# GPL # "author": "DreamPainter"

import bpy
from math import sqrt
from mathutils import Vector
from functools import reduce
from bpy.props import (
        FloatProperty,
        EnumProperty,
        BoolProperty,
        )
from bpy_extras.object_utils import object_data_add


# this function creates a chain of quads and, when necessary, a remaining tri
# for each polygon created in this script. be aware though, that this function
# assumes each polygon is convex.
#  poly: list of faces, or a single face, like those
#        needed for mesh.from_pydata.
#  returns the tessellated faces.

def createPolys(poly):
    # check for faces
    if len(poly) == 0:
        return []
    # one or more faces
    if type(poly[0]) == type(1):
        poly = [poly]  # if only one,  make it a list of one face
    faces = []
    for i in poly:
        L = len(i)
        # let all faces of 3 or 4 verts be
        if L < 5:
            faces.append(i)
        # split all polygons in half and bridge the two halves
        else:
            f = [[i[x], i[x + 1], i[L - 2 - x], i[L - 1 - x]] for x in range(L // 2 - 1)]
            faces.extend(f)
            if L & 1 == 1:
                faces.append([i[L // 2 - 1 + x] for x in [0, 1, 2]])
    return faces


# function to make the reduce function work as a workaround to sum a list of vectors

def vSum(list):
    return reduce(lambda a, b: a + b, list)


# creates the 5 platonic solids as a base for the rest
#  plato: should be one of {"4","6","8","12","20"}. decides what solid the
#         outcome will be.
#  returns a list of vertices and faces

def source(plato):
    verts = []
    faces = []

    # Tetrahedron
    if plato == "4":
        # Calculate the necessary constants
        s = sqrt(2) / 3.0
        t = -1 / 3
        u = sqrt(6) / 3

        # create the vertices and faces
        v = [(0, 0, 1), (2 * s, 0, t), (-s, u, t), (-s, -u, t)]
        faces = [[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 2]]

    # Hexahedron (cube)
    elif plato == "6":
        # Calculate the necessary constants
        s = 1 / sqrt(3)

        # create the vertices and faces
        v = [(-s, -s, -s), (s, -s, -s), (s, s, -s), (-s, s, -s), (-s, -s, s), (s, -s, s), (s, s, s), (-s, s, s)]
        faces = [[0, 3, 2, 1], [0, 1, 5, 4], [0, 4, 7, 3], [6, 5, 1, 2], [6, 2, 3, 7], [6, 7, 4, 5]]

    # Octahedron
    elif plato == "8":
        # create the vertices and faces
        v = [(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1)]
        faces = [[4, 0, 2], [4, 2, 1], [4, 1, 3], [4, 3, 0], [5, 2, 0], [5, 1, 2], [5, 3, 1], [5, 0, 3]]

    # Dodecahedron
    elif plato == "12":
        # Calculate the necessary constants
        s = 1 / sqrt(3)
        t = sqrt((3 - sqrt(5)) / 6)
        u = sqrt((3 + sqrt(5)) / 6)

        # create the vertices and faces
        v = [(s, s, s), (s, s, -s), (s, -s, s), (s, -s, -s), (-s, s, s), (-s, s, -s), (-s, -s, s), (-s, -s, -s),
             (t, u, 0), (-t, u, 0), (t, -u, 0), (-t, -u, 0), (u, 0, t), (u, 0, -t), (-u, 0, t), (-u, 0, -t), (0, t, u),
             (0, -t, u), (0, t, -u), (0, -t, -u)]
        faces = [[0, 8, 9, 4, 16], [0, 12, 13, 1, 8], [0, 16, 17, 2, 12], [8, 1, 18, 5, 9], [12, 2, 10, 3, 13],
                 [16, 4, 14, 6, 17], [9, 5, 15, 14, 4], [6, 11, 10, 2, 17], [3, 19, 18, 1, 13], [7, 15, 5, 18, 19],
                 [7, 11, 6, 14, 15], [7, 19, 3, 10, 11]]

    # Icosahedron
    elif plato == "20":
        # Calculate the necessary constants
        s = (1 + sqrt(5)) / 2
        t = sqrt(1 + s * s)
        s = s / t
        t = 1 / t

