# GPL # "author": "DreamPainter"
import bpy
from math import sqrt
from mathutils import Vector
from functools import reduce
from bpy.props import (
FloatProperty,
EnumProperty,
BoolProperty,
)
from bpy_extras.object_utils import object_data_add
# this function creates a chain of quads and, when necessary, a remaining tri
# for each polygon created in this script. be aware though, that this function
# assumes each polygon is convex.
# poly: list of faces, or a single face, like those
# needed for mesh.from_pydata.
# returns the tessellated faces.
def createPolys(poly):
# check for faces
if len(poly) == 0:
return []
# one or more faces
if type(poly[0]) == type(1):
poly = [poly] # if only one, make it a list of one face
faces = []
for i in poly:
L = len(i)
# let all faces of 3 or 4 verts be
if L < 5:
faces.append(i)
# split all polygons in half and bridge the two halves
else:
f = [[i[x], i[x + 1], i[L - 2 - x], i[L - 1 - x]] for x in range(L // 2 - 1)]
faces.extend(f)
if L & 1 == 1:
faces.append([i[L // 2 - 1 + x] for x in [0, 1, 2]])
return faces
# function to make the reduce function work as a workaround to sum a list of vectors
def vSum(list):
return reduce(lambda a, b: a + b, list)
# creates the 5 platonic solids as a base for the rest
# plato: should be one of {"4","6","8","12","20"}. decides what solid the
# outcome will be.
# returns a list of vertices and faces
def source(plato):
verts = []
faces = []
# Tetrahedron
if plato == "4":
# Calculate the necessary constants
s = sqrt(2) / 3.0
t = -1 / 3
u = sqrt(6) / 3
# create the vertices and faces
v = [(0, 0, 1), (2 * s, 0, t), (-s, u, t), (-s, -u, t)]
faces = [[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 2]]
# Hexahedron (cube)
elif plato == "6":
# Calculate the necessary constants
s = 1 / sqrt(3)
# create the vertices and faces
v = [(-s, -s, -s), (s, -s, -s), (s, s, -s), (-s, s, -s), (-s, -s, s), (s, -s, s), (s, s, s), (-s, s, s)]
faces = [[0, 3, 2, 1], [0, 1, 5, 4], [0, 4, 7, 3], [6, 5, 1, 2], [6, 2, 3, 7], [6, 7, 4, 5]]
# Octahedron
elif plato == "8":
# create the vertices and faces
v = [(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1)]
faces = [[4, 0, 2], [4, 2, 1], [4, 1, 3], [4, 3, 0], [5, 2, 0], [5, 1, 2], [5, 3, 1], [5, 0, 3]]
# Dodecahedron
elif plato == "12":
# Calculate the necessary constants
s = 1 / sqrt(3)
t = sqrt((3 - sqrt(5)) / 6)
u = sqrt((3 + sqrt(5)) / 6)
# create the vertices and faces
v = [(s, s, s), (s, s, -s), (s, -s, s), (s, -s, -s), (-s, s, s), (-s, s, -s), (-s, -s, s), (-s, -s, -s),
(t, u, 0), (-t, u, 0), (t, -u, 0), (-t, -u, 0), (u, 0, t), (u, 0, -t), (-u, 0, t), (-u, 0, -t), (0, t, u),
(0, -t, u), (0, t, -u), (0, -t, -u)]
faces = [[0, 8, 9, 4, 16], [0, 12, 13, 1, 8], [0, 16, 17, 2, 12], [8, 1, 18, 5, 9], [12, 2, 10, 3, 13],
[16, 4, 14, 6, 17], [9, 5, 15, 14, 4], [6, 11, 10, 2, 17], [3, 19, 18, 1, 13], [7, 15, 5, 18, 19],
[7, 11, 6, 14, 15], [7, 19, 3, 10, 11]]
# Icosahedron
elif plato == "20":
# Calculate the necessary constants
s = (1 + sqrt(5)) / 2
t = sqrt(1 + s * s)
s = s / t
t = 1 / t
