def calc_temcor_side(pgon, pyramid_ht, base_ht, freq):
freq += 1
inrad = pgon.inradius()
axis = Vec(-inrad, 0, pyramid_ht) # axis to rotate plane around
A = Vec(0, 0, base_ht + pyramid_ht) # apex
B = Vec(inrad, 0.5, base_ht) # base polygon vertex
n0 = Vec.cross(A, B).unit()
edge_ang = anti_lib.angle_around_axis(Vec(B[0], 0, B[2]), B, axis)
ang_inc = edge_ang/freq
points = []
faces = []
for i in range(freq):
n_inc = Mat.rot_axis_ang(axis, i*ang_inc) * Vec(0, 1, 0)
edge_v = Vec.cross(n_inc, n0).unit()
last_idx = i*(i-1)//2
new_idx = i*(i+1)//2
for j in range(i + 1):
v = Mat.rot_axis_ang(axis, -2*j*ang_inc) * edge_v
points.append(v)
if new_idx and j < i:
faces.append([new_idx+j, new_idx+j+1, last_idx+j])
if j < i-1:
faces.append([new_idx+j+1, last_idx+j+1, last_idx+j])
return (points, faces)
def j89_get_principal_verts(pgon, ang, flags):
bad = flags.strip('ABC')
if bad:
raise ValueError('Unrecognised form flag(s) \'' + bad + '\'')
ridge_down = 'A' in flags
ridge2_down = 'B' in flags
belt_back = 'C' in flags
pgon.N *= 2
# p_ang2 = pgon2.angle()
A, B, B2, C = get_pstt_cap_verts(pgon, ang, ridge_down)
pgon.N //= 2
p_ang = pgon.angle() / 2
A2_rad = pgon.circumradius(edge) # circumradius of top polygon
sq_mid = (B + B2) / 2
sq_mid_rad = Vec(sq_mid[0], sq_mid[1], 0).mag()
tri_ht2 = 3 / 4 - (A2_rad - sq_mid_rad)**2
if tri_ht2 < -epsilon:
raise ValueError(
'Not possible to calculate upper equilateral triangle')
A2_ht = (1 - 2 * belt_back) * sqrt(tri_ht2) + B[2]
A2 = Vec(A2_rad, 0, A2_ht).rot_z(p_ang / 2)
A2_minus1 = A2.rot_z(-2 * p_ang)
B2_minus1 = B2.rot_z(-2 * p_ang)
C2 = get_three_line_vert(A2_minus1, A2, B2_minus1, B, ridge2_down)
return [pt.rot_z(p_ang / 2) for pt in [A, B, B2, C, A2, C2]]
def j88_get_principal_verts(pgon, ang, flags):
bad = flags.strip('AB')
if bad:
raise ValueError('Unrecognised form flag(s) \'' + bad + '\'')
ridge = 'A' not in flags
belt_back = 'B' in flags
A, B, B2, C = get_pstts_cap_verts(pgon, ang, ridge)
p_ang = pgon.angle() / 2
sq_mid = (B + B2.rot_z(2 * p_ang)) / 2
sq_mid_rad = Vec(sq_mid[0], sq_mid[1], 0).mag()
A_rad = A[0]
tri_ht2 = 3 * edge / 4 - (A_rad - sq_mid_rad)**2
if tri_ht2 < -epsilon:
raise ValueError(
'Not possible to calculate upper equilateral triangle')
A2_ht = (1 - 2 * belt_back) * sqrt(tri_ht2) + B[2]
A2 = Vec(A_rad, 0, A2_ht).rot_z(p_ang)
mid_B_B1 = Vec(B[0], 0, B[2])
ax = C - mid_B_B1
rot = Mat.rot_axis_ang(ax, math.pi)
pt = A - mid_B_B1
C2 = rot * pt + mid_B_B1
return A, B, B2, C, A2, C2
def make_equ_antiherm(pgon, dih_ang):
"""Make a hermaphrodite with equilateral triangles"""