        # create the vertices and faces
        v = [(s, t, 0), (-s, t, 0), (s, -t, 0), (-s, -t, 0), (t, 0, s), (t, 0, -s), (-t, 0, s), (-t, 0, -s),
             (0, s, t), (0, -s, t), (0, s, -t), (0, -s, -t)]
        faces = [[0, 8, 4], [0, 5, 10], [2, 4, 9], [2, 11, 5], [1, 6, 8], [1, 10, 7], [3, 9, 6], [3, 7, 11],
                 [0, 10, 8], [1, 8, 10], [2, 9, 11], [3, 11, 9], [4, 2, 0], [5, 0, 2], [6, 1, 3], [7, 3, 1],
                 [8, 6, 4], [9, 4, 6], [10, 5, 7], [11, 7, 5]]

    # convert the tuples to Vectors
    verts = [Vector(i) for i in v]

    return verts, faces


# processes the raw data from source

def createSolid(plato, vtrunc, etrunc, dual, snub):
    # the duals from each platonic solid
    dualSource = {"4": "4",
                  "6": "8",
                  "8": "6",
                  "12": "20",
                  "20": "12"}

    # constants saving space and readability
    vtrunc *= 0.5
    etrunc *= 0.5
    supposedSize = 0
    noSnub = (snub == "None") or (etrunc == 0.5) or (etrunc == 0)
    lSnub = (snub == "Left") and (0 < etrunc < 0.5)
    rSnub = (snub == "Right") and (0 < etrunc < 0.5)

    # no truncation
    if vtrunc == 0:
        if dual:  # dual is as simple as another, but mirrored platonic solid
            vInput, fInput = source(dualSource[plato])
            supposedSize = vSum(vInput[i] for i in fInput[0]).length / len(fInput[0])
            vInput = [-i * supposedSize for i in vInput]            # mirror it
            return vInput, fInput
        return source(plato)
    elif 0 < vtrunc <= 0.5:  # simple truncation of the source
        vInput, fInput = source(plato)
    else:
        # truncation is now equal to simple truncation of the dual of the source
        vInput, fInput = source(dualSource[plato])
        supposedSize = vSum(vInput[i] for i in fInput[0]).length / len(fInput[0])
        vtrunc = 1 - vtrunc  # account for the source being a dual
        if vtrunc == 0:    # no truncation needed
            if dual:
                vInput, fInput = source(plato)
                vInput = [i * supposedSize for i in vInput]
                return vInput, fInput
            vInput = [-i * supposedSize for i in vInput]
            return vInput, fInput

    # generate connection database
    vDict = [{} for i in vInput]
    # for every face, store what vertex comes after and before the current vertex
    for x in range(len(fInput)):
        i = fInput[x]
        for j in range(len(i)):
            vDict[i[j - 1]][i[j]] = [i[j - 2], x]
            if len(vDict[i[j - 1]]) == 1:
                vDict[i[j - 1]][-1] = i[j]