# create the vertices and faces
v = [(s, t, 0), (-s, t, 0), (s, -t, 0), (-s, -t, 0), (t, 0, s), (t, 0, -s), (-t, 0, s), (-t, 0, -s),
(0, s, t), (0, -s, t), (0, s, -t), (0, -s, -t)]
faces = [[0, 8, 4], [0, 5, 10], [2, 4, 9], [2, 11, 5], [1, 6, 8], [1, 10, 7], [3, 9, 6], [3, 7, 11],
[0, 10, 8], [1, 8, 10], [2, 9, 11], [3, 11, 9], [4, 2, 0], [5, 0, 2], [6, 1, 3], [7, 3, 1],
[8, 6, 4], [9, 4, 6], [10, 5, 7], [11, 7, 5]]
# convert the tuples to Vectors
verts = [Vector(i) for i in v]
return verts, faces
# processes the raw data from source
def createSolid(plato, vtrunc, etrunc, dual, snub):
# the duals from each platonic solid
dualSource = {"4": "4",
"6": "8",
"8": "6",
"12": "20",
"20": "12"}
# constants saving space and readability
vtrunc *= 0.5
etrunc *= 0.5
supposedSize = 0
noSnub = (snub == "None") or (etrunc == 0.5) or (etrunc == 0)
lSnub = (snub == "Left") and (0 < etrunc < 0.5)
rSnub = (snub == "Right") and (0 < etrunc < 0.5)
# no truncation
if vtrunc == 0:
if dual: # dual is as simple as another, but mirrored platonic solid
vInput, fInput = source(dualSource[plato])
supposedSize = vSum(vInput[i] for i in fInput[0]).length / len(fInput[0])
vInput = [-i * supposedSize for i in vInput] # mirror it
return vInput, fInput
return source(plato)
elif 0 < vtrunc <= 0.5: # simple truncation of the source
vInput, fInput = source(plato)
else:
# truncation is now equal to simple truncation of the dual of the source
vInput, fInput = source(dualSource[plato])
supposedSize = vSum(vInput[i] for i in fInput[0]).length / len(fInput[0])
vtrunc = 1 - vtrunc # account for the source being a dual
if vtrunc == 0: # no truncation needed
if dual:
vInput, fInput = source(plato)
vInput = [i * supposedSize for i in vInput]
return vInput, fInput
vInput = [-i * supposedSize for i in vInput]
return vInput, fInput
# generate connection database
vDict = [{} for i in vInput]
# for every face, store what vertex comes after and before the current vertex
for x in range(len(fInput)):
i = fInput[x]
for j in range(len(i)):
vDict[i[j - 1]][i[j]] = [i[j - 2], x]
if len(vDict[i[j - 1]]) == 1:
vDict[i[j - 1]][-1] = i[j]
# the actual connection database: exists out of:
# [vtrunc pos, etrunc pos, connected vert IDs, connected face IDs]
vData = [[[], [], [], []] for i in vInput]
fvOutput = [] # faces created from truncated vertices
feOutput = [] # faces created from truncated edges
vOutput = [] # newly created vertices
for x in range(len(vInput)):
i = vDict[x] # lookup the current vertex
current = i[-1]
while True: # follow the chain to get a ccw order of connected verts and faces
vData[x][2].append(i[current][0])
vData[x][3].append(i[current][1])
# create truncated vertices
vData[x][0].append((1 - vtrunc) * vInput[x] + vtrunc * vInput[vData[x][2][-1]])
current = i[current][0]
if current == i[-1]:
break # if we're back at the first: stop the loop
fvOutput.append([]) # new face from truncated vert
fOffset = x * (len(i) - 1) # where to start off counting faceVerts
# only create one vert where one is needed (v1 todo: done)
if etrunc == 0.5:
for j in range(len(i) - 1):
