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# GPL # Author, Anthony D'Agostino
import bpy, mathutils, math
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)
# ========================
# === Torus Knot Block ===
# ========================
def k1(t):
x = math.cos(t) - 2*math.cos(2*t)
y = math.sin(t) + 2*math.sin(2*t)
z = math.sin(3*t)
return mathutils.Vector([x,y,z])
def k2(t):
x = 10 * (math.cos(t) + math.cos(3*t)) + math.cos(2*t) + math.cos(4*t)
y = 6 * math.sin(t) + 10 * math.sin(3*t)
z = 4 * math.sin(3*t) * math.sin(5*t/2) + 4*math.sin(4*t) - 2*math.sin(6*t)
return mathutils.Vector([x,y,z]) * 0.2
def k3(t):
x = 2.5*math.cos(t+math.pi)/3 + 2*math.cos(3*t)
y = 2.5*math.sin(t)/3 + 2*math.sin(3*t)
z = 1.5*math.sin(4*t) + math.sin(2*t)/3
return mathutils.Vector([x,y,z])
def make_verts(ures, vres, r2, knotfunc):
verts = []
for i in range(ures):
t1 = (i+0) * 2*math.pi/ures
t2 = (i+1) * 2*math.pi/ures
a = knotfunc(t1) # curr point
b = knotfunc(t2) # next point
a,b = map(mathutils.Vector, (a,b))
e = a-b
f = a+b
g = e.cross(f)
h = e.cross(g)
g.normalize()
h.normalize()
for j in range(vres):
k = j * 2*math.pi/vres
l = (math.cos(k),0.0,math.sin(k))
l = mathutils.Vector(l)
m = l * r2
x,y,z = m
n = h*x
o = g*z
p = n+o
q = a+p
verts.append(q)
return verts
def make_faces(ures, vres):
faces = []
for u in range(0, ures):
for v in range(0, vres):
p1 = v + u*vres
p2 = v + ((u+1)%ures)*vres
p4 = (v+1)%vres + u*vres
p3 = (v+1)%vres + ((u+1)%ures)*vres
faces.append([p4, p3, p2, p1])
return faces
def make_knot(knotidx, ures):
knots = [k1,k2,k3]
knotfunc = knots[knotidx-1]
vres = ures//10
r2 = 0.5
verts = make_verts(ures, vres, r2, knotfunc)
faces = make_faces(ures, vres)
return (verts, faces)
class AddTorusKnot(bpy.types.Operator):
"""Add a torus-knot mesh"""
bl_idname = "mesh.primitive_torusknot_add"
bl_label = "Add Torus Knot"
bl_options = {"REGISTER", "UNDO"}
resolution = bpy.props.IntProperty(name="Resolution",
description="Resolution of the Torus Knot",
default=80, min=30, max=256)
objecttype = bpy.props.IntProperty(name="Knot Type",
description="Type of Knot",
default=1, min=1, max=3)
def execute(self, context):
verts, faces = make_knot(self.objecttype,
self.resolution)
obj = create_mesh_object(context, verts, [], faces, "Torus Knot")
return {'FINISHED'}
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