def arc_by_center(x, y, arc_box, constant_length, thickness, gaussian_width):
"""
Arc with Gaussian fall-off after the solid ring-shaped region and specified
by point of tangency (x and y) and arc width and height.
This function calculates the start and end radian from the given width and
height, and then calls arc_by_radian function to draw the curve.
"""
arc_w = arc_box[0]
arc_h = abs(arc_box[1])
if arc_w == 0.0: # arc_w=0, don't draw anything
radius = 0.0
angles = (0.0, 0.0)
elif arc_h == 0.0: # draw a horizontal line, width=arc_w
return smooth_rectangle(x, y, arc_w, thickness, 0.0, gaussian_width)
else:
if constant_length:
curvature = arc_h / arc_w
radius = arc_w / (2 * pi * curvature)
angle = curvature * (2 * pi) / 2.0
else: # constant width
radius = arc_h / 2.0 + arc_w**2.0 / (8 * arc_h)
angle = arcsin(arc_w / 2.0 / radius)
if arc_box[1] < 0: # convex shape
y = y + radius
angles = (3.0 / 2.0 * pi - angle, 3.0 / 2.0 * pi + angle)
else: # concave shape
y = y - radius
angles = (pi / 2.0 - angle, pi / 2.0 + angle)
return arc_by_radian(x, y, radius * 2.0, angles, thickness, gaussian_width)
def arc_by_center(x, y, arc_box, constant_length, thickness, gaussian_width):
"""
Arc with Gaussian fall-off after the solid ring-shaped region and specified
by point of tangency (x and y) and arc width and height.
This function calculates the start and end radian from the given width and
height, and then calls arc_by_radian function to draw the curve.
"""
arc_w=arc_box[0]
arc_h=abs(arc_box[1])
if arc_w==0.0: # arc_w=0, don't draw anything
radius=0.0
angles=(0.0,0.0)
elif arc_h==0.0: # draw a horizontal line, width=arc_w
return smooth_rectangle(x, y, arc_w, thickness, 0.0, gaussian_width)
else:
if constant_length:
curvature=arc_h/arc_w
radius=arc_w/(2*pi*curvature)
angle=curvature*(2*pi)/2.0
else: # constant width
radius=arc_h/2.0+arc_w**2.0/(8*arc_h)
angle=arcsin(arc_w/2.0/radius)
if arc_box[1]<0: # convex shape
y=y+radius
angles=(3.0/2.0*pi-angle, 3.0/2.0*pi+angle)
else: # concave shape
y=y-radius
angles=(pi/2.0-angle, pi/2.0+angle)
return arc_by_radian(x, y, radius*2.0, angles, thickness, gaussian_width)
def arc_by_radian(x, y, height, radian_range, thickness, gaussian_width):
"""
Radial arc with Gaussian fall-off after the solid ring-shaped
region with the given thickness, with shape specified by the
(start,end) radian_range.
"""
# Create a circular ring (copied from the ring function)
radius = height/2.0
half_thickness = thickness/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0-bitwise_xor(greater_equal(distance_inside_inner_disk,0.0),greater_equal(distance_outside_outer_disk,0.0))
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
inner_falloff = x*0.0
outer_falloff = x*0.0
else:
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_inner_disk*distance_inside_inner_disk, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_outer_disk*distance_outside_outer_disk, 2.0*sigmasq))
output_ring = maximum(inner_falloff,maximum(outer_falloff,ring))
# Calculate radians (in 4 phases) and cut according to the set range)
# RZHACKALERT:
# Function float_error_ignore() cannot catch the exception when
# both dividend and divisor are 0.0, and when only divisor is 0.0
# it returns 'Inf' rather than 0.0. In x, y and
# distance_from_origin, only one point in distance_from_origin can
# be 0.0 (circle center) and in this point x and y must be 0.0 as
# well. So here is a hack to avoid the 'invalid value encountered
# in divide' error by turning 0.0 to 1e-5 in distance_from_origin.
distance_from_origin += where(distance_from_origin == 0.0, 1e-5, 0)
with float_error_ignore():
sines = divide(y, distance_from_origin)
cosines = divide(x, distance_from_origin)
arcsines = arcsin(sines)
phase_1 = where(logical_and(sines >= 0, cosines >= 0), 2*pi-arcsines, 0)
phase_2 = where(logical_and(sines >= 0, cosines < 0), pi+arcsines, 0)
phase_3 = where(logical_and(sines < 0, cosines < 0), pi+arcsines, 0)
phase_4 = where(logical_and(sines < 0, cosines >= 0), -arcsines, 0)
arcsines = phase_1 + phase_2 + phase_3 + phase_4
if radian_range[0] <= radian_range[1]:
return where(logical_and(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
else:
return where(logical_or(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
def arc_by_radian(x, y, height, radian_range, thickness, gaussian_width):
"""
Radial arc with Gaussian fall-off after the solid ring-shaped
region with the given thickness, with shape specified by the
(start,end) radian_range.
"""
# Create a circular ring (copied from the ring function)
radius = height/2.0
half_thickness = thickness/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0-bitwise_xor(greater_equal(distance_inside_inner_disk,0.0),greater_equal(distance_outside_outer_disk,0.0))
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
inner_falloff = x*0.0
outer_falloff = x*0.0
else:
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_inner_disk*distance_inside_inner_disk, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_outer_disk*distance_outside_outer_disk, 2.0*sigmasq))
output_ring = maximum(inner_falloff,maximum(outer_falloff,ring))
# Calculate radians (in 4 phases) and cut according to the set range)
# RZHACKALERT:
# Function float_error_ignore() cannot catch the exception when
# both dividend and divisor are 0.0, and when only divisor is 0.0
# it returns 'Inf' rather than 0.0. In x, y and
# distance_from_origin, only one point in distance_from_origin can
# be 0.0 (circle center) and in this point x and y must be 0.0 as
# well. So here is a hack to avoid the 'invalid value encountered
# in divide' error by turning 0.0 to 1e-5 in distance_from_origin.
distance_from_origin += where(distance_from_origin == 0.0, 1e-5, 0)
with float_error_ignore():
sines = divide(y, distance_from_origin)
cosines = divide(x, distance_from_origin)
arcsines = arcsin(sines)
phase_1 = where(logical_and(sines >= 0, cosines >= 0), 2*pi-arcsines, 0)
phase_2 = where(logical_and(sines >= 0, cosines < 0), pi+arcsines, 0)
phase_3 = where(logical_and(sines < 0, cosines < 0), pi+arcsines, 0)
phase_4 = where(logical_and(sines < 0, cosines >= 0), -arcsines, 0)
arcsines = phase_1 + phase_2 + phase_3 + phase_4
if radian_range[0] <= radian_range[1]:
return where(logical_and(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
else:
return where(logical_or(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
