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# GPL # "author": "DreamPainter"
import bpy
from bpy.props import (
FloatProperty,
BoolProperty,
IntProperty,
)
from math import pi, cos, sin
from mathutils import Vector
# Create a new mesh (object) from verts/edges/faces
# verts/edges/faces ... List of vertices/edges/faces for the
# new mesh (as used in from_pydata)
# name ... Name of the new mesh (& object)
def create_mesh_object(context, verts, edges, faces, name):
# Create new mesh
mesh = bpy.data.meshes.new(name)
# Make a mesh from a list of verts/edges/faces.
mesh.from_pydata(verts, edges, faces)
# Update mesh geometry after adding stuff.
mesh.update()
from bpy_extras import object_utils
return object_utils.object_data_add(context, mesh, operator=None)
# A very simple "bridge" tool
def createFaces(vertIdx1, vertIdx2, closed=False, flipped=False):
faces = []
if not vertIdx1 or not vertIdx2:
return None
if len(vertIdx1) < 2 and len(vertIdx2) < 2:
return None
fan = False
if (len(vertIdx1) != len(vertIdx2)):
if (len(vertIdx1) == 1 and len(vertIdx2) > 1):
fan = True
else:
return None
total = len(vertIdx2)
if closed:
# Bridge the start with the end.
if flipped:
face = [
vertIdx1[0],
vertIdx2[0],
vertIdx2[total - 1]]
if not fan:
face.append(vertIdx1[total - 1])
faces.append(face)
else:
face = [vertIdx2[0], vertIdx1[0]]
if not fan:
face.append(vertIdx1[total - 1])
face.append(vertIdx2[total - 1])
faces.append(face)
# Bridge the rest of the faces.
for num in range(total - 1):
if flipped:
if fan:
face = [vertIdx2[num], vertIdx1[0], vertIdx2[num + 1]]
else:
face = [vertIdx2[num], vertIdx1[num],
vertIdx1[num + 1], vertIdx2[num + 1]]
faces.append(face)
else:
if fan:
face = [vertIdx1[0], vertIdx2[num], vertIdx2[num + 1]]
else:
face = [vertIdx1[num], vertIdx2[num],
vertIdx2[num + 1], vertIdx1[num + 1]]
faces.append(face)
return faces
def power(a, b):
if a < 0:
return -((-a) ** b)
return a ** b
def supertoroid(R, r, u, v, n1, n2):
"""
R = big radius
r = small radius
u = lateral segmentation
v = radial segmentation
n1 = value determines the shape of the torus
n2 = value determines the shape of the cross-section
"""
# create the necessary constants
a = 2 * pi / u
b = 2 * pi / v
verts = []
faces = []
# create each cross-section by calculating each vector on the
# the wannabe circle
# x = (cos(theta) ** n1)*(R + r * (cos(phi) ** n2))
# y = (sin(theta) ** n1)*(R + r * (cos(phi) ** n2))
# z = (r * sin(phi) ** n2)
# with theta and phi rangeing from 0 to 2pi
for i in range(u):
s = power(sin(i * a), n1)
c = power(cos(i * a), n1)
for j in range(v):
c2 = R + r * power(cos(j * b), n2)
s2 = r * power(sin(j * b), n2)
verts.append(Vector((c * c2, s * c2, s2)))
# bridge the last circle with the previous circle
if i > 0: # but not for the first circle, 'cus there's no previous before the first
f = createFaces(range((i - 1) * v, i * v), range(i * v, (i + 1) * v), closed=True)
faces.extend(f)
# bridge the last circle with the first
f = createFaces(range((u - 1) * v, u * v), range(v), closed=True)
faces.extend(f)
return verts, faces
class add_supertoroid(bpy.types.Operator):
bl_idname = "mesh.primitive_supertoroid_add"
bl_label = "Add SuperToroid"
bl_description = "Construct a supertoroid mesh"
bl_options = {'REGISTER', 'UNDO', 'PRESET'}
R: FloatProperty(
name="Big radius",
description="The radius inside the tube",
default=1.0,
min=0.01, max=100.0
)
r: FloatProperty(
name="Small radius",
description="The radius of the tube",
default=0.3,
min=0.01, max=100.0
)
u: IntProperty(
name="U-segments",
description="Radial segmentation",
default=16,
min=3, max=265
)
v: IntProperty(
name="V-segments",
description="Lateral segmentation",
default=8,
min=3, max=265
)
n1: FloatProperty(
name="Ring manipulator",
description="Manipulates the shape of the Ring",
default=1.0,
min=0.01, max=100.0
)
n2: FloatProperty(
name="Cross manipulator",
description="Manipulates the shape of the cross-section",
default=1.0,
min=0.01, max=100.0
)
ie: BoolProperty(
name="Use Int. and Ext. radii",
description="Use internal and external radii",
default=False
)
edit: BoolProperty(
name="",
description="",
default=False,
options={'HIDDEN'}
)
def execute(self, context):
props = self.properties
# check how the radii properties must be used
if props.ie:
rad1 = (props.R + props.r) / 2
rad2 = (props.R - props.r) / 2
# for consistency in the mesh, ie no crossing faces, make the largest of the two
# the outer radius
if rad2 > rad1:
[rad1, rad2] = [rad2, rad1]
else:
rad1 = props.R
rad2 = props.r
# again for consistency, make the radius in the tube,
# at least as big as the radius of the tube
if rad2 > rad1:
rad1 = rad2
# create mesh
verts, faces = supertoroid(rad1,
rad2,
props.u,
props.v,
props.n1,
props.n2
)
# create the object
obj = create_mesh_object(context, verts, [], faces, "SuperToroid")
return {'FINISHED'}
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