vOutput.append((vData[x][0][j] + vData[x][0][j - 1]) * etrunc) # create vert
fvOutput[x].append(fOffset + j) # add to face
fvOutput[x] = fvOutput[x][1:] + [fvOutput[x][0]] # rotate face for ease later on
# create faces from truncated edges.
for j in range(len(i) - 1):
if x > vData[x][2][j]: # only create when other vertex has been added
index = vData[vData[x][2][j]][2].index(x)
feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
fvOutput[vData[x][2][j]][index],
fvOutput[vData[x][2][j]][index - 1]])
# edge truncation between none and full
elif etrunc > 0:
for j in range(len(i) - 1):
# create snubs from selecting verts from rectified meshes
if rSnub:
vOutput.append(etrunc * vData[x][0][j] + (1 - etrunc) * vData[x][0][j - 1])
fvOutput[x].append(fOffset + j)
elif lSnub:
vOutput.append((1 - etrunc) * vData[x][0][j] + etrunc * vData[x][0][j - 1])
fvOutput[x].append(fOffset + j)
else: # noSnub, select both verts from rectified mesh
vOutput.append(etrunc * vData[x][0][j] + (1 - etrunc) * vData[x][0][j - 1])
vOutput.append((1 - etrunc) * vData[x][0][j] + etrunc * vData[x][0][j - 1])
fvOutput[x].append(2 * fOffset + 2 * j)
fvOutput[x].append(2 * fOffset + 2 * j + 1)
# rotate face for ease later on
if noSnub:
fvOutput[x] = fvOutput[x][2:] + fvOutput[x][:2]
else:
fvOutput[x] = fvOutput[x][1:] + [fvOutput[x][0]]
# create single face for each edge
if noSnub:
for j in range(len(i) - 1):
if x > vData[x][2][j]:
index = vData[vData[x][2][j]][2].index(x)
feOutput.append([fvOutput[x][j * 2], fvOutput[x][2 * j - 1],
fvOutput[vData[x][2][j]][2 * index],
fvOutput[vData[x][2][j]][2 * index - 1]])
# create 2 tri's for each edge for the snubs
elif rSnub:
for j in range(len(i) - 1):
if x > vData[x][2][j]:
index = vData[vData[x][2][j]][2].index(x)
feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
fvOutput[vData[x][2][j]][index]])
feOutput.append([fvOutput[x][j], fvOutput[vData[x][2][j]][index],
fvOutput[vData[x][2][j]][index - 1]])
elif lSnub:
for j in range(len(i) - 1):
if x > vData[x][2][j]:
index = vData[vData[x][2][j]][2].index(x)
feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
fvOutput[vData[x][2][j]][index - 1]])
feOutput.append([fvOutput[x][j - 1], fvOutput[vData[x][2][j]][index],
fvOutput[vData[x][2][j]][index - 1]])
# special rules for birectified mesh (v1 todo: done)
elif vtrunc == 0.5:
for j in range(len(i) - 1):
if x < vData[x][2][j]: # use current vert, since other one has not passed yet
vOutput.append(vData[x][0][j])
fvOutput[x].append(len(vOutput) - 1)
else:
# search for other edge to avoid duplicity
connectee = vData[x][2][j]
fvOutput[x].append(fvOutput[connectee][vData[connectee][2].index(x)])
else: # vert truncation only
vOutput.extend(vData[x][0]) # use generated verts from way above
for j in range(len(i) - 1): # create face from them
fvOutput[x].append(fOffset + j)
# calculate supposed vertex length to ensure continuity
if supposedSize and not dual: # this to make the vtrunc > 1 work
supposedSize *= len(fvOutput[0]) / vSum(vOutput[i] for i in fvOutput[0]).length
vOutput = [-i * supposedSize for i in vOutput]
# create new faces by replacing old vert IDs by newly generated verts
ffOutput = [[] for i in fInput]
for x in range(len(fInput)):
# only one generated vert per vertex, so choose accordingly
if etrunc == 0.5 or (etrunc == 0 and vtrunc == 0.5) or lSnub or rSnub:
ffOutput[x] = [fvOutput[i][vData[i][3].index(x) - 1] for i in fInput[x]]
