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# GPL # Author: Alain Ducharme (phymec)
import bpy
from bpy_extras import object_utils
from itertools import permutations
from math import (
copysign, pi,
sqrt,
)
from bpy.types import Operator
from bpy.props import (
BoolProperty,
EnumProperty,
FloatProperty,
FloatVectorProperty,
IntProperty,
StringProperty,
)
def round_cube(radius=1.0, arcdiv=4, lindiv=0., size=(0., 0., 0.),
div_type='CORNERS', odd_axis_align=False, info_only=False):
# subdiv bitmasks
CORNERS, EDGES, ALL = 0, 1, 2
try:
subdiv = ('CORNERS', 'EDGES', 'ALL').index(div_type)
except ValueError:
subdiv = CORNERS # fallback
radius = max(radius, 0.)
if not radius:
# No sphere
arcdiv = 1
odd_axis_align = False
if arcdiv <= 0:
arcdiv = max(round(pi * radius * lindiv * 0.5), 1)
arcdiv = max(round(arcdiv), 1)
if lindiv <= 0. and radius:
lindiv = 1. / (pi / (arcdiv * 2.) * radius)
lindiv = max(lindiv, 0.)
if not lindiv:
subdiv = CORNERS
odd = arcdiv % 2 # even = arcdiv % 2 ^ 1
step_size = 2. / arcdiv
odd_aligned = 0
vi = -1.
steps = arcdiv + 1
if odd_axis_align and odd:
odd_aligned = 1
vi += 0.5 * step_size
steps = arcdiv
axis_aligned = not odd or odd_aligned
if arcdiv == 1 and not odd_aligned and subdiv == EDGES:
subdiv = CORNERS
half_chord = 0. # ~ spherical cap base radius
sagitta = 0. # ~ spherical cap height
if not axis_aligned:
half_chord = sqrt(3.) * radius / (3. * arcdiv)
id2 = 1. / (arcdiv * arcdiv)
sagitta = radius - radius * sqrt(id2 * id2 / 3. - id2 + 1.)
# Extrusion per axis
exyz = [0. if s < 2. * (radius - sagitta) else (s - 2. * (radius - sagitta)) * 0.5 for s in size]
ex, ey, ez = exyz
dxyz = [0, 0, 0] # extrusion divisions per axis
dssxyz = [0., 0., 0.] # extrusion division step sizes per axis
for i in range(3):
sc = 2. * (exyz[i] + half_chord)
dxyz[i] = round(sc * lindiv) if subdiv else 0
if dxyz[i]:
dssxyz[i] = sc / dxyz[i]
dxyz[i] -= 1
else:
dssxyz[i] = sc
if info_only:
ec = sum(1 for n in exyz if n)
if subdiv:
fxyz = [d + (e and axis_aligned) for d, e in zip(dxyz, exyz)]
dvc = arcdiv * 4 * sum(fxyz)
if subdiv == ALL:
dvc += sum(p1 * p2 for p1, p2 in permutations(fxyz, 2))
elif subdiv == EDGES and axis_aligned:
# (0, 0, 2, 4) * sum(dxyz) + (0, 0, 2, 6)
dvc += ec * ec // 2 * sum(dxyz) + ec * (ec - 1)
else:
dvc = (arcdiv * 4) * ec + ec * (ec - 1) if axis_aligned else 0
vert_count = int(6 * arcdiv * arcdiv + (0 if odd_aligned else 2) + dvc)
if not radius and not max(size) > 0:
vert_count = 1
return arcdiv, lindiv, vert_count
if not radius and not max(size) > 0:
# Single vertex
return [(0, 0, 0)], []
# uv lookup table
uvlt = []
v = vi
for j in range(1, steps + 1):
v2 = v * v
uvlt.append((v, v2, radius * sqrt(18. - 6. * v2) / 6.))
v = vi + j * step_size # v += step_size # instead of accumulating errors
# clear fp errors / signs at axis
if abs(v) < 1e-10:
v = 0.0
# Sides built left to right bottom up
# xp yp zp xd yd zd
sides = ((0, 2, 1, (-1, 1, 1)), # Y+ Front
(1, 2, 0, (-1, -1, 1)), # X- Left
(0, 2, 1, (1, -1, 1)), # Y- Back
(1, 2, 0, (1, 1, 1)), # X+ Right
(0, 1, 2, (-1, 1, -1)), # Z- Bottom
(0, 1, 2, (-1, -1, 1))) # Z+ Top
# side vertex index table (for sphere)
svit = [[[] for i in range(steps)] for i in range(6)]
# Extend svit rows for extrusion
yer = zer = 0
if ey:
yer = axis_aligned + (dxyz[1] if subdiv else 0)
svit[4].extend([[] for i in range(yer)])
svit[5].extend([[] for i in range(yer)])
if ez:
zer = axis_aligned + (dxyz[2] if subdiv else 0)
for side in range(4):
svit[side].extend([[] for i in range(zer)])
# Extend svit rows for odd_aligned
if odd_aligned:
for side in range(4):
svit[side].append([])
hemi = steps // 2
# Create vertices and svit without dups
vert = [0., 0., 0.]
