def quinto(poly: polyhedron) -> polyhedron:
flag = polyflag()
for i, f in enumerate(poly.faces):
lv = list(map(lambda i: poly.vertices[i], f))
centroid = calc_centroid(lv)
v1, v2 = f[-2:]
for v3 in f:
midpt = midpoint(poly.vertices[v1], poly.vertices[v2])
innerpt = midpoint(midpt, centroid)
flag.newV(midName(v1, v2), midpt)
flag.newV(f'inner_{i}_{midName(v1, v2)}', innerpt)
flag.newV(f'{v2}', poly.vertices[v2])
flag.newFlag(f'f{i}_{v2}', f'inner_{i}_{midName(v1, v2)}',
midName(v1, v2))
flag.newFlag(f'f{i}_{v2}', midName(v1, v2), f'{v2}')
flag.newFlag(f'f{i}_{v2}', f'{v2}', midName(v2, v3))
flag.newFlag(f'f{i}_{v2}', midName(v2, v3),
f'inner_{i}_{midName(v2, v3)}')
flag.newFlag(f'f{i}_{v2}', f'inner_{i}_{midName(v2, v3)}',
f'inner_{i}_{midName(v1, v2)}')
# inner rotated face of same vertex-number as original
flag.newFlag(f'f_in_{i}', f'inner_{i}_{midName(v1, v2)}',
f'inner_{i}_{midName(v2, v3)}')
# shift over one
v1, v2 = v2, v3
newpoly = flag.topoly()
newpoly.name = f'q{poly.name}'
return newpoly
def gyro(poly: polyhedron) -> polyhedron:
flag = polyflag()
for i, v in enumerate(
poly.vertices): # each old vertex is a new vertex
flag.newV(f'v{i}', unit(v))
for i, f in enumerate(poly.faces):
flag.newV(f'center{i}', unit(poly.centersArray[i]))
for i, f in enumerate(poly.faces):
v1, v2 = f[-2:]
for j, v in enumerate(f):
v3 = v
flag.newV(f'{v1}~{v2}',
oneThird(poly.vertices[v1],
poly.vertices[v2])) # new v in face
fname = f'{i}f{v1}'
flag.newFlag(fname, f'center{i}',
f'{v1}~{v2}') # five new flags
flag.newFlag(fname, f'{v1}~{v2}', f'{v2}~{v1}')
flag.newFlag(fname, f'{v2}~{v1}', f'v{v2}')
flag.newFlag(fname, f'v{v2}', f'{v2}~{v3}')
flag.newFlag(fname, f'{v2}~{v3}', f'center{i}')
v1, v2 = v2, v3
newpoly = flag.topoly()
newpoly.name = f'g{poly.name}'
return newpoly
def chamfer(poly: polyhedron, dist=0.5) -> polyhedron:
normals = poly.normals # [calc_normal([poly.vertices[ic] for ic in f]) for f in poly.faces]
flag = polyflag()
for i, f in enumerate(
poly.faces): # For each face f in the original poly
v1 = f[-1]
v1new = f'{i}_{v1}'
for v2 in f:
flag.newV(v2, mult(1.0 + dist, poly.vertices[v2]))
v2new = f'{i}_{v2}'
flag.newV(v2new,
add(poly.vertices[v2], mult(dist * 1.5, normals[i])))
flag.newFlag(f'orig{i}', v1new, v2new)
facename = f'hex{v1}_{v2}' if v1 < v2 else f'hex{v2}_{v1}'
flag.newFlag(facename, v2, v2new)
flag.newFlag(facename, v2new, v1new)
flag.newFlag(facename, v1new, v1)
v1 = v2
v1new = v2new
newpoly = flag.topoly()
newpoly.name = f'c{poly.name}'
return newpoly
def dual(poly: polyhedron) -> polyhedron:
flag = polyflag()
face = [{} for _ in range(len(poly.vertices))]
for i, f in enumerate(poly.faces):
v1 = f[-1]
for v2 in f:
face[v1][f'v{v2}'] = f'{i}'
v1 = v2
centers = poly.centers
for i, _ in enumerate(poly.faces):
flag.newV(f'{i}', centers[i])
for i, f in enumerate(poly.faces):
v1 = f[-1]
for v2 in f:
flag.newFlag(v1, face[v2][f'v{v1}'], f'{i}')
v1 = v2
dpoly = flag.topoly() # build topological dual from flags
# match F index ordering to V index ordering on dual
sortF = [[] for _ in range(len(dpoly.faces))]
for f in dpoly.faces:
k = intersect(poly.faces[f[0]], poly.faces[f[1]], poly.faces[f[2]])
sortF[k] = f
dpoly.faces = sortF
if poly.name[0] != 'd':
dpoly.name = f'd{poly.name}'
else:
dpoly.name = poly.name[1:]
return dpoly
def propellor(poly: polyhedron) -> polyhedron:
flag = polyflag()
for i, v in enumerate(
poly.vertices): # each old vertex is a new vertex
flag.newV(f'v{i}', unit(v))
for i, f in enumerate(poly.faces):
