def function(self,params):
"""Archemidean spiral function."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
thickness = params['thickness']
gaussian_width = params['smoothing']
size = params['size']
half_thickness = thickness/2.0
spacing = size*2*pi
distance_from_origin = sqrt(x**2+y**2)
distance_from_spiral_middle = fmod(spacing + distance_from_origin - size*arctan2(y,x),spacing)
distance_from_spiral_middle = minimum(distance_from_spiral_middle,spacing - distance_from_spiral_middle)
distance_from_spiral = distance_from_spiral_middle - half_thickness
spiral = 1.0 - greater_equal(distance_from_spiral,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_spiral*distance_from_spiral, 2.0*sigmasq))
return maximum(falloff, spiral)
def __init__(self,
crv,
pnt=[0., 0., 0.],
vector=[1., 0., 0.],
theta=2. * math.pi):
if not isinstance(crv, Crv.Crv):
raise NURBSError, 'Parameter crv not derived from Crv class!'
# Translate and rotate the curve into alignment with the z-axis
T = translate(-numerix.asarray(pnt, numerix.Float))
# Normalize vector
vector = numerix.asarray(vector, numerix.Float)
len = numerix.sqrt(numerix.add.reduce(vector * vector))
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
vector = vector / len
if vector[0] == 0.:
angx = 0.
else:
angx = math.atan2(vector[0], vector[2])
RY = roty(-angx)
vectmp = numerix.ones((4, ), numerix.Float)
vectmp[0:3] = vector
vectmp = numerix.dot(RY, vectmp)
if vectmp[1] == 0.:
angy = 0.
else:
angy = math.atan2(vector[1], vector[2])
RX = rotx(angy)
crv.trans(numerix.dot(RX, numerix.dot(RY, T)))
arc = Crv.Arc(1., [0., 0., 0.], 0., theta)
narc = arc.cntrl.shape[1]
ncrv = crv.cntrl.shape[1]
coefs = numerix.zeros((4, narc, ncrv), numerix.Float)
angle = numerix.arctan2(crv.cntrl[1, :], crv.cntrl[0, :])
vectmp = crv.cntrl[0:2, :]
radius = numerix.sqrt(numerix.add.reduce(vectmp * vectmp))
for i in xrange(0, ncrv):
coefs[:, :, i] = numerix.dot(
rotz(angle[i]),
numerix.dot(
translate((0., 0., crv.cntrl[2, i])),
numerix.dot(scale((radius[i], radius[i])), arc.cntrl)))
coefs[3, :, i] = coefs[3, :, i] * crv.cntrl[3, i]
Srf.__init__(self, coefs, arc.uknots, crv.uknots)
T = translate(pnt)
RX = rotx(-angy)
RY = roty(angx)
self.trans(numerix.dot(T, numerix.dot(RY, RX)))
def radial(x, y, wide, gaussian_width):
"""
Radial grating - A sector of a circle with Gaussian fall-off.
Parameter wide determines in wide of sector in radians.
"""
angle = absolute(arctan2(y,x))
half_wide = wide/2
radius = 1.0 - greater_equal(angle,half_wide)
distance = angle - half_wide
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance*distance, 2.0*sigmasq))
return maximum(radius,falloff)
def __init__(self, crv, pnt = [0., 0., 0.], vector = [1., 0., 0.], theta = 2.*math.pi):
if not isinstance(crv, Crv.Crv):
raise NURBSError, 'Parameter crv not derived from Crv class!'
# Translate and rotate the curve into alignment with the z-axis
T = translate(-numerix.asarray(pnt, numerix.Float))
# Normalize vector
vector = numerix.asarray(vector, numerix.Float)
len = numerix.sqrt(numerix.add.reduce(vector*vector))
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
vector = vector/len
if vector[0] == 0.:
angx = 0.
else:
angx = math.atan2(vector[0], vector[2])
RY = roty(-angx)
vectmp = numerix.ones((4,), numerix.Float)
vectmp[0:3] = vector
vectmp = numerix.dot(RY, vectmp)
if vectmp[1] == 0.:
angy = 0.
else:
angy = math.atan2(vector[1], vector[2])
RX = rotx(angy)
crv.trans(numerix.dot(RX, numerix.dot(RY, T)))
arc = Crv.Arc(1., [0., 0., 0.], 0., theta)
narc = arc.cntrl.shape[1]
ncrv = crv.cntrl.shape[1]
coefs = numerix.zeros((4, narc, ncrv), numerix.Float)
angle = numerix.arctan2(crv.cntrl[1,:], crv.cntrl[0,:])
vectmp = crv.cntrl[0:2,:]
radius = numerix.sqrt(numerix.add.reduce(vectmp*vectmp))
for i in xrange(0, ncrv):
coefs[:,:,i] = numerix.dot(rotz(angle[i]),
numerix.dot(translate((0., 0., crv.cntrl[2,i])),
numerix.dot(scale((radius[i], radius[i])), arc.cntrl)))
coefs[3,:,i] = coefs[3,:,i] * crv.cntrl[3,i]
Srf.__init__(self, coefs, arc.uknots, crv.uknots)
T = translate(pnt)
RX = rotx(-angy)
RY = roty(angx)
self.trans(numerix.dot(T, numerix.dot(RY, RX)))
def function(self,params):
"""Radial function."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
gaussian_width = params['smoothing']
angle = absolute(arctan2(y,x))
half_length = params['arc_length']/2
radius = 1.0 - greater_equal(angle,half_length)
distance = angle - half_length
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance*distance, 2.0*sigmasq))
return maximum(radius, falloff)
def spiral(x, y, thickness, gaussian_width, density):
"""
Archemidean spiral with Gaussian fall-off outside the spiral curve.
"""
half_thickness = thickness/2.0
spacing = density*2*pi
distance_from_origin = sqrt(x**2+y**2)
distance_from_spiral_middle = fmod(spacing + distance_from_origin - density*arctan2(y,x),spacing)
distance_from_spiral_middle = minimum(distance_from_spiral_middle,spacing - distance_from_spiral_middle)
distance_from_spiral = distance_from_spiral_middle - half_thickness
spiral = 1.0 - greater_equal(distance_from_spiral,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_spiral*distance_from_spiral, 2.0*sigmasq))
return maximum(falloff,spiral)