# two generated verts per vertex
elif etrunc > 0:
for i in fInput[x]:
ffOutput[x].append(fvOutput[i][2 * vData[i][3].index(x) - 1])
ffOutput[x].append(fvOutput[i][2 * vData[i][3].index(x) - 2])
else: # cutting off corners also makes 2 verts
for i in fInput[x]:
ffOutput[x].append(fvOutput[i][vData[i][3].index(x)])
ffOutput[x].append(fvOutput[i][vData[i][3].index(x) - 1])
if not dual:
return vOutput, fvOutput + feOutput + ffOutput
else:
# do the same procedure as above, only now on the generated mesh
# generate connection database
vDict = [{} for i in vOutput]
dvOutput = [0 for i in fvOutput + feOutput + ffOutput]
dfOutput = []
for x in range(len(dvOutput)): # for every face
i = (fvOutput + feOutput + ffOutput)[x] # choose face to work with
# find vertex from face
normal = (vOutput[i[0]] - vOutput[i[1]]).cross(vOutput[i[2]] - vOutput[i[1]]).normalized()
dvOutput[x] = normal / (normal.dot(vOutput[i[0]]))
for j in range(len(i)): # create vert chain
vDict[i[j - 1]][i[j]] = [i[j - 2], x]
if len(vDict[i[j - 1]]) == 1:
vDict[i[j - 1]][-1] = i[j]
# calculate supposed size for continuity
supposedSize = vSum([vInput[i] for i in fInput[0]]).length / len(fInput[0])
supposedSize /= dvOutput[-1].length
dvOutput = [i * supposedSize for i in dvOutput]
# use chains to create faces
for x in range(len(vOutput)):
i = vDict[x]
current = i[-1]
face = []
while True:
face.append(i[current][1])
current = i[current][0]
if current == i[-1]:
break
dfOutput.append(face)
return dvOutput, dfOutput
class Solids(bpy.types.Operator):
"""Add one of the (regular) solids (mesh)"""
bl_idname = "mesh.primitive_solid_add"
bl_label = "(Regular) solids"
bl_description = "Add one of the Platonic, Archimedean or Catalan solids"
bl_options = {'REGISTER', 'UNDO', 'PRESET'}
source: EnumProperty(
items=(("4", "Tetrahedron", ""),
("6", "Hexahedron", ""),
("8", "Octahedron", ""),
("12", "Dodecahedron", ""),
("20", "Icosahedron", "")),
name="Source",
description="Starting point of your solid"
)
size: FloatProperty(
name="Size",
description="Radius of the sphere through the vertices",
min=0.01,
soft_min=0.01,
max=100,
soft_max=100,
default=1.0
)
vTrunc: FloatProperty(
name="Vertex Truncation",
description="Amount of vertex truncation",
min=0.0,
soft_min=0.0,
max=2.0,
soft_max=2.0,
default=0.0,
precision=3,
step=0.5
)
eTrunc: FloatProperty(
name="Edge Truncation",
description="Amount of edge truncation",
min=0.0,
soft_min=0.0,
max=1.0,
soft_max=1.0,
default=0.0,
precision=3,
step=0.2
)
snub: EnumProperty(
items=(("None", "No Snub", ""),
("Left", "Left Snub", ""),
("Right", "Right Snub", "")),
name="Snub",
description="Create the snub version"
)
dual: BoolProperty(
name="Dual",
description="Create the dual of the current solid",
default=False
)
keepSize: BoolProperty(
name="Keep Size",
description="Keep the whole solid at a constant size",
default=False
)
preset: EnumProperty(
items=(("0", "Custom", ""),
("t4", "Truncated Tetrahedron", ""),
("r4", "Cuboctahedron", ""),
("t6", "Truncated Cube", ""),
("t8", "Truncated Octahedron", ""),
("b6", "Rhombicuboctahedron", ""),
("c6", "Truncated Cuboctahedron", ""),
("s6", "Snub Cube", ""),
("r12", "Icosidodecahedron", ""),
("t12", "Truncated Dodecahedron", ""),
("t20", "Truncated Icosahedron", ""),
("b12", "Rhombicosidodecahedron", ""),
("c12", "Truncated Icosidodecahedron", ""),
("s12", "Snub Dodecahedron", ""),
