def centerline(F, dir, nx=2, mode=2, th=0.2):
"""Compute the centerline in the direction dir.
"""
bb = F.bbox()
x0 = F.center()
x1 = F.center()
x0[dir] = bb[0][dir]
x1[dir] = bb[1][dir]
n = array((0, 0, 0))
n[dir] = nx
grid = simple.regularGrid(x0, x1, n, swapaxes=True).reshape((-1, 3))
th *= (x1[dir] - x0[dir]) / nx
n = zeros((3, ))
n[dir] = 1.0
def localCenter(X, P, n):
"""Return the local center of points X in the plane P,n"""
test = abs(X.distanceFromPlane(P, n)) < th # points close to plane
if mode == 1:
C = X[test].center()
elif mode == 2:
C = X[test].centroid()
return C
center = [localCenter(F, P, n) for P in grid]
return PolyLine(center)
def create():
"""Create a closed surface and a set of points."""
nx, ny, nz = npts
# Create surface
if surface == 'file':
S = TriSurface.read(filename).centered()
elif surface == 'sphere':
S = simple.sphere(ndiv=grade)
if refine > S.nedges():
S = S.refine(refine)
draw(S, color='red')
if not S.isClosedManifold():
warning("This is not a closed manifold surface. Try another.")
return None, None
# Create points
if points == 'grid':
P = simple.regularGrid([-1., -1., -1.], [1., 1., 1.], [nx-1, ny-1, nz-1])
else:
P = random.rand(nx*ny*nz*3)
sc = array(scale)
siz = array(S.sizes())
tr = array(trl)
P = Formex(P.reshape(-1, 3)).resized(sc*siz).centered().translate(tr*siz)
draw(P, marksize=1, color='black')
zoomAll()
return S, P
def run():
clear()
# Create a grid of points with
X = Coords(
regularGrid([0., 0., 0.], [1., 1., 0.], [3, 3, 0]).reshape(-1, 3))
X = X.addNoise(rsize=0.05, asize=0.0)
draw(X)
drawNumbers(X)
ind = geomtools.closest(X)
M = connect([X, X[ind]]).toMesh().removeDuplicate()
# Hint: the connect() function transforms all items in the first
# argument to Formices. Thus it also works directly with Coords objects.
draw(M)
drawNumbers(M, color='red')
def cone1(r0, r1, h, t=360., nr=1, nt=24, diag=None):
"""Constructs a Formex which is (a sector of) a
circle / (truncated) cone / cylinder.
r0,r1,h are the lower and upper radius and the height of the truncated
cone. All can be positive, negative or zero.
Special cases:
r0 = r1 : cylinder
h = 0 : (flat) circle
r0 = 0 or r1 = 0 : untruncated cone
Only a sector of the structure, with opening angle t, is modeled.
The default results in a full circumference.
The cone is modeled by nr elements in height direction and nt elements in
circumferential direction.
By default, the result is a 4-plex Formex whose elements are quadrilaterals
(some of which may collapse into triangles).
If diag='up' or diag = 'down', all quads are divided by an up directed
diagonal and a plex-3 Formex results.
"""
r0, r1, h, t = [float(f) for f in (r0, r1, h, t)]
p = Formex(
simple.regularGrid([r0, 0., 0.], [r1, h, 0.],
[0, nr, 0]).reshape(-1, 3))
#draw(p,color=red)
a = (r1 - r0) / h
if a != 0.:
p = p.shear(0, 1, a)
#draw(p)
q = p.rotate(t / nt, axis=1)
#draw(q,color=green)
if diag == 'u':
F = connect([p, p, q], bias=[0, 1, 1]) + \
connect([p, q, q], bias=[1, 2, 1])
elif diag == 'd':
F = connect([q, p, q], bias=[0, 1, 1]) + \
connect([p, p, q], bias=[1, 2, 1])
else:
F = connect([p, p, q, q], bias=[0, 1, 1, 0])
F = Formex.concatenate([F.rotate(i * t / nt, 1) for i in range(nt)])
return F
def run():
clear()
transparent()
nquad = 1
nsphere = 5
S = sphere(nsphere)
#Creating the points to define the intersecting lines
R = regularGrid([0., 0., 0.], [0., 1., 1.], [1, nquad, nquad])
L0 = Coords(R.reshape(-1, 3)).trl([-2., -1. / 2, -1. / 2]).fuse()[0]
L1 = L0.trl([4., 0., 0.])
P, X = S.intersectionWithLines(q=L0, q2=L1, method='line', atol=1e-5)
# Retrieving the index of the points and the correspending lines and hit triangles
id_pts = X[:, 0]
id_intersected_line = X[:, 1]
id_hit_triangle = X[:, 2]
hitsxline = inverseIndex(id_intersected_line.reshape(-1, 1))
Nhitsxline = (hitsxline > -1).sum(axis=1)
ptsok = id_pts[hitsxline[where(hitsxline > -1)]]
hittriangles = id_hit_triangle[hitsxline[where(hitsxline > -1)]]
colors = ['red', 'green', 'blue', 'cyan']
[
draw(Formex([[p0, p1]]), color=c, linewidth=2, alpha=0.7)
for p0, p1, c in zip(L0, L1, colors)
]
id = 0
for icolor, nhits in enumerate(Nhitsxline):
for i in range(nhits):
draw(P[ptsok][id], color=colors[icolor], marksize=5, alpha=1)
draw(S.select([hittriangles[id]]),
ontop=True,
color=colors[icolor])
id += 1
draw(S, alpha=0.3)
)
Hex20.drawfaces = [Hex20.faces.selectNodes(i) for i in Quad8.drawfaces]
Hex20.drawfaces2 = [Hex20.faces]
Hex20.drawgl2edges = [Hex20.edges.selectNodes(i) for i in Line3.drawgl2faces]
Hex20.drawgl2faces = [Hex20.faces.selectNodes(i) for i in Quad8.drawgl2faces]
# THIS ELEMENT USES A REGULAR NODE NUMBERING!!
# WE MIGHT SWITCH OTHER ELEMENTS TO THIS REGULAR SCHEME TOO
# AND ADD THE RENUMBERING TO THE FE OUTPUT MODULES
from pyformex.simple import regularGrid
Hex27 = createElementType(
'hex27',
"A 27-node hexahedron",
ndim=3,
vertices=regularGrid([0., 0., 0.], [1., 1., 1.], [2, 2, 2]).reshape(-1, 3),
edges=(
'line3',
[(0, 1, 2), (6, 7, 8), (18, 19, 20), (24, 25, 26), (0, 3, 6),
(2, 5, 8), (18, 21, 24), (20, 23, 26), (0, 9, 18), (2, 11, 20),
(6, 15, 24), (8, 17, 26)],
),
faces=(
'quad9',
[
(0, 18, 24, 6, 9, 21, 15, 3, 12),
(2, 8, 26, 20, 5, 17, 23, 11, 14),
(0, 2, 20, 18, 1, 11, 19, 9, 10),
(6, 24, 26, 8, 15, 25, 17, 7, 16),
(0, 6, 8, 2, 3, 7, 5, 1, 4),
(18, 20, 26, 24, 19, 23, 25, 21, 22),