add_mesh_3d_function_surface.py

# ##### BEGIN GPL LICENSE BLOCK #####
#
#  This program is free software; you can redistribute it and/or
#  modify it under the terms of the GNU General Public License
#  as published by the Free Software Foundation; either version 2
#  of the License, or (at your option) any later version.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  You should have received a copy of the GNU General Public License
#  along with this program; if not, write to the Free Software Foundation,
#  Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# ##### END GPL LICENSE BLOCK #####
'''
bl_info = {
    "name": "3D Function Surfaces",
    "author": "Buerbaum Martin (Pontiac), Elod Csirmaz",
    "version": (0, 3, 8),
    "blender": (2, 5, 7),
    "location": "View3D > Add > Mesh",
    "description": "Create Objects using Math Formulas",
    "warning": "",
    "wiki_url": "http://wiki.blender.org/index.php/Extensions:2.5/Py/"\
        "Scripts/Add_Mesh/Add_3d_Function_Surface",
    "tracker_url": "https://projects.blender.org/tracker/index.php?"\
        "func=detail&aid=21444",
    "category": "Add Mesh"}
'''

import bpy
from mathutils import *
from math import *
from bpy.props import *

# List of safe functions for eval()
safe_list = ['math', 'acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh',
    'degrees', 'e', 'exp', 'fabs', 'floor', 'fmod', 'frexp', 'hypot',
    'ldexp', 'log', 'log10', 'modf', 'pi', 'pow', 'radians',
    'sin', 'sinh', 'sqrt', 'tan', 'tanh']

# Use the list to filter the local namespace
safe_dict = dict((k, globals().get(k, None)) for k in safe_list)


# Stores the values of a list of properties and the
# operator id in a property group ('recall_op') inside the object.
# Could (in theory) be used for non-objects.
# Note: Replaces any existing property group with the same name!
# ob ... Object to store the properties in.
# op ... The operator that should be used.
# op_args ... A dictionary with valid Blender
#             properties (operator arguments/parameters).


# 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


class AddZFunctionSurface(bpy.types.Operator):
    """Add a surface defined defined by a function z=f(x,y)"""
    bl_idname = "mesh.primitive_z_function_surface"
    bl_label = "Add Z Function Surface"
    bl_options = {'REGISTER', 'UNDO', 'PRESET'}

    equation = StringProperty(name="Z Equation",
        description="Equation for z=f(x,y)",
        default="1 - ( x**2 + y**2 )")

    div_x = IntProperty(name="X Subdivisions",
        description="Number of vertices in x direction",
        default=16,
        min=3,
        max=256)
    div_y = IntProperty(name="Y Subdivisions",
        description="Number of vertices in y direction",
        default=16,
        min=3,
        max=256)

    size_x = FloatProperty(name="X Size",
        description="Size of the x axis",
        default=2.0,
        min=0.01,
        max=100.0,
        unit="LENGTH")
    size_y = FloatProperty(name="Y Size",
        description="Size of the y axis",
        default=2.0,
        min=0.01,
        max=100.0,
        unit="LENGTH")

    def execute(self, context):
        equation = self.equation
        div_x = self.div_x
        div_y = self.div_y
        size_x = self.size_x
        size_y = self.size_y

        verts = []
        faces = []

        delta_x = size_x / float(div_x - 1)
        delta_y = size_y / float(div_y - 1)
        start_x = -(size_x / 2.0)
        start_y = -(size_y / 2.0)

        edgeloop_prev = []

        try:
            expr_args = (
                compile(equation, __file__, 'eval'),
                {"__builtins__": None},
                safe_dict)
        except:
            import traceback
            self.report({'ERROR'}, "Error parsing expression: "
                + traceback.format_exc(limit=1))
            return {'CANCELLED'}

        for row_x in range(div_x):
            edgeloop_cur = []
            x = start_x + row_x * delta_x

            for row_y in range(div_y):
                y = start_y + row_y * delta_y
                z = 0.0

                safe_dict['x'] = x
                safe_dict['y'] = y

                # Try to evaluate the equation.
                try:
                    z = float(eval(*expr_args))
                except:
                    import traceback
                    self.report({'ERROR'}, "Error evaluating expression: "
                        + traceback.format_exc(limit=1))
                    return {'CANCELLED'}

                edgeloop_cur.append(len(verts))
                verts.append((x, y, z))

            if len(edgeloop_prev) > 0:
                faces_row = createFaces(edgeloop_prev, edgeloop_cur)
                faces.extend(faces_row)

            edgeloop_prev = edgeloop_cur

        base = create_mesh_object(context, verts, [], faces, "Z Function")

        return {'FINISHED'}


def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
    range_u_min, range_u_max, range_u_step, wrap_u,
    range_v_min, range_v_max, range_v_step, wrap_v,
    a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v):

    verts = []
    faces = []