N = pgon.N
a = pgon.angle()/2
R = pgon.circumradius()
tri_alt = sqrt(3)/2
tri_ht = tri_alt * sin(dih_ang)
R2 = pgon.inradius() + tri_alt * cos(dih_ang)
points = [Vec(0, 0, 0)]*(2*N+1)
for i in range(N):
points[i] = Vec(R*cos(2*i*a), R*sin(2*i*a), 0)
points[i+N] = Vec(R2*cos(2*i*a+a), R2*sin(2*i*a+a), tri_ht)
A = sqrt(points[0][0]**2 + points[0][1]**2)
mid = anti_lib.centroid([points[N], points[2*N-1]])
B = sqrt(mid[0]**2 + mid[1]**2)
z_diff = mid[2] - points[0][2]
points[2*N][2] = A * z_diff / (A - B)
faces = []
faces.append([i for i in range(N)]) # bottom
for i in range(N):
faces.append([i, (i + 1) % N, N + i])
faces.append([N + i, 2*N, N + (i + 1) % N, (i + 1) % N])
return points, faces
def calculate_belt_points(pgon, model_type):
ang = pgon.angle() / 2
tan_a = math.sin(ang) / (math.cos(ang) + phi) # half of unit edge
P = Vec(1 / (2 * tan_a), -1 / 2, 0)
tan_b = math.sin(ang) / (math.cos(ang) + 1 / phi) # half of phi edge
Q = Vec(phi / (2 * tan_b), -phi / 2, 0)
bar_ht = math.cos(math.pi / 10) # planar height of pentagon "bar"
diff_r = P[0] - Q[0]
try:
ht0 = math.sqrt(bar_ht**2 - diff_r**2) / 2
except:
raise ValueError('model is not constructible')
P[2] = -ht0
Q[2] = ht0
pent_ht = math.sqrt(5 + 2 * math.sqrt(5)) / 2 # planar height of pentagon
x_cap = P[0] - pent_ht * (diff_r / bar_ht)
z_cap = -ht0 + pent_ht * ((2 * ht0) / bar_ht)
R = Vec(x_cap, 0, z_cap)
S = Vec(x_cap * math.cos(ang), x_cap * math.sin(ang), -z_cap)
cap_inrad = x_cap * math.cos(ang)
apex_ht = 0
if model_type == 'a':
try:
apex_ht = z_cap + cap_inrad * (z_cap + P[2]) / (P[0] - cap_inrad)
except:
raise ValueError('could not calculate apex height')
A = Vec(0, 0, apex_ht)
return [P, Q, R, S, A]
def j89_get_principal_verts(pgon, ang, flags):
bad = flags.strip('ABC')
if bad:
raise ValueError('Unrecognised form flag(s) \''+bad+'\'')
ridge_down = 'A' in flags
ridge2_down = 'B' in flags
belt_back = 'C' in flags
pgon.N *= 2
# p_ang2 = pgon2.angle()
A, B, B2, C = get_pstt_cap_verts(pgon, ang, ridge_down)
pgon.N //= 2
p_ang = pgon.angle()/2
A2_rad = pgon.circumradius(edge) # circumradius of top polygon
sq_mid = (B + B2) / 2
sq_mid_rad = Vec(sq_mid[0], sq_mid[1], 0).mag()
tri_ht2 = 3/4 - (A2_rad - sq_mid_rad)**2
if tri_ht2 < -epsilon:
raise ValueError(
'Not possible to calculate upper equilateral triangle')
A2_ht = (1 - 2*belt_back)*sqrt(tri_ht2) + B[2]
A2 = Vec(A2_rad, 0, A2_ht).rot_z(p_ang/2)
A2_minus1 = A2.rot_z(-2*p_ang)
B2_minus1 = B2.rot_z(-2*p_ang)
C2 = get_three_line_vert(A2_minus1, A2, B2_minus1, B, ridge2_down)
return [pt.rot_z(p_ang/2) for pt in [A, B, B2, C, A2, C2]]
