_structure(self):
"""Build structure listing triangles belonging to each node
Two arrays are created and store as mesh attributes
number_of_triangles_per_node: An integer array of length N
listing for each node how many triangles use it. N is the number of
nodes in mesh.
vertex_value_indices: An array of length M listing indices into
triangles ordered by node number. The (triangle_id, vertex_id)
pairs are obtained from each index as (index/3, index%3) or each
index can be used directly into a flat triangles array. This
is for example the case in the quantity.c where this structure is
used to average vertex values efficiently.
Example:
a = [0.0, 0.0] # node 0
b = [0.0, 2.0] # node 1
c = [2.0, 0.0] # node 2
d = [0.0, 4.0] # node 3
e = [2.0, 2.0] # node 4
f = [4.0, 0.0] # node 5
nodes = array([a, b, c, d, e, f])
# bac, bce, ecf, dbe
triangles = array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]])
For this structure:
number_of_triangles_per_node = [1 3 3 1 3 1]
which means that node a has 1 triangle associated with it, node b
has 3, node has 3 and so on.
vertex_value_indices = [ 1 0 3 10 2 4 7 9 5 6 11 8]
which reflects the fact that
node 0 is used by triangle 0, vertex 1 (index = 1)
node 1 is used by triangle 0, vertex 0 (index = 0)
and by triangle 1, vertex 0 (index = 3)
and by triangle 3, vertex 1 (index = 10)
node 2 is used by triangle 0, vertex 2 (index = 2)
and by triangle 1, vertex 1 (index = 4)
and by triangle 2, vertex 1 (index = 7)
node 3 is used by triangle 3, vertex 0 (index = 9)
node 4 is used by triangle 1, vertex 2 (index = 5)
and by triangle 2, vertex 0 (index = 6)
and by triangle 3, vertex 2 (index = 11)
node 5 is used by triangle 2, vertex 2 (index = 8)
Preconditions:
self.nodes and self.triangles are defined
Postcondition:
self.number_of_triangles_per_node is built
self.vertex_value_indices is built
"""
# Count number of triangles per node
# number_of_triangles_per_node = num.zeros(self.number_of_nodes,
# num.int) #array default#
# for volume_id, triangle in enumerate(self.get_triangles()):
# for vertex_id in triangle:
# number_of_triangles_per_node[vertex_id] += 1
# Need to pad number_of_triangles_per_node in case lone nodes at end of list
#number_of_triangles_per_node = num.zeros(self.number_of_nodes, num.int)
number_of_triangles_per_node = num.bincount(self.triangles.flat)
number_of_lone_nodes = self.number_of_nodes - len(number_of_triangles_per_node)
#print number_of_lone_nodes
if number_of_lone_nodes > 0:
number_of_triangles_per_node = \
num.append(number_of_triangles_per_node,num.zeros(number_of_lone_nodes,num.int))
#assert num.allclose(number_of_triangles_per_node_new, number_of_triangles_per_node)
# Allocate space for inverted structure
number_of_entries = num.sum(number_of_triangles_per_node)
assert number_of_entries == 3*self.number_of_triangles
#vertex_value_indices = num.zeros(number_of_entries, num.int) #array default#
# Array of vertex_indices (3*vol_id+vertex_id) sorted into contiguous
# order around each node. Use with number_of_triangles_per_node to
# find vertices associated with a node.
# ie There are number_of_triangles_per_node[i] vertices
vertex_value_indices = num.argsort(self.triangles.flat)
#vertex_value_indices = num.argsort(self.triangles.flatten())
# node_index = num.zeros((self.number_of_nodes)+1, dtype = num.int)
# node_index[0] = 0
# for i in xrange(self.number_of_nodes):
# node_index[i+1] = node_index[i] + number_of_triangles_per_node[i]
node_index = num.zeros((self.number_of_nodes)+1, dtype = num.int)
node_index[1:] = num.cumsum(number_of_triangles_per_node)
#assert num.allclose(node_index,node_index_new)
# Save structures
self.node_index = node_index
self.number_of_triangles_per_node = number_of_triangles_per_node
self.vertex_value_indices = vertex_value_indices
def get_extent(self, absolute=False):
"""Return min and max of all x and y coordinates
Boolean keyword argument absolute determines whether coordinates
are to be made absolute by taking georeference into account
"""
C = self.get_vertex_coordinates(absolute=absolute)
X = C[:,0:6:2].copy()
Y = C[:,1:6:2].copy()
xmin = num.min(X)
xmax = num.max(X)
ymin = num.min(Y)
ymax = num.max(Y)
return xmin, xmax, ymin, ymax
def get_areas(self):
"""Get areas of all individual triangles."""
return self.areas
def get_area(self):
"""Return total area of mesh"""
return num.sum(self.areas)
def set_georeference(self, g):
self.geo_reference = g
def get_georeference(self):
return self.geo_reference
