def circle_segment(theta,
r=1,
center=(0, 0, 0),
normal=(0, 0, 1),
xaxis=(1, 0, 0)):
""" Create a circle segment starting parallel to the rotated x-axis.
:param float theta: Angle in radians
:param float r: Radius
:param array-like center: circle segment center
:param array-like normal: normal vector to the plane that contains circle
:param array-like xaxis: direction of the parametric start point t=0
:return: A quadratic rational curve
:rtype: Curve
:raises ValueError: If radius is not positive
:raises ValueError: If theta is not in the range *[-2pi, 2pi]*
"""
# error test input
if abs(theta) > 2 * pi:
raise ValueError('theta needs to be in range [-2pi,2pi]')
if r <= 0:
raise ValueError('radius needs to be positive')
if theta == 2 * pi:
return circle(r, center, normal)
# build knot vector
knot_spans = int(ceil(abs(theta) / (2 * pi / 3)))
knot = [0]
for i in range(knot_spans + 1):
knot += [i] * 2
knot += [knot_spans] # knot vector [0,0,0,1,1,2,2,..,n,n,n]
knot = np.array(knot) / float(
knot[-1]) * theta # set parametric space to [0,theta]
n = (knot_spans - 1) * 2 + 3 # number of control points needed
cp = []
t = 0 # current angle
dt = float(theta) / knot_spans / 2 # angle step
# build control points
for i in range(n):
w = 1 - (i % 2) * (1 - cos(dt)
) # weights = 1 and cos(dt) every other i
x = r * cos(t)
y = r * sin(t)
cp += [[x, y, w]]
t += dt
if theta < 0:
cp.reverse()
result = Curve(BSplineBasis(3, np.flip(knot, 0)), cp, True)
else:
result = Curve(BSplineBasis(3, knot), cp, True)
result.rotate(rotate_local_x_axis(xaxis, normal))
return flip_and_move_plane_geometry(result, center, normal)
def circle(r=1, center=(0,0,0), normal=(0,0,1), type='p2C0', xaxis=(1,0,0)):
""" Create a circle.
:param float r: Radius
:param array-like center: local origin
:param array-like normal: local normal
:param string type: The type of parametrization ('p2C0' or 'p4C1')
:param array-like xaxis: direction of sem, i.e. parametric start point t=0
:return: A periodic, quadratic rational curve
:rtype: Curve
:raises ValueError: If radius is not positive
"""
if r <= 0:
raise ValueError('radius needs to be positive')
if type == 'p2C0' or type == 'C0p2':
w = 1.0 / sqrt(2)
controlpoints = [[1, 0, 1],
[w, w, w],
[0, 1, 1],
[-w, w, w],
[-1, 0, 1],
[-w, -w, w],
[0, -1, 1],
[w, -w, w]]
knot = np.array([-1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5]) / 4.0 * 2 * pi
result = Curve(BSplineBasis(3, knot, 0), controlpoints, True)
elif type.lower() == 'p4c1' or type.lower() == 'c1p4':
w = 2*sqrt(2)/3
a = 1.0/2/sqrt(2)
b = 1.0/6 * (4*sqrt(2)-1)
controlpoints = [[ 1,-a, 1],
[ 1, a, 1],
[ b, b, w],
[ a, 1, 1],
[-a, 1, 1],
[-b, b, w],
[-1, a, 1],
[-1,-a, 1],
[-b,-b, w],
[-a,-1, 1],
[ a,-1, 1],
[ b,-b, w]]
knot = np.array([ -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5]) / 4.0 * 2 * pi
result = Curve(BSplineBasis(5, knot, 1), controlpoints, True)
else:
raise ValueError('Unkown type: %s' %(type))
result *= r
result.rotate(rotate_local_x_axis(xaxis, normal))
return flip_and_move_plane_geometry(result, center, normal)
