def sector(r, t, nr, nt, h=0., diag=None):
"""Constructs a Formex which is a sector of a circle/cone.
A sector with radius r and angle t is modeled by dividing the
radius in nr parts and the angle in nt parts and then creating
straight line segments.
If a nonzero value of h is given, a conical surface results with its
top at the origin and the base circle of the cone at z=h.
The default is for all points to be in the (x,y) plane.
By default, a plex-4 Formex results. The central quads will collapse
into triangles.
If diag='up' or diag = 'down', all quads are divided by an up directed
diagonal and a plex-3 Formex results.
"""
r = float(r)
t = float(t)
p = Formex(regularGrid([0., 0., 0.], [r, 0., 0.], [nr, 0, 0],swapaxes=True).reshape(-1, 3))
if h != 0.:
p = p.shear(2, 0, h / r)
q = p.rotate(t / nt)
if isinstance(diag, str):
diag = diag[0]
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) for i in range(nt)])
return F
def connectCurves(curve1, curve2, n):
"""Connect two curves to form a surface.
curve1, curve2 are plex-2 Formices with the same number of elements.
The two curves are connected by a surface of quadrilaterals, with n
elements in the direction between the curves.
"""
if curve1.nelems() != curve2.nelems():
raise ValueError("Both curves should have same number of elements")
# Create the interpolations
curves = interpolate(curve1, curve2, n).split(curve1.nelems())
quads = [connect([c1, c1, c2, c2], nodid=[0, 1, 1, 0])
for c1, c2 in zip(curves[:-1], curves[1:])]
return Formex.concatenate(quads)
def rect(p1=[0., 0., 0.], p2=[1., 0., 0.], nx=1, ny=1):
"""Return a Formex which is a the circumference of a rectangle.
p1 and p2 are two opposite corner points of the rectangle.
The edges of the rectangle are in planes parallel to the z-axis.
There will always be two opposite edges that are parallel with the x-axis.
The other two will only be parallel with the y-axis if both points
have the same z-value, but in any case they will be parallel with the
y-z plane.
The edges parallel with the x-axis are divide in nx parts, the other
ones in ny parts.
"""
p1 = Coords(p1)
p2 = Coords(p2)
p12 = Coords([p2[0], p1[1], p1[2]])
p21 = Coords([p1[0], p2[1], p2[2]])
return Formex.concatenate([
line(p1, p12, nx),
line(p12, p2, ny),
line(p2, p21, nx),
line(p21, p1, ny)
])
def __init__(self,val,pos,prefix='',**kargs):
# Make sure we have strings
val = [ str(i) for i in val ]
pos = at.checkArray(pos,shape=(len(val),-1))
if len(val) != pos.shape[0]:
raise ValueError("val and pos should have same length")
# concatenate all strings
val = [ prefix+str(v) for v in val ]
cs = at.cumsum([0,] + [ len(v) for v in val ])
val = ''.join(val)
nc = cs[1:] - cs[:-1]
pos = [ at.multiplex(p,n,0) for p,n in zip(pos,nc) ]
pos = np.concatenate(pos,axis=0)
pos = at.multiplex(pos,4,1)
# Create the grids for the strings
F = Formex('4:0123')
grid = Formex.concatenate([ F.replic(n) for n in nc ])
# Create a text with the concatenation
Text.__init__(self,val,pos=pos,grid=grid,**kargs)