    # Distance of each step in Blender Units
    uStep = (range_u_max - range_u_min) / range_u_step
    vStep = (range_v_max - range_v_min) / range_v_step

    # Number of steps in the vertex creation loops.
    # Number of steps is the number of faces
    #   => Number of points is +1 unless wrapped.
    uRange = range_u_step + 1
    vRange = range_v_step + 1

    if wrap_u:
        uRange = uRange - 1

    if wrap_v:
        vRange = vRange - 1

    try:
        expr_args_x = (
            compile(x_eq, __file__.replace(".py", "_x.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_y = (
            compile(y_eq, __file__.replace(".py", "_y.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_z = (
            compile(z_eq, __file__.replace(".py", "_z.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_a = (
            compile(a_eq, __file__.replace(".py", "_a.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_b = (
            compile(b_eq, __file__.replace(".py", "_b.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_c = (
            compile(c_eq, __file__.replace(".py", "_c.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_f = (
            compile(f_eq, __file__.replace(".py", "_f.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_g = (
            compile(g_eq, __file__.replace(".py", "_g.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
        expr_args_h = (
            compile(h_eq, __file__.replace(".py", "_h.py"), 'eval'),
            {"__builtins__": None},
            safe_dict)
    except:
        import traceback
        self.report({'ERROR'}, "Error parsing expression: "
            + traceback.format_exc(limit=1))
        return [], []

    for vN in range(vRange):
        v = range_v_min + (vN * vStep)

        for uN in range(uRange):
            u = range_u_min + (uN * uStep)

            safe_dict['u'] = u
            safe_dict['v'] = v

            safe_dict['n'] = n

            # Try to evaluate the equations.
            try:
                a = float(eval(*expr_args_a))
                b = float(eval(*expr_args_b))
                c = float(eval(*expr_args_c))

                safe_dict['a'] = a
                safe_dict['b'] = b
                safe_dict['c'] = c

                f = float(eval(*expr_args_f))
                g = float(eval(*expr_args_g))
                h = float(eval(*expr_args_h))

                safe_dict['f'] = f
                safe_dict['g'] = g
                safe_dict['h'] = h

                verts.append((
                    float(eval(*expr_args_x)),
                    float(eval(*expr_args_y)),
                    float(eval(*expr_args_z))))

            except:
                import traceback
                self.report({'ERROR'}, "Error evaluating expression: "
                    + traceback.format_exc(limit=1))
                return [], []

    for vN in range(range_v_step):
        vNext = vN + 1

        if wrap_v and (vNext >= vRange):
            vNext = 0

        for uN in range(range_u_step):
            uNext = uN + 1

            if wrap_u and (uNext >= uRange):
                uNext = 0

            faces.append([(vNext * uRange) + uNext,
                (vNext * uRange) + uN,
                (vN * uRange) + uN,
                (vN * uRange) + uNext])

    if close_v and wrap_u and (not wrap_v):
        for uN in range(1, range_u_step - 1):
            faces.append([
                range_u_step - 1,
                range_u_step - 1 - uN,
                range_u_step - 2 - uN])
            faces.append([
                range_v_step * uRange,
                range_v_step * uRange + uN,
                range_v_step * uRange + uN + 1])

