# SPDX-License-Identifier: GPL-2.0-or-later # Author: DreamPainter import bpy from bpy.props import ( FloatProperty, BoolProperty, IntProperty, StringProperty, ) from math import pi, cos, sin from mathutils import Vector from bpy_extras import object_utils # 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 ranging 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, object_utils.AddObjectHelper): bl_idname = "mesh.primitive_supertoroid_add" bl_label = "Add SuperToroid" bl_description = "Construct a supertoroid mesh" bl_options = {'REGISTER', 'UNDO', 'PRESET'} SuperToroid : BoolProperty(name = "SuperToroid", default = True, description = "SuperToroid") change : BoolProperty(name = "Change", default = False, description = "change SuperToroid") 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 draw(self, context): layout = self.layout layout.prop(self, 'R', expand=True) layout.prop(self, 'r', expand=True) layout.prop(self, 'u', expand=True) layout.prop(self, 'v', expand=True) layout.prop(self, 'n1', expand=True) layout.prop(self, 'n2', expand=True) layout.prop(self, 'ie', expand=True) 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 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 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 if bpy.context.mode == "OBJECT": if context.selected_objects != [] and context.active_object and \ (context.active_object.data is not None) and ('SuperToroid' in context.active_object.data.keys()) and \ (self.change == True): obj = context.active_object oldmesh = obj.data oldmeshname = obj.data.name verts, faces = supertoroid(rad1, rad2, props.u, props.v, props.n1, props.n2 ) mesh = bpy.data.meshes.new('SuperToroid') 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 = supertoroid(rad1, rad2, props.u, props.v, props.n1, props.n2 ) mesh = bpy.data.meshes.new('SuperToroid') mesh.from_pydata(verts, [], faces) obj = object_utils.object_data_add(context, mesh, operator=self) obj.data["SuperToroid"] = True obj.data["change"] = False for prm in SuperToroidParameters(): 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 = supertoroid(rad1, rad2, props.u, props.v, props.n1, props.n2 ) mesh = bpy.data.meshes.new('SuperToroid') 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 SuperToroidParameters(): SuperToroidParameters = [ "R", "r", "u", "v", "n1", "n2", "ie", "edit", ] return SuperToroidParameters