v1, v2 = f[-2:]
for v in f:
v3 = v
flag.newV(
f'{v1}~{v2}', oneThird(
poly.vertices[v1],
poly.vertices[v2])) # new v in face, 1/3rd along edge
fname = f'{i}f{v2}'
flag.newFlag(f'v{i}', f'{v1}~{v2}',
f'{v2}~{v3}') # five new flags
flag.newFlag(fname, f'{v1}~{v2}', f'{v2}~{v1}')
flag.newFlag(fname, f'{v2}~{v1}', f'v{v2}')
flag.newFlag(fname, f'v{v2}', f'{v2}~{v3}')
flag.newFlag(fname, f'{v2}~{v3}', f'{v1}~{v2}')
v1, v2 = v2, v3
newpoly = flag.topoly()
newpoly.name = f'p{poly.name}'
return newpoly
def hollow(poly: polyhedron, inset_dist=0.5, thickness=0.2) -> polyhedron:
dualnormals = transform.dual(poly).calc_normals()
normals = poly.normals # poly.calc_normals()
centers = poly.centers # poly.calc_centers()
flag = polyflag()
for i, p in enumerate(poly.vertices):
flag.newV(f'v{i}', p)
flag.newV(f'downv{i}', add(p, mult(-1 * thickness,
dualnormals[i])))
for i, f in enumerate(poly.faces):
for v in f:
flag.newV(f'fin{i}v{v}',
tween(poly.vertices[v], centers[i], inset_dist))
flag.newV(
f'findown{i}v{v}',
add(tween(poly.vertices[v], centers[i], inset_dist),
mult(-1 * thickness, normals[i])))
for i, f in enumerate(poly.faces):
v1 = f'v{f[-1]}'
for v in f:
v2 = f'v{v}'
fname = f'{i}{v1}'
flag.newFlag(fname, v1, v2)
flag.newFlag(fname, v2, f'fin{i}{v2}')
flag.newFlag(fname, f'fin{i}{v2}', f'fin{i}{v1}')
flag.newFlag(fname, f'fin{i}{v1}', v1)
fname = f'sides{i}{v1}'
flag.newFlag(fname, f'fin{i}{v1}', f'fin{i}{v2}')
flag.newFlag(fname, f'fin{i}{v2}', f'findown{i}{v2}')
flag.newFlag(fname, f'findown{i}{v2}', f'findown{i}{v1}')
flag.newFlag(fname, f'findown{i}{v1}', f'fin{i}{v1}')
fname = f'bottom{i}{v1}'
flag.newFlag(fname, f'down{v2}', f'down{v1}')
flag.newFlag(fname, f'down{v1}', f'findown{i}{v1}')
flag.newFlag(fname, f'findown{i}{v1}', f'findown{i}{v2}')
flag.newFlag(fname, f'findown{i}{v2}', f'down{v2}')
v1 = v2
newpoly = flag.topoly()
newpoly.name = f'H{poly.name}'
return newpoly
def ambo(poly: polyhedron) -> polyhedron:
flag = polyflag()
for i, f in enumerate(poly.faces):
v1, v2 = f[-2:]
for v3 in f:
if v1 < v2: # vertices are the midpoints of all edges of original poly
flag.newV(midName(v1, v2),
midpoint(poly.vertices[v1], poly.vertices[v2]))
# two new flags: One whose face corresponds to the original f:
flag.newFlag(f'orig{i}', midName(v1, v2), midName(v2, v3))
# Another flag whose face corresponds to (the truncated) v2:
flag.newFlag(f'dual{v2}', midName(v2, v3), midName(v1, v2))
# shift over one
v1, v2 = v2, v3
newpoly = flag.topoly()
newpoly.name = f'a{poly.name}'
return newpoly
def insetN(poly: polyhedron,
n=0,
inset_dist=0.5,
popout_dist=-0.2) -> polyhedron:
flag = polyflag()
for i, p in enumerate(poly.vertices):
flag.newV(f'v{i}', p)
normals = poly.normals # poly.calc_normals()
centers = poly.centers # poly.calc_centers()
for i, f in enumerate(poly.faces):
if len(f) == n or n == 0:
for v in f:
flag.newV(
f'f{i}v{v}',
add(tween(poly.vertices[v], centers[i], inset_dist),
mult(popout_dist, normals[i])))
foundAny = False
for i, f in enumerate(poly.faces):
v1 = f'v{f[-1]}'
for v in f:
v2 = f'v{v}'
if len(f) == n or n == 0:
foundAny = True
fname = f'{i}{v1}'
flag.newFlag(fname, v1, v2)
flag.newFlag(fname, v2, f'f{i}{v2}')
flag.newFlag(fname, f'f{i}{v2}', f'f{i}{v1}')
flag.newFlag(fname, f'f{i}{v1}', v1)
# new inset, extruded face
flag.newFlag(f'ex{i}', f'f{i}{v1}', f'f{i}{v2}')
else:
flag.newFlag(i, v1, v2) # same old flag, if non-n
v1 = v2
if not foundAny:
print(f'No {n}-fold components were found.')
newpoly = flag.topoly()
newpoly.name = f'n{"" if n==0 else n}{poly.name}'
return newpoly
def perspectiva1(poly: polyhedron) -> polyhedron:
centers = poly.calc_centers()
flag = polyflag()
for i, p in enumerate(poly.vertices):
flag.newV(f'v{i}', p)
for i, f in enumerate(poly.faces):
v1 = f'v{f[-2]}'
v2 = f'v{f[-1]}'
vert1 = poly.vertices[f[-2]]
vert2 = poly.vertices[f[-1]]
for v in f:
v3 = f'v{v}'
vert3 = poly.vertices[v]
v12 = f'{v1}~{v2}' # names for "oriented" midpoint
v21 = f'{v2}~{v1}'
v23 = f'{v2}~{v3}'
# on each Nface, N new points inset from edge midpoints towards center = "stellated" points
flag.newV(v12, midpoint(midpoint(vert1, vert2), centers[i]))
flag.newFlag(f'in{i}', v12, v23)
# new tri face constituting the remainder of the stellated Nface
flag.newFlag(f'f{i}{v2}', v23, v12)
flag.newFlag(f'f{i}{v2}', v12, v2)
flag.newFlag(f'f{i}{v2}', v2, v23)
# one of the two new triangles replacing old edge between v1->v2
flag.newFlag(f'f{v12}', v1, v21)
flag.newFlag(f'f{v12}', v21, v12)
flag.newFlag(f'f{v12}', v12, v1)
v1, v2 = v2, v3 # current becomes previous
vert1, vert2 = vert2, vert3
newpoly = flag.topoly()
newpoly.name = f'P{poly.name}'
return newpoly
def kisN(poly: polyhedron, n: int = 0, apexdist=0.1) -> polyhedron:
flag = polyflag()
for i, v in enumerate(
poly.vertices): # each old vertex is a new vertex
flag.newV(f'v{i}', v)
normals = poly.normals
centers = poly.calc_centers()
foundAny = False
for i in range(len(poly.faces)):
f = poly.faces[i]
v1 = f'v{f[len(f) - 1]}'
for v in f:
v2 = f'v{v}'
if len(f) == n or n == 0:
foundAny = True
apex = f'apex{i}'
fname = f'{i}{v1}'
# new vertices in centers of n-sided face
flag.newV(apex, add(centers[i], mult(apexdist,
normals[i])))
flag.newFlag(fname, v1,
v2) # the old edge of original face
flag.newFlag(fname, v2, apex) # up to apex of pyramid
flag.newFlag(fname, apex, v1) # and back down again
else:
flag.newFlag(f'{i}', v1, v2) # same old flag, if non-n
# current becomes previous
v1 = v2
if not foundAny:
pass
# print(f'No {n} - fold components were found.')
newpoly = flag.topoly()
newpoly.name = f'k{"" if n is 0 else n}{poly.name}'
return newpoly
def whirl(poly: polyhedron, n=0) -> polyhedron:
flag = polyflag()
for i, v in enumerate(
poly.vertices): # each old vertex is a new vertex
flag.newV(f'v{i}', unit(v))
centers = poly.centers
for i, f in enumerate(poly.faces):
v1, v2 = f[-2:]
for j, v in enumerate(f):
v3 = v
# New vertex along edge
v1_2 = oneThird(poly.vertices[v1], poly.vertices[v2])
flag.newV(f'{v1}~{v2}', v1_2)
# New vertices near center of face
cv1name = f'center{i}~{v1}'
cv2name = f'center{i}~{v2}'
flag.newV(cv1name, unit(oneThird(centers[i], v1_2)))
fname = f'{i}f{v1}'
# New hexagon for each original edge
flag.newFlag(fname, cv1name, f'{v1}~{v2}')
flag.newFlag(fname, f'{v1}~{v2}', f'{v2}~{v1}')
flag.newFlag(fname, f'{v2}~{v1}', f'v{v2}')
flag.newFlag(fname, f'v{v2}', f'{v2}~{v3}')
flag.newFlag(fname, f'{v2}~{v3}', cv2name)
flag.newFlag(fname, cv2name, cv1name)
# New face in center of each old face
flag.newFlag(f'c{i}', cv1name, cv2name)
v1, v2 = v2, v3
newpoly = flag.topoly()
newpoly.name = f'w{poly.name}'
return newpoly