def get_default_angle(pgon, radius_top, radius_bottom, height):
a = pgon.angle() / 2
P1 = Vec(radius_top, 0, height)
Q1 = Vec(radius_bottom * cos(a), radius_bottom * sin(a), 0.0)
Q2 = Vec(radius_bottom * cos(-a), radius_bottom * sin(-a), 0.0)
v0 = (Q1 - P1).unit()
v1 = (Q2 - P1).unit()
cos_a = anti_lib.safe_for_trig(Vec.dot(v0, v1))
ang = acos(cos_a)
return pi - ang
def read_coords():
points = []
while 1:
line = sys.stdin.readline()
if line == '\n':
continue
if line == "":
break
m = re.search('^ *([^ ,]+) *,? *([^ ,]+) *,? *([^ ,\n]+) *$', line)
if not m:
sys.stderr.write(
'error: did not find x, y and z values in following '
'line (1):\n')
sys.stderr.write(line)
sys.exit(1)
else:
try:
points.append(
Vec(*[float(m.group(i)) for i in range(1, 3 + 1)]))
except:
sys.stderr.write(
'error: did not find x, y and z values in following '
'linei (2):\n')
sys.stderr.write(line)
sys.exit(1)
return points
def main():
"""Entry point"""
parser = argparse.ArgumentParser(description=__doc__)
parser.add_argument('num_balls_on_ring',
help='Number of balls on each ring',
type=int,
nargs='?',
default=10)
parser.add_argument('-o',
'--outfile',
help='output file name (default: standard output)',
type=argparse.FileType('w'),
default=sys.stdout)
args = parser.parse_args()
ring_centres = read_coords()
if not len(ring_centres):
parser.error('no coordinates in input')
R = ring_centres[0].mag()
dist = find_minimum_separation(ring_centres)
a = math.asin(dist / (2 * R))
ball_points, ball_ang = make_ring(R, args.num_balls_on_ring, a)
print('ball radius = %.14f' % (2 * R * math.sin(ball_ang / 2)),
file=sys.stderr)
out = anti_lib.OffFile(args.outfile)
out.print_header(len(ring_centres) * len(ball_points), 0)
for cent in ring_centres:
mat = Mat.rot_from_to(Vec(0, 0, 1), cent)
out.print_verts([mat * p for p in ball_points])
def touching_spheres(R, p0, r0, p1, r1, p2, r2):
# Add R to the radii, the intersection points of the three sheres are
# the centres of the touching ball(s)
r0 += R
r1 += R
r2 += R
# find centre of circle nd readius where first two spheres intersect
pc1, rc1 = sphere_intersection(p0, r0, p1, r1)
if pc1 is None:
return None, None
# the second circle is defined by th plane of first circle intersecting
# the third sphere
# find centre of second circle
p2_pc1 = pc1 - p2
p0_p1 = p1 - p0
unit_p0_p1 = p0_p1.unit()
len_p2_pc2 = Vec.dot(p2_pc1, unit_p0_p1)
# is circle outside of third sphere
if not (r2 > len_p2_pc2 > -r2):
return None, None
p2_pc2 = unit_p0_p1 * len_p2_pc2
pc2 = p2 + p2_pc2
rc2 = math.sqrt(r2**2 - len_p2_pc2**2)