    # the actual connection database: exists out of:
    # [vtrunc pos, etrunc pos, connected vert IDs, connected face IDs]
    vData = [[[], [], [], []] for i in vInput]
    fvOutput = []      # faces created from truncated vertices
    feOutput = []      # faces created from truncated edges
    vOutput = []       # newly created vertices
    for x in range(len(vInput)):
        i = vDict[x]   # lookup the current vertex
        current = i[-1]
        while True:    # follow the chain to get a ccw order of connected verts and faces
            vData[x][2].append(i[current][0])
            vData[x][3].append(i[current][1])
            # create truncated vertices
            vData[x][0].append((1 - vtrunc) * vInput[x] + vtrunc * vInput[vData[x][2][-1]])
            current = i[current][0]
            if current == i[-1]:
                break                   # if we're back at the first: stop the loop
        fvOutput.append([])             # new face from truncated vert
        fOffset = x * (len(i) - 1)      # where to start off counting faceVerts
        # only create one vert where one is needed (v1 todo: done)
        if etrunc == 0.5:
            for j in range(len(i) - 1):
                vOutput.append((vData[x][0][j] + vData[x][0][j - 1]) * etrunc)  # create vert
                fvOutput[x].append(fOffset + j)                                 # add to face
            fvOutput[x] = fvOutput[x][1:] + [fvOutput[x][0]]                    # rotate face for ease later on
            # create faces from truncated edges.
            for j in range(len(i) - 1):
                if x > vData[x][2][j]:     # only create when other vertex has been added
                    index = vData[vData[x][2][j]][2].index(x)
                    feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
                                     fvOutput[vData[x][2][j]][index],
                                     fvOutput[vData[x][2][j]][index - 1]])
        # edge truncation between none and full
        elif etrunc > 0:
            for j in range(len(i) - 1):
                # create snubs from selecting verts from rectified meshes
                if rSnub:
                    vOutput.append(etrunc * vData[x][0][j] + (1 - etrunc) * vData[x][0][j - 1])
                    fvOutput[x].append(fOffset + j)
                elif lSnub:
                    vOutput.append((1 - etrunc) * vData[x][0][j] + etrunc * vData[x][0][j - 1])
                    fvOutput[x].append(fOffset + j)
                else:   # noSnub,  select both verts from rectified mesh
                    vOutput.append(etrunc * vData[x][0][j] + (1 - etrunc) * vData[x][0][j - 1])
                    vOutput.append((1 - etrunc) * vData[x][0][j] + etrunc * vData[x][0][j - 1])
                    fvOutput[x].append(2 * fOffset + 2 * j)
                    fvOutput[x].append(2 * fOffset + 2 * j + 1)
            # rotate face for ease later on
            if noSnub:
                fvOutput[x] = fvOutput[x][2:] + fvOutput[x][:2]
            else:
                fvOutput[x] = fvOutput[x][1:] + [fvOutput[x][0]]
            # create single face for each edge
            if noSnub:
                for j in range(len(i) - 1):
                    if x > vData[x][2][j]:
                        index = vData[vData[x][2][j]][2].index(x)
                        feOutput.append([fvOutput[x][j * 2], fvOutput[x][2 * j - 1],
                                         fvOutput[vData[x][2][j]][2 * index],
                                         fvOutput[vData[x][2][j]][2 * index - 1]])
            # create 2 tri's for each edge for the snubs
            elif rSnub:
                for j in range(len(i) - 1):
                    if x > vData[x][2][j]:
                        index = vData[vData[x][2][j]][2].index(x)
                        feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
                                         fvOutput[vData[x][2][j]][index]])
                        feOutput.append([fvOutput[x][j], fvOutput[vData[x][2][j]][index],
                                         fvOutput[vData[x][2][j]][index - 1]])
            elif lSnub:
                for j in range(len(i) - 1):
                    if x > vData[x][2][j]:
                        index = vData[vData[x][2][j]][2].index(x)
                        feOutput.append([fvOutput[x][j], fvOutput[x][j - 1],
                                         fvOutput[vData[x][2][j]][index - 1]])
                        feOutput.append([fvOutput[x][j - 1], fvOutput[vData[x][2][j]][index],
                                         fvOutput[vData[x][2][j]][index - 1]])
        # special rules for birectified mesh (v1 todo: done)
        elif vtrunc == 0.5:
            for j in range(len(i) - 1):
                if x < vData[x][2][j]:  # use current vert,  since other one has not passed yet
                    vOutput.append(vData[x][0][j])
                    fvOutput[x].append(len(vOutput) - 1)
                else:
                    # search for other edge to avoid duplicity
                    connectee = vData[x][2][j]
                    fvOutput[x].append(fvOutput[connectee][vData[connectee][2].index(x)])
        else:   # vert truncation only
            vOutput.extend(vData[x][0])   # use generated verts from way above
            for j in range(len(i) - 1):   # create face from them
                fvOutput[x].append(fOffset + j)

    # calculate supposed vertex length to ensure continuity
    if supposedSize and not dual:                    # this to make the vtrunc > 1 work
        supposedSize *= len(fvOutput[0]) / vSum(vOutput[i] for i in fvOutput[0]).length
        vOutput = [-i * supposedSize for i in vOutput]

    # create new faces by replacing old vert IDs by newly generated verts
    ffOutput = [[] for i in fInput]
    for x in range(len(fInput)):
        # only one generated vert per vertex,  so choose accordingly
        if etrunc == 0.5 or (etrunc == 0 and vtrunc == 0.5) or lSnub or rSnub:
            ffOutput[x] = [fvOutput[i][vData[i][3].index(x) - 1] for i in fInput[x]]
        # two generated verts per vertex
        elif etrunc > 0:
            for i in fInput[x]:
                ffOutput[x].append(fvOutput[i][2 * vData[i][3].index(x) - 1])
                ffOutput[x].append(fvOutput[i][2 * vData[i][3].index(x) - 2])
        else:   # cutting off corners also makes 2 verts
            for i in fInput[x]:
                ffOutput[x].append(fvOutput[i][vData[i][3].index(x)])
                ffOutput[x].append(fvOutput[i][vData[i][3].index(x) - 1])