verts = []
if arcdiv == 1 and not odd_aligned and subdiv == ALL:
# Special case: Grid Cuboid
for side, (xp, yp, zp, dir) in enumerate(sides):
svitc = svit[side]
rows = len(svitc)
if rows < dxyz[yp] + 2:
svitc.extend([[] for i in range(dxyz[yp] + 2 - rows)])
vert[zp] = (half_chord + exyz[zp]) * dir[zp]
for j in range(dxyz[yp] + 2):
vert[yp] = (j * dssxyz[yp] - half_chord - exyz[yp]) * dir[yp]
for i in range(dxyz[xp] + 2):
vert[xp] = (i * dssxyz[xp] - half_chord - exyz[xp]) * dir[xp]
if (side == 5) or ((i < dxyz[xp] + 1 and j < dxyz[yp] + 1) and (side < 4 or (i and j))):
svitc[j].append(len(verts))
verts.append(tuple(vert))
else:
for side, (xp, yp, zp, dir) in enumerate(sides):
svitc = svit[side]
exr = exyz[xp]
eyr = exyz[yp]
ri = 0 # row index
rij = zer if side < 4 else yer
if side == 5:
span = range(steps)
elif side < 4 or odd_aligned:
span = range(arcdiv)
else:
span = range(1, arcdiv)
ri = 1
for j in span: # rows
v, v2, mv2 = uvlt[j]
tv2mh = 1. / 3. * v2 - 0.5
hv2 = 0.5 * v2
if j == hemi and rij:
# Jump over non-edge row indices
ri += rij
for i in span: # columns
u, u2, mu2 = uvlt[i]
vert[xp] = u * mv2
vert[yp] = v * mu2
vert[zp] = radius * sqrt(u2 * tv2mh - hv2 + 1.)
vert[0] = (vert[0] + copysign(ex, vert[0])) * dir[0]
vert[1] = (vert[1] + copysign(ey, vert[1])) * dir[1]
vert[2] = (vert[2] + copysign(ez, vert[2])) * dir[2]
rv = tuple(vert)
if exr and i == hemi:
rx = vert[xp] # save rotated x
vert[xp] = rxi = (-exr - half_chord) * dir[xp]
if axis_aligned:
svitc[ri].append(len(verts))
verts.append(tuple(vert))
if subdiv:
offsetx = dssxyz[xp] * dir[xp]
for k in range(dxyz[xp]):
vert[xp] += offsetx
svitc[ri].append(len(verts))
verts.append(tuple(vert))
if eyr and j == hemi and axis_aligned:
vert[xp] = rxi
vert[yp] = -eyr * dir[yp]
svitc[hemi].append(len(verts))
verts.append(tuple(vert))
if subdiv:
offsety = dssxyz[yp] * dir[yp]
ry = vert[yp]
for k in range(dxyz[yp]):
vert[yp] += offsety
svitc[hemi + axis_aligned + k].append(len(verts))
verts.append(tuple(vert))
vert[yp] = ry
for k in range(dxyz[xp]):
vert[xp] += offsetx
svitc[hemi].append(len(verts))
verts.append(tuple(vert))
if subdiv & ALL:
for l in range(dxyz[yp]):
vert[yp] += offsety
svitc[hemi + axis_aligned + l].append(len(verts))
verts.append(tuple(vert))
vert[yp] = ry
vert[xp] = rx # restore
if eyr and j == hemi:
vert[yp] = (-eyr - half_chord) * dir[yp]
if axis_aligned:
svitc[hemi].append(len(verts))
verts.append(tuple(vert))
if subdiv:
offsety = dssxyz[yp] * dir[yp]
for k in range(dxyz[yp]):
vert[yp] += offsety
if exr and i == hemi and not axis_aligned and subdiv & ALL:
vert[xp] = rxi
for l in range(dxyz[xp]):
vert[xp] += offsetx
svitc[hemi + k].append(len(verts))
verts.append(tuple(vert))
vert[xp] = rx
svitc[hemi + axis_aligned + k].append(len(verts))
verts.append(tuple(vert))
svitc[ri].append(len(verts))
verts.append(rv)
ri += 1
# Complete svit edges (shared vertices)
# Sides' right edge
for side, rows in enumerate(svit[:4]):
for j, row in enumerate(rows[:-1]):
svit[3 if not side else side - 1][j].append(row[0])
# Sides' top edge
svit[0][-1].extend(svit[5][0])
svit[2][-1].extend(svit[5][-1][::-1])
for row in svit[5]:
svit[3][-1].insert(0, row[0])
svit[1][-1].append(row[-1])
if odd_aligned:
for side in svit[:4]:
side[-1].append(-1)
# Bottom edges
if odd_aligned:
svit[4].insert(0, [-1] + svit[2][0][-2::-1] + [-1])
for i, col in enumerate(svit[3][0][:-1]):
svit[4][i + 1].insert(0, col)
svit[4][i + 1].append(svit[1][0][-i - 2])
svit[4].append([-1] + svit[0][0][:-1] + [-1])
else:
svit[4][0].extend(svit[2][0][::-1])