    return verts, faces


# Original Script "Parametric.py" by Ed Mackey.
# -> http://www.blinken.com/blender-plugins.php
# Partly converted for Blender 2.5 by tuga3d.
#
# Sphere:
# x = sin(2*pi*u)*sin(pi*v)
# y = cos(2*pi*u)*sin(pi*v)
# z = cos(pi*v)
# u_min = v_min = 0
# u_max = v_max = 1
#
# "Snail shell"
# x = 1.2**v*(sin(u)**2 *sin(v))
# y = 1.2**v*(sin(u)*cos(u))
# z = 1.2**v*(sin(u)**2 *cos(v))
# u_min = 0
# u_max = pi
# v_min = -pi/4,
# v max = 5*pi/2
class AddXYZFunctionSurface(bpy.types.Operator):
    """Add a surface defined defined by 3 functions:""" \
    """ x=F1(u,v), y=F2(u,v) and z=F3(u,v)"""
    bl_idname = "mesh.primitive_xyz_function_surface"
    bl_label = "Add X,Y,Z Function Surface"
    bl_options = {'REGISTER', 'UNDO', 'PRESET'}

    x_eq = StringProperty(name="X equation",
        description="Equation for x=F(u,v). " \
            "Also available: n, a, b, c, f, g, h",
        default="cos(v)*(1+cos(u))*sin(v/8)")

    y_eq = StringProperty(name="Y equation",
        description="Equation for y=F(u,v). " \
            "Also available: n, a, b, c, f, g, h",
        default="sin(u)*sin(v/8)+cos(v/8)*1.5")

    z_eq = StringProperty(name="Z equation",
        description="Equation for z=F(u,v). " \
            "Also available: n, a, b, c, f, g, h",
        default="sin(v)*(1+cos(u))*sin(v/8)")

    range_u_min = FloatProperty(name="U min",
        description="Minimum U value. Lower boundary of U range",
        min=-100.00,
        max=0.00,
        default=0.00)

    range_u_max = FloatProperty(name="U max",
        description="Maximum U value. Upper boundary of U range",
        min=0.00,
        max=100.00,
        default=2 * pi)

    range_u_step = IntProperty(name="U step",
        description="U Subdivisions",
        min=1,
        max=1024,
        default=32)

    wrap_u = BoolProperty(name="U wrap",
        description="U Wrap around",
        default=True)

    range_v_min = FloatProperty(name="V min",
        description="Minimum V value. Lower boundary of V range",
        min=-100.00,
        max=0.00,
        default=0.00)

    range_v_max = FloatProperty(name="V max",
        description="Maximum V value. Upper boundary of V range",
        min=0.00,
        max=100.00,
        default=4 * pi)

    range_v_step = IntProperty(name="V step",
        description="V Subdivisions",
        min=1,
        max=1024,
        default=128)

    wrap_v = BoolProperty(name="V wrap",
        description="V Wrap around",
        default=False)

    close_v = BoolProperty(name="Close V",
        description="Create faces for first and last " \
            "V values (only if U is wrapped)",
        default=False)

    n_eq = IntProperty(name="Number of objects (n=0..N-1)",
        description="The parameter n will be the index " \
            "of the current object, 0 to N-1",
        min=1,
        max=100,
        default=1)

    a_eq = StringProperty(name="A helper function",
        description="Equation for a=F(u,v). Also available: n",
        default="0")

    b_eq = StringProperty(name="B helper function",
        description="Equation for b=F(u,v). Also available: n",
        default="0")

    c_eq = StringProperty(name="C helper function",
        description="Equation for c=F(u,v). Also available: n",
        default="0")

    f_eq = StringProperty(name="F helper function",
        description="Equation for f=F(u,v). Also available: n, a, b, c",
        default="0")

    g_eq = StringProperty(name="G helper function",
        description="Equation for g=F(u,v). Also available: n, a, b, c",
        default="0")

    h_eq = StringProperty(name="H helper function",
        description="Equation for h=F(u,v). Also available: n, a, b, c",
        default="0")

    def execute(self, context):

        for n in range(0, self.n_eq):

            verts, faces = xyz_function_surface_faces(
                                self,
                                self.x_eq,
                                self.y_eq,
                                self.z_eq,
                                self.range_u_min,
                                self.range_u_max,
                                self.range_u_step,
                                self.wrap_u,
                                self.range_v_min,
                                self.range_v_max,
                                self.range_v_step,
                                self.wrap_v,
                                self.a_eq,
                                self.b_eq,
                                self.c_eq,
                                self.f_eq,
                                self.g_eq,
                                self.h_eq,
                                n,
                                self.close_v)

            if not verts:
                return {'CANCELLED'}

            obj = create_mesh_object(context, verts, [], faces, "XYZ Function")

        return {'FINISHED'}