    if not dual:
        return vOutput, fvOutput + feOutput + ffOutput
    else:
        # do the same procedure as above,  only now on the generated mesh
        # generate connection database
        vDict = [{} for i in vOutput]
        dvOutput = [0 for i in fvOutput + feOutput + ffOutput]
        dfOutput = []

        for x in range(len(dvOutput)):               # for every face
            i = (fvOutput + feOutput + ffOutput)[x]  # choose face to work with
            # find vertex from face
            normal = (vOutput[i[0]] - vOutput[i[1]]).cross(vOutput[i[2]] - vOutput[i[1]]).normalized()
            dvOutput[x] = normal / (normal.dot(vOutput[i[0]]))
            for j in range(len(i)):  # create vert chain
                vDict[i[j - 1]][i[j]] = [i[j - 2], x]
                if len(vDict[i[j - 1]]) == 1:
                    vDict[i[j - 1]][-1] = i[j]

        # calculate supposed size for continuity
        supposedSize = vSum([vInput[i] for i in fInput[0]]).length / len(fInput[0])
        supposedSize /= dvOutput[-1].length
        dvOutput = [i * supposedSize for i in dvOutput]

        # use chains to create faces
        for x in range(len(vOutput)):
            i = vDict[x]
            current = i[-1]
            face = []
            while True:
                face.append(i[current][1])
                current = i[current][0]
                if current == i[-1]:
                    break
            dfOutput.append(face)

        return dvOutput, dfOutput


class Solids(bpy.types.Operator):
    """Add one of the (regular) solids (mesh)"""
    bl_idname = "mesh.primitive_solid_add"
    bl_label = "(Regular) solids"
    bl_description = "Add one of the Platonic, Archimedean or Catalan solids"
    bl_options = {'REGISTER', 'UNDO', 'PRESET'}

    source: EnumProperty(
                    items=(("4", "Tetrahedron", ""),
                            ("6", "Hexahedron", ""),
                            ("8", "Octahedron", ""),
                            ("12", "Dodecahedron", ""),
                            ("20", "Icosahedron", "")),
                    name="Source",
                    description="Starting point of your solid"
                    )
    size: FloatProperty(
                    name="Size",
                    description="Radius of the sphere through the vertices",
                    min=0.01,
                    soft_min=0.01,
                    max=100,
                    soft_max=100,
                    default=1.0
                    )
    vTrunc: FloatProperty(
                    name="Vertex Truncation",
                    description="Amount of vertex truncation",
                    min=0.0,
                    soft_min=0.0,
                    max=2.0,
                    soft_max=2.0,
                    default=0.0,
                    precision=3,
                    step=0.5
                    )
    eTrunc: FloatProperty(
                    name="Edge Truncation",
                    description="Amount of edge truncation",
                    min=0.0,
                    soft_min=0.0,
                    max=1.0,
                    soft_max=1.0,
                    default=0.0,
                    precision=3,
                    step=0.2
                    )
    snub: EnumProperty(
                    items=(("None", "No Snub", ""),
                           ("Left", "Left Snub", ""),
                           ("Right", "Right Snub", "")),
                    name="Snub",
                    description="Create the snub version"
                    )
    dual: BoolProperty(
                    name="Dual",
                    description="Create the dual of the current solid",
                    default=False
                    )
    keepSize: BoolProperty(
                    name="Keep Size",
                    description="Keep the whole solid at a constant size",
                    default=False
                    )
    preset: EnumProperty(
                    items=(("0", "Custom", ""),
                           ("t4", "Truncated Tetrahedron", ""),
                           ("r4", "Cuboctahedron", ""),
                           ("t6", "Truncated Cube", ""),
                           ("t8", "Truncated Octahedron", ""),
                           ("b6", "Rhombicuboctahedron", ""),
                           ("c6", "Truncated Cuboctahedron", ""),
                           ("s6", "Snub Cube", ""),
                           ("r12", "Icosidodecahedron", ""),
                           ("t12", "Truncated Dodecahedron", ""),
                           ("t20", "Truncated Icosahedron", ""),
                           ("b12", "Rhombicosidodecahedron", ""),
                           ("c12", "Truncated Icosidodecahedron", ""),
                           ("s12", "Snub Dodecahedron", ""),
                           ("dt4", "Triakis Tetrahedron", ""),
                           ("dr4", "Rhombic Dodecahedron", ""),
                           ("dt6", "Triakis Octahedron", ""),
                           ("dt8", "Tetrakis Hexahedron", ""),
                           ("db6", "Deltoidal Icositetrahedron", ""),
                           ("dc6", "Disdyakis Dodecahedron", ""),
                           ("ds6", "Pentagonal Icositetrahedron", ""),
                           ("dr12", "Rhombic Triacontahedron", ""),
                           ("dt12", "Triakis Icosahedron", ""),
                           ("dt20", "Pentakis Dodecahedron", ""),
                           ("db12", "Deltoidal Hexecontahedron", ""),
                           ("dc12", "Disdyakis Triacontahedron", ""),
                           ("ds12", "Pentagonal Hexecontahedron", "")),
                    name="Presets",
                    description="Parameters for some hard names"
                    )