for i, col in enumerate(svit[3][0][1:-1]):
svit[4][i + 1].insert(0, col)
svit[4][i + 1].append(svit[1][0][-i - 2])
svit[4][-1].extend(svit[0][0])
# Build faces
faces = []
if not axis_aligned:
hemi -= 1
for side, rows in enumerate(svit):
xp, yp = sides[side][:2]
oa4 = odd_aligned and side == 4
if oa4: # special case
hemi += 1
for j, row in enumerate(rows[:-1]):
tri = odd_aligned and (oa4 and not j or rows[j + 1][-1] < 0)
for i, vi in enumerate(row[:-1]):
# odd_aligned triangle corners
if vi < 0:
if not j and not i:
faces.append((row[i + 1], rows[j + 1][i + 1], rows[j + 1][i]))
elif oa4 and not i and j == len(rows) - 2:
faces.append((vi, row[i + 1], rows[j + 1][i + 1]))
elif tri and i == len(row) - 2:
if j:
faces.append((vi, row[i + 1], rows[j + 1][i]))
else:
if oa4 or arcdiv > 1:
faces.append((vi, rows[j + 1][i + 1], rows[j + 1][i]))
else:
faces.append((vi, row[i + 1], rows[j + 1][i]))
# subdiv = EDGES (not ALL)
elif subdiv and len(rows[j + 1]) < len(row) and (i >= hemi):
if (i == hemi):
faces.append((vi, row[i + 1 + dxyz[xp]], rows[j + 1 + dxyz[yp]][i + 1 + dxyz[xp]],
rows[j + 1 + dxyz[yp]][i]))
elif i > hemi + dxyz[xp]:
faces.append((vi, row[i + 1], rows[j + 1][i + 1 - dxyz[xp]], rows[j + 1][i - dxyz[xp]]))
elif subdiv and len(rows[j + 1]) > len(row) and (i >= hemi):
if (i > hemi):
faces.append((vi, row[i + 1], rows[j + 1][i + 1 + dxyz[xp]], rows[j + 1][i + dxyz[xp]]))
elif subdiv and len(row) < len(rows[0]) and i == hemi:
pass
else:
# Most faces...
faces.append((vi, row[i + 1], rows[j + 1][i + 1], rows[j + 1][i]))
if oa4:
hemi -= 1
return verts, faces
class AddRoundCube(Operator, object_utils.AddObjectHelper):
bl_idname = "mesh.primitive_round_cube_add"
bl_label = "Add Round Cube"
bl_description = ("Create mesh primitives: Quadspheres, "
"Capsules, Rounded Cuboids, 3D Grids etc")
bl_options = {"REGISTER", "UNDO", "PRESET"}
sanity_check_verts = 200000
vert_count = 0
Roundcube : BoolProperty(name = "Roundcube",
default = True,
description = "Roundcube")
change : BoolProperty(name = "Change",
default = False,
description = "change Roundcube")
radius: FloatProperty(
name="Radius",
description="Radius of vertices for sphere, capsule or cuboid bevel",
default=0.2, min=0.0, soft_min=0.01, step=10
)
size: FloatVectorProperty(
name="Size",
description="Size",
subtype='XYZ',
default=(2.0, 2.0, 2.0),
)
arc_div: IntProperty(
name="Arc Divisions",
description="Arc curve divisions, per quadrant, 0=derive from Linear",
default=4, min=1
)
lin_div: FloatProperty(
name="Linear Divisions",
description="Linear unit divisions (Edges/Faces), 0=derive from Arc",
default=0.0, min=0.0, step=100, precision=1
)
div_type: EnumProperty(
name='Type',
description='Division type',
items=(
('CORNERS', 'Corners', 'Sphere / Corners'),
('EDGES', 'Edges', 'Sphere / Corners and extruded edges (size)'),
('ALL', 'All', 'Sphere / Corners, extruded edges and faces (size)')),
default='CORNERS',
)
odd_axis_align: BoolProperty(
name='Odd Axis Align',
description='Align odd arc divisions with axes (Note: triangle corners!)',
)
no_limit: BoolProperty(
name='No Limit',
description='Do not limit to ' + str(sanity_check_verts) + ' vertices (sanity check)',
options={'HIDDEN'}
)
def execute(self, context):
# turn off 'Enter Edit Mode'
use_enter_edit_mode = bpy.context.preferences.edit.use_enter_edit_mode
bpy.context.preferences.edit.use_enter_edit_mode = False
if self.arc_div <= 0 and self.lin_div <= 0:
self.report({'ERROR'},
"Either Arc Divisions or Linear Divisions must be greater than zero")
return {'CANCELLED'}
if not self.no_limit:
if self.vert_count > self.sanity_check_verts:
self.report({'ERROR'}, 'More than ' + str(self.sanity_check_verts) +
' vertices! Check "No Limit" to proceed')
return {'CANCELLED'}
if bpy.context.mode == "OBJECT":
if context.selected_objects != [] and context.active_object and \
(context.active_object.data is not None) and ('Roundcube' in context.active_object.data.keys()) and \
(self.change == True):
obj = context.active_object
oldmesh = obj.data
oldmeshname = obj.data.name
verts, faces = round_cube(self.radius, self.arc_div, self.lin_div,
self.size, self.div_type, self.odd_axis_align)
mesh = bpy.data.meshes.new('Roundcube')
mesh.from_pydata(verts, [], faces)
obj.data = mesh
for material in oldmesh.materials:
obj.data.materials.append(material)
bpy.data.meshes.remove(oldmesh)
obj.data.name = oldmeshname
else:
verts, faces = round_cube(self.radius, self.arc_div, self.lin_div,
self.size, self.div_type, self.odd_axis_align)
mesh = bpy.data.meshes.new('Roundcube')
mesh.from_pydata(verts, [], faces)
obj = object_utils.object_data_add(context, mesh, operator=self)
obj.data["Roundcube"] = True
obj.data["change"] = False
for prm in RoundCubeParameters():
obj.data[prm] = getattr(self, prm)
if bpy.context.mode == "EDIT_MESH":
active_object = context.active_object
name_active_object = active_object.name
bpy.ops.object.mode_set(mode='OBJECT')
verts, faces = round_cube(self.radius, self.arc_div, self.lin_div,
self.size, self.div_type, self.odd_axis_align)
mesh = bpy.data.meshes.new('Roundcube')
mesh.from_pydata(verts, [], faces)
obj = object_utils.object_data_add(context, mesh, operator=self)
obj.select_set(True)
active_object.select_set(True)
bpy.context.view_layer.objects.active = active_object
bpy.ops.object.join()
context.active_object.name = name_active_object
bpy.ops.object.mode_set(mode='EDIT')
if use_enter_edit_mode:
bpy.ops.object.mode_set(mode = 'EDIT')
# restore pre operator state
bpy.context.preferences.edit.use_enter_edit_mode = use_enter_edit_mode
return {'FINISHED'}
def check(self, context):
self.arcdiv, self.lindiv, self.vert_count = round_cube(
self.radius, self.arc_div, self.lin_div,
self.size, self.div_type, self.odd_axis_align,
True
)
return True
def invoke(self, context, event):
self.check(context)
return self.execute(context)
def draw(self, context):
self.check(context)
layout = self.layout
layout.prop(self, 'radius')
layout.column().prop(self, 'size', expand=True)
box = layout.box()
row = box.row()
row.alignment = 'CENTER'
row.scale_y = 0.1
row.label(text='Divisions')
row = box.row()
col = row.column()
col.alignment = 'RIGHT'
col.label(text='Arc:')
col.prop(self, 'arc_div', text='')
col.label(text='[ {} ]'.format(self.arcdiv))
col = row.column()
col.alignment = 'RIGHT'
col.label(text='Linear:')
col.prop(self, 'lin_div', text='')
col.label(text='[ {:.3g} ]'.format(self.lindiv))
box.row().prop(self, 'div_type')
row = box.row()
row.active = self.arcdiv % 2
row.prop(self, 'odd_axis_align')
row = layout.row()
row.alert = self.vert_count > self.sanity_check_verts
row.prop(self, 'no_limit', text='No limit ({})'.format(self.vert_count))
if self.change == False:
col = layout.column(align=True)
col.prop(self, 'align', expand=True)
col = layout.column(align=True)
col.prop(self, 'location', expand=True)
col = layout.column(align=True)
col.prop(self, 'rotation', expand=True)
def RoundCubeParameters():
RoundCubeParameters = [
"radius",
"size",
"arc_div",
"lin_div",
"div_type",
"odd_axis_align",
"no_limit",
]
return RoundCubeParameters
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