'''
bl_info = {
    "name": "Add Mesh: SuperToroid",
    "author": "DreamPainter",
    "version": (1, 0, 0),
    "blender": (2, 53, 0),
    "location": "View3D > Add > Mesh > SuperToroid",
    "description": "Add a SuperToroid mesh",
    "url": "http://wiki.blender.org/index.php/Extensions:2.5/Py/" \
        "Scripts/Add_Mesh/",  # no url
    "category": "Add Mesh"}
'''
import bpy
from bpy.props import FloatProperty,BoolProperty,IntProperty
from math import pi, cos, sin
from mathutils import Vector
from bpy_extras import object_utils

# 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.
# Connects two equally long vertex rows with faces.
# Returns a list of the new faces (list of  lists)
#
# vertIdx1 ... First vertex list (list of vertex indices).
# vertIdx2 ... Second vertex list (list of vertex indices).
# closed ... Creates a loop (first & last are closed).
# flipped ... Invert the normal of the face(s).
#
# Note: You can set vertIdx1 to a single vertex index to create
#       a fan/star of faces.
# Note: If both vertex idx list are the same length they have
#       to have at least 2 vertices.
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):
    """Add a SuperToroid"""
    bl_idname = "mesh.primitive_supertoroid_add"
    bl_label = "Add SuperToroid"
    bl_description = "Create a SuperToroid"
    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.+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'}
'''
menu_func = lambda self, context: self.layout.operator(add_supertoroid.bl_idname,
                                    text = "SuperToroid", icon = 'PLUGIN')

def register():
    bpy.types.register(add_supertoroid)
    bpy.types.INFO_MT_mesh_add.append(menu_func)

def unregister():
    bpy.types.unregister(add_supertoroid)
    bpy.types.INFO_MT_mesh_add.remove(menu_func)

if __name__ == "__main__":
    register()
'''