    # actual preset values
    p = {"t4": ["4", 2 / 3, 0, 0, "None"],
         "r4": ["4", 1, 1, 0, "None"],
         "t6": ["6", 2 / 3, 0, 0, "None"],
         "t8": ["8", 2 / 3, 0, 0, "None"],
         "b6": ["6", 1.0938, 1, 0, "None"],
         "c6": ["6", 1.0572, 0.585786, 0, "None"],
         "s6": ["6", 1.0875, 0.704, 0, "Left"],
         "r12": ["12", 1, 0, 0, "None"],
         "t12": ["12", 2 / 3, 0, 0, "None"],
         "t20": ["20", 2 / 3, 0, 0, "None"],
         "b12": ["12", 1.1338, 1, 0, "None"],
         "c12": ["20", 0.921, 0.553, 0, "None"],
         "s12": ["12", 1.1235, 0.68, 0, "Left"],
         "dt4": ["4", 2 / 3, 0, 1, "None"],
         "dr4": ["4", 1, 1, 1, "None"],
         "dt6": ["6", 2 / 3, 0, 1, "None"],
         "dt8": ["8", 2 / 3, 0, 1, "None"],
         "db6": ["6", 1.0938, 1, 1, "None"],
         "dc6": ["6", 1.0572, 0.585786, 1, "None"],
         "ds6": ["6", 1.0875, 0.704, 1, "Left"],
         "dr12": ["12", 1, 0, 1, "None"],
         "dt12": ["12", 2 / 3, 0, 1, "None"],
         "dt20": ["20", 2 / 3, 0, 1, "None"],
         "db12": ["12", 1.1338, 1, 1, "None"],
         "dc12": ["20", 0.921, 0.553, 1, "None"],
         "ds12": ["12", 1.1235, 0.68, 1, "Left"]}

    # previous preset, for User-friendly reasons
    previousSetting = ""

    def execute(self, context):
        # piece of code to make presets remain until parameters are changed
        if self.preset != "0":
            # if preset, set preset
            if self.previousSetting != self.preset:
                using = self.p[self.preset]
                self.source = using[0]
                self.vTrunc = using[1]
                self.eTrunc = using[2]
                self.dual = using[3]
                self.snub = using[4]
            else:
                using = self.p[self.preset]
                result0 = self.source == using[0]
                result1 = abs(self.vTrunc - using[1]) < 0.004
                result2 = abs(self.eTrunc - using[2]) < 0.0015
                result4 = using[4] == self.snub or ((using[4] == "Left") and
                                                self.snub in ["Left", "Right"])
                if (result0 and result1 and result2 and result4):
                    if self.p[self.previousSetting][3] != self.dual:
                        if self.preset[0] == "d":
                            self.preset = self.preset[1:]
                        else:
                            self.preset = "d" + self.preset
                else:
                    self.preset = "0"

        self.previousSetting = self.preset

        # generate mesh
        verts, faces = createSolid(self.source,
                                   self.vTrunc,
                                   self.eTrunc,
                                   self.dual,
                                   self.snub
                                   )

        # turn n-gons in quads and tri's
        faces = createPolys(faces)

        # resize to normal size, or if keepSize, make sure all verts are of length 'size'
        if self.keepSize:
            rad = self.size / verts[-1 if self.dual else 0].length
        else:
            rad = self.size
        verts = [i * rad for i in verts]

        # generate object
        # Create new mesh
        mesh = bpy.data.meshes.new("Solid")

        # Make a mesh from a list of verts/edges/faces.
        mesh.from_pydata(verts, [], faces)

        # Update mesh geometry after adding stuff.
        mesh.update()

        object_data_add(context, mesh, operator=None)
        # object generation done

        return {'FINISHED'}