("dt4", "Triakis Tetrahedron", ""),
("dr4", "Rhombic Dodecahedron", ""),
("dt6", "Triakis Octahedron", ""),
("dt8", "Tetrakis Hexahedron", ""),
("db6", "Deltoidal Icositetrahedron", ""),
("dc6", "Disdyakis Dodecahedron", ""),
("ds6", "Pentagonal Icositetrahedron", ""),
("dr12", "Rhombic Triacontahedron", ""),
("dt12", "Triakis Icosahedron", ""),
("dt20", "Pentakis Dodecahedron", ""),
("db12", "Deltoidal Hexecontahedron", ""),
("dc12", "Disdyakis Triacontahedron", ""),
("ds12", "Pentagonal Hexecontahedron", "")),
name="Presets",
description="Parameters for some hard names"
)
# actual preset values
p = {"t4": ["4", 2 / 3, 0, 0, "None"],
"r4": ["4", 1, 1, 0, "None"],
"t6": ["6", 2 / 3, 0, 0, "None"],
"t8": ["8", 2 / 3, 0, 0, "None"],
"b6": ["6", 1.0938, 1, 0, "None"],
"c6": ["6", 1.0572, 0.585786, 0, "None"],
"s6": ["6", 1.0875, 0.704, 0, "Left"],
"r12": ["12", 1, 0, 0, "None"],
"t12": ["12", 2 / 3, 0, 0, "None"],
"t20": ["20", 2 / 3, 0, 0, "None"],
"b12": ["12", 1.1338, 1, 0, "None"],
"c12": ["20", 0.921, 0.553, 0, "None"],
"s12": ["12", 1.1235, 0.68, 0, "Left"],
"dt4": ["4", 2 / 3, 0, 1, "None"],
"dr4": ["4", 1, 1, 1, "None"],
"dt6": ["6", 2 / 3, 0, 1, "None"],
"dt8": ["8", 2 / 3, 0, 1, "None"],
"db6": ["6", 1.0938, 1, 1, "None"],
"dc6": ["6", 1.0572, 0.585786, 1, "None"],
"ds6": ["6", 1.0875, 0.704, 1, "Left"],
"dr12": ["12", 1, 0, 1, "None"],
"dt12": ["12", 2 / 3, 0, 1, "None"],
"dt20": ["20", 2 / 3, 0, 1, "None"],
"db12": ["12", 1.1338, 1, 1, "None"],
"dc12": ["20", 0.921, 0.553, 1, "None"],
"ds12": ["12", 1.1235, 0.68, 1, "Left"]}
# previous preset, for User-friendly reasons
previousSetting = ""
def execute(self, context):
# turn off undo for better performance (3-5x faster), also makes sure
# that mesh ops are undoable and entire script acts as one operator
bpy.context.preferences.edit.use_global_undo = False
# piece of code to make presets remain until parameters are changed
if self.preset != "0":
# if preset, set preset
if self.previousSetting != self.preset:
using = self.p[self.preset]
self.source = using[0]
self.vTrunc = using[1]
self.eTrunc = using[2]
self.dual = using[3]
self.snub = using[4]
else:
using = self.p[self.preset]
result0 = self.source == using[0]
result1 = abs(self.vTrunc - using[1]) < 0.004
result2 = abs(self.eTrunc - using[2]) < 0.0015
result4 = using[4] == self.snub or ((using[4] == "Left") and
self.snub in ["Left", "Right"])
if (result0 and result1 and result2 and result4):
if self.p[self.previousSetting][3] != self.dual:
if self.preset[0] == "d":
self.preset = self.preset[1:]
else:
self.preset = "d" + self.preset
else:
self.preset = "0"
self.previousSetting = self.preset
# generate mesh
verts, faces = createSolid(self.source,
self.vTrunc,
self.eTrunc,
self.dual,
self.snub
)
# turn n-gons in quads and tri's
faces = createPolys(faces)
# resize to normal size, or if keepSize, make sure all verts are of length 'size'
if self.keepSize:
rad = self.size / verts[-1 if self.dual else 0].length
else:
rad = self.size
verts = [i * rad for i in verts]
# generate object
# Create new mesh
mesh = bpy.data.meshes.new("Solid")
# Make a mesh from a list of verts/edges/faces.
mesh.from_pydata(verts, [], faces)
# Update mesh geometry after adding stuff.
mesh.update()
object_data_add(context, mesh, operator=None)
# object generation done
# turn undo back on
bpy.context.preferences.edit.use_global_undo = True
return {'FINISHED'}