# find pt - intersection of plane of sphere centres and line joining
# touching spheres, and R distance pt to a touching sphere centre.
pt, R = sphere_intersection(pc1, rc1, pc2, rc2)
if pt is None:
return None, None
# make a vector length R perpendicular to the plane of the sphere centres
R_norm = Vec.cross(p1 - p0, p2 - p0)
len_R_norm = R_norm.mag()
if not len_R_norm:
return None, None
R_norm = R_norm * R/len_R_norm
return pt + R_norm, pt - R_norm
def get_pstt_cap_verts(pgon, ang, ridge_down):
p_ang = pgon.angle()/2
rad = pgon.circumradius(edge)
# Polygon vertex
A = Vec(rad, 0, 0)
# First and last square vertices
B = Vec(rad + edge*cos(ang)*cos(p_ang),
edge*cos(ang)*sin(p_ang),
edge*sin(ang))
B2 = Vec(B[0], -B[1], B[2]).rot_z(2*p_ang)
A_minus1 = A.rot_z(-2*p_ang)
B2_minus1 = B2.rot_z(-4*p_ang)
C = get_three_line_vert(A, A_minus1, B, B2_minus1, ridge_down)
return A, B, B2, C
def get_default_angle(pgon, radius_top, radius_bottom, height):
a = pgon.angle()/2
P1 = Vec(radius_top, 0, height)
Q1 = Vec(radius_bottom * cos(a), radius_bottom * sin(a), 0.0)
Q2 = Vec(radius_bottom * cos(-a), radius_bottom * sin(-a), 0.0)
v0 = (Q1-P1).unit()
v1 = (Q2-P1).unit()
cos_a = anti_lib.safe_for_trig(Vec.dot(v0, v1))
ang = acos(cos_a)
return pi-ang
def make_frame(frame_elems, axis_angle, rad, num_segs):
points = []
faces = []
if frame_elems:
v0 = Vec(0, 0, -1)
v1 = Vec(math.sin(axis_angle), 0, -math.cos(axis_angle))
if 'r' in frame_elems:
ps, fs = make_arc(v0, v1, num_segs, 0)
points += ps
faces += fs
if 'a' in frame_elems:
num_pts = len(points)
points += [v0, -v0, v1, -v1]
faces += [[num_pts + 0, num_pts + 1], [num_pts + 2, num_pts + 3]]
points = [rad * p for p in points]
faces += [[i] for i in range(len(points))]
return points, faces
def calc_polygons2(pgon0, r0, ang, pgon1, r1, angle_between_axes):
# rotate initial vertex of polygon0 by ang. Common
# point lies on a line through vertex in the direction
# of axis0 (z-axis). Common vertex lies on a cylinder
# radius r1 with axis on axis1.
# rotate model so axis1 is on z-axis, to simplify the
# calculation of the intersection
rot = Mat.rot_axis_ang(Vec(0, 1, 0), angle_between_axes)
# initial vertex turned on axis
V = Vec(r0, 0, 0).rot_z(ang)
# vertex in rotated model
Q = rot * V
# direction of line in rotated model
u = rot * Vec(0, 0, 1)
# equation of line is P = Q + tu for components x y z and parameter t
# equation of cylinder at z=0 is x^2 + y^2 = r1^2
a = u[0]**2 + u[1]**2
b = 2 * (Q[0] * u[0] + Q[1] * u[1])
c = Q[0]**2 + Q[1]**2 - r1**2
disc = b**2 - 4 * a * c
if disc < -epsilon:
raise Exception("model is not geometrically constructible")
elif disc < 0:
disc = 0
t = (-b - math.sqrt(disc)) / (2 * a) # negative gives most distant point
P = V + Vec(0, 0, t) # the common point
points = []
points += [P.rot_z(i * pgon0.angle()) for i in range(pgon0.N)]
faces = [[i for i in range(pgon0.N)]]
Q = rot * P
rot_inv = Mat.rot_axis_ang(Vec(0, 1, 0), -angle_between_axes)
points += [rot_inv * Q.rot_z(i * pgon1.angle()) for i in range(pgon1.N)]
faces += [[i + pgon0.N for i in range(pgon1.N)]]
return points, faces
def bifrustum_model(pgon, arg_type):
"""Construct bifrustum model with golden trapziums"""
N = pgon.N
ang = pgon.angle() / 2
R0 = phi / (2 * sin(ang))
R1 = 1 / (2 * sin(ang))
ht = sqrt(phi**2 - (R0 - R1)**2)
points = []
points += [Vec(R0, 0, ht).rot_z(2 * i * ang) for i in range(N)]
points += [Vec(R1, 0, 0).rot_z(2 * i * ang) for i in range(N)]
points += [Vec(R0, 0, -ht).rot_z(2 * i * ang) for i in range(N)]
faces = []
faces.append([i for i in range(N)])
faces.append([i + 2 * N for i in range(N)])
for i in range(N):
faces.append([i, (i + 1) % N, N + (i + 1) % N, N + i])
faces.append([N + i, N + (i + 1) % N, 2 * N + (i + 1) % N, 2 * N + i])
return points, faces
def calc_polygons(pgon0, pgon1, ang, ratio, angle_between_axes):
# rotate initial vertex of polygon0 by ang. Common
# point lies on a line through vertex in the direction
# of axis0 (z-axis). Common vertex lies on a cylinder
# radius r1 with axis on axis1.
# rotate model so axis1 is on z-axis, to simplify the
# calculation of the intersection
rot = Mat.rot_axis_ang(Vec(0, 1, 0), angle_between_axes)
# initial vertex turned on axis
V = Vec(pgon0.circumradius(), 0, 0).rot_z(ang)
# vertex in rotated model
Q = rot * V
# direction of line in rotated model
u = rot * Vec(0, 0, 1)
# equation of line is P = Q + tu for components x y z and parameter t
# equation of cylinder at z=0 is x^2 + y^2 = r1^2
a = u[0]**2 + u[1]**2
b = 2 * (Q[0] * u[0] + Q[1] * u[1])
c = Q[0]**2 + Q[1]**2 - (pgon1.circumradius() * ratio)**2
disc = b**2 - 4 * a * c
if disc < -epsilon:
raise Exception("model is not geometrically constructible")
elif disc < 0:
disc = 0
t = (-b - math.sqrt(disc)) / (2 * a)
P = V + Vec(0, 0, t) # the common point
points = pgon0.get_points(P)
faces = pgon0.get_faces()
Q = rot * P
rot_inv = Mat.rot_axis_ang(Vec(0, 1, 0), -angle_between_axes)
points += [rot_inv * p for p in pgon1.get_points(Q)]
faces += pgon1.get_faces(pgon0.N * pgon0.parts)
return points, faces
def get_three_line_vert(A0, A1, B0, B1, ridge_down):
A_edge = A1 - A0
B_edge = B0 - A0
cos_gamma = Vec.dot(A_edge.unit(), B_edge.unit())
if abs(cos_gamma) > 1:
cos_gamma /= abs(cos_gamma)
gamma = acos(cos_gamma)
d = (edge / 2) * tan(gamma / 2)
h2 = 3 * edge / 4 - d**2
if h2 < -epsilon:
raise ValueError(
'Not possible to calculate a three-line-fill triangle')
h = (1 - 2 * ridge_down) * sqrt(h2)
A_mid = (A0 + A1) / 2
B_mid = (B0 + B1) / 2
mid_dir = (B_mid - A_mid).unit()
norm = Vec.cross(B_edge, A_edge).unit()
P_from_A_mid = mid_dir * d + norm * h
return A_mid + P_from_A_mid
def make_arc(v0, v1, num_segs, start_idx):
axis = Vec.cross(v0, v1).unit()
ang = anti_lib.angle_around_axis(v0, v1, axis)
points = [v0]
faces = []
mat = Mat.rot_axis_ang(axis, ang/num_segs)
for i in range(num_segs):
# accumulated error
points.append(mat * points[-1])
faces.append([start_idx + i, start_idx + i+1])
return points, faces
def get_three_line_vert(A0, A1, B0, B1, ridge_down):
A_edge = A1 - A0
B_edge = B0 - A0
cos_gamma = Vec.dot(A_edge.unit(), B_edge.unit())
if abs(cos_gamma) > 1:
cos_gamma /= abs(cos_gamma)
gamma = acos(cos_gamma)
d = (edge/2)*tan(gamma/2)
h2 = 3*edge/4 - d**2
if h2 < -epsilon:
raise ValueError(
'Not possible to calculate a three-line-fill triangle')
h = (1 - 2*ridge_down) * sqrt(h2)
A_mid = (A0 + A1) / 2
B_mid = (B0 + B1) / 2
mid_dir = (B_mid - A_mid).unit()
norm = Vec.cross(B_edge, A_edge).unit()
P_from_A_mid = mid_dir*d + norm*h
return A_mid + P_from_A_mid
def antiprism_model(pgon, arg_type):
"""Construct antiprism model with golden trapziums"""
N = pgon.N
ang = pgon.angle() / 2
P = tri_antiprism_pt(pgon, gold_trap_diag, 1, phi)
Q = Vec(P[0], -P[1], -P[2])
points = []
for i in range(N):
points.append(P.rot_z(2 * i * ang))
for i in range(N):
points.append(Q.rot_z(2 * i * ang))
R = points[N - 1] + (P - Q) * phi
for i in range(N):
points.append(R.rot_z(2 * i * ang))
S = Vec(R[0], -R[1], -R[2])
for i in range(N):
points.append(S.rot_z(2 * i * ang))
faces = []
faces.append([2 * N + i for i in range(N)])
faces.append([3 * N + i for i in range(N)])
for i in range(N):
faces.append([i, 2 * N + i, 2 * N + ((i + 1) % N)])
faces.append([N + i, 3 * N + i, 3 * N + ((i - 1) % N)])
faces.append(
[i, 2 * N + ((i + 1) % N), ((i + 1) % N), N + ((i + 1) % N)])
faces.append([i, N + ((i + 1) % N), 3 * N + i, N + i])
return points, faces
def make_frame(frame_elems, pgon, axis_angle, num_segs):
points = []
faces = []
if frame_elems:
v0 = Vec(0, 0, 1)
v1 = Vec(-math.sin(axis_angle), 0, math.cos(axis_angle))
v2 = v1.rot_z(pgon.angle()/2)
v2[2] *= -1
if 'r' in frame_elems:
ps, fs = make_arc(v0, v1, num_segs, 0)
points += ps
faces += fs
ps, fs = make_arc(v1, v2, num_segs, num_segs+1)
points += ps
faces += fs
if 'a' in frame_elems:
faces += [[len(points)+i, len(points)+i+1] for i in range(0, 6, 2)]
points += [v0, -v0, v1, -v1, v2, -v2]
rad = calc_polygons(pgon, 0, axis_angle, -1)[0][0].mag()
points = [rad * p for p in points]
faces += [[i] for i in range(len(points))]
return points, faces
def tri_antiprism_pt(pgon, a, b, c):
"""Return construct point for antiprism model"""
s = (a + b + c) / 2
alt = 2 * math.sqrt(s * (s - a) * (s - b) *
(s - c)) / a # planar height of A
ang = pgon.angle() / 2
R = pgon.circumradius(a) # polygon circumradius (side a)
r = pgon.inradius(a) # polygon inradius (side a)
a0 = math.sqrt(b**2 - alt**2) # from C to perpendicular from A
y = a0 - a / 2
x = math.sqrt(R**2 - y**2)
alt_proj_x = x - r # projection of alt onto x dir
z = math.sqrt(alt**2 - alt_proj_x**2) / 2
ang_to_A = math.atan2(y, x) # adjust point for dih axis
ang_off = (ang_to_A - ang) / 2
return Vec(x, y, z).rot_z(-ang_off)
def make_ring(R, N, a):
b = ring_ball_ang(N, a)
P = Vec(R*math.sin(a-b), 0, R*math.cos(a-b))
return [P.rot_z(2*math.pi*i/N) for i in range(N)], b
def main():
"""Entry point"""
epilog = '''
notes:
Depends on anti_lib.py. Use poly_kscope to repeat the model.
examples:
Icosahedral model
twister.py I[5,3] | poly_kscope -s I| antiview
Twisted icosahedral model with hexagons
twister.py I[5,3] 1 2 -a 0.5e | poly_kscope -s I| antiview
Dihedral model with frame
twister.py D6[6,2] 1 2 -f ra | poly_kscope -s D6 | antiview
'''
parser = argparse.ArgumentParser(formatter_class=anti_lib.DefFormatter,
description=__doc__, epilog=epilog)
parser.add_argument(
'symmetry_axes',
help=']Axes given in the form: sym_type[axis1,axis2]id_no\n'
' sym_type: rotational symmetry group, can be T, O, I,\n'
' or can be D followed by an integer (e.g D5)\n'
' axis1,axis2: rotational order of each of the two axes\n'
' id_no (default: 1): integer to select between\n'
' non-equivalent pairs of axes having the same\n'
' symmetry group and rotational orders\n'
'e.g. T[2,3], I[5,2]2, D7[7,2], D11[2,2]4\n'
'Axis pairs are from the following\n'
' T: [3, 3], [3, 2], [2, 2]\n'
' O: [4, 4], [4, 3], [4, 2]x2, [3, 3], [3, 2]x2,\n'
' [2, 2]x2\n'
' I: [5, 5], [5, 3]x2, [5, 2]x3, [3, 3]x2, [3, 2]x4,\n'
' [2, 2]x4\n'
' Dn: [n 2], [2,2]x(n/2 rounded down)\n',
type=read_axes,
nargs='?',
default='O[4,3]')
parser.add_argument(
'multiplier1',
help='integer or fractional multiplier for axis 1 '
'(default: 1). If the axis is N/D and the '
'multiplier is n/d the polygon used will be N*n/d',
type=read_axis_multiplier,
nargs='?',
default="1")
parser.add_argument(
'multiplier2',
help='integer or fractional multiplier for axis 2 '
'(default: 1). If the axis is N/D and the '
'multiplier is n/d the polygon used will be N*n/d',
type=read_axis_multiplier,
nargs='?',
default="1")
parser.add_argument(
'-r', '--ratio',
help='ratio of edge lengths (default: 1.0)',
type=float,
default=1.0)
parser.add_argument(
'-a', '--angle',
help='amount to turn polygon on axis0 in degrees '
'(default: 0), or a value followed by \'e\', '
'where 1.0e is half the central angle of an edge, '
'which produces an edge-connected model (negative '
'values may have to be specified as, e.g. -a=-1.0e), '
'or a value followed by x, which is like e but with '
'a half turn offset',
type=read_turn_angle,
default='0')
parser.add_argument(
'-f', '--offset',
help='amount to offset the first polygon to avoid '
'coplanarity with the second polygon, for example '
'0.0001 (default: 0.0)',
type=float,
default=0.0)
parser.add_argument(
'-F', '--frame',
help='include frame elements in output, any from: '
'r - rhombic tiling edges, '
'a - rotation axes (default: no elements)',
type=frame_type,
default='')
parser.add_argument(
'-o', '--outfile',
help='output file name (default: standard output)',
type=argparse.FileType('w'),
default=sys.stdout)
args = parser.parse_args()
axis_pair = args.symmetry_axes
pgons = []
for i, m in enumerate([args.multiplier1, args.multiplier2]):
try:
pgons.append(anti_lib.Polygon(
axis_pair['nfolds'][i]*m.N, m.D))
except Exception as e:
parser.error('multiplier%d: ' % (i) + e.args[0])
axes = axis_pair['axes']
if args.angle[1] == 'e': # units: half edge central angle
turn_angle = args.angle[0] * pgons[0].angle()/2
elif args.angle[1] == 'x': # units: half edge central angle
turn_angle = math.pi + args.angle[0] * pgons[0].angle()/2
else: # units: degrees
turn_angle = math.radians(args.angle[0])
sin_angle_between_axes = Vec.cross(axes[0], axes[1]).mag()
if abs(sin_angle_between_axes) > 1:
sin_angle_between_axes = -1 if sin_angle_between_axes < 0 else 1
angle_between_axes = math.asin(sin_angle_between_axes)
if(Vec.dot(axes[0], axes[1]) > 0):
axes[1] *= -1
try:
(points, faces) = calc_polygons(
pgons[0], pgons[1], turn_angle, args.ratio, angle_between_axes)
except Exception as e:
parser.error(e.args[0])
if args.offset:
for i in range(len(faces[0])):
points[i][2] += args.offset
frame_rad = calc_polygons(pgons[0], pgons[1], 0, args.ratio,
angle_between_axes)[0][0].mag()
frame_points, frame_faces = make_frame(args.frame, angle_between_axes,
frame_rad, 10)
rot = Mat.rot_from_to2(Vec(0, 0, 1), Vec(1, 0, 0), axes[0], axes[1])
all_points = [rot * point for point in points+frame_points]
out = anti_lib.OffFile(args.outfile)
out.print_header(len(all_points), len(faces)+len(frame_faces))
out.print_verts(all_points)
for i in range(pgons[0].parts+pgons[1].parts):
out.print_face(faces[i], 0, int(i < pgons[0].parts))
out.print_faces(frame_faces, len(points), 2)