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),
    "api": 37329,
    "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"}
"""
"""
Z Function Surface

This script lets the user create a surface where the z coordinate
is a function of the x and y coordinates.

    z = F1(x,y)

X,Y,Z Function Surface

This script lets the user create a surface where the x, y and z
coordinates are defiend by a function.

    x = F1(u,v)
    y = F2(u,v)
    z = F3(u,v)

Usage:
You have to activated the script in the "Add-Ons" tab (user preferences).
The functionality can then be accessed via the
"Add Mesh" -> "Z Function Surface"
and
"Add Mesh" -> "X,Y,Z Function Surface"
menu.

Version history:
v0.3.8 - Patch by Elod Csirmaz
    Modified the "Add X,Y,Z Function Surface" part:
    Changed how wrapping is done to avoid
    generating unnecessary vertices and make the result more intuitive.
    Added helper functions the results of which can be used in
    x(u,v), y(u,v), z(u,v).
    The script can now close the ends of an U-wrapped surface.
    It's now possible to create multiple objects with one set of formulae.
v0.3.7
    Removed the various "edit" properties - not used anymore.
    Use generic tracker URL (Blender-Extensions r1369)
    bl_addon_info now called bl_info
    Removed align_matrix
    create_mesh_object now doesn't handle editmode. (See create_mesh_object)
    This script is now used by the "Extra Objects" script
v0.3.6 - Various updates to match current Blender API.
    Removed recall functionality.
    Better code for align_matrix
    Hopefully fixed bug where uMax was never reached. May cause other stuