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 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 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 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 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_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 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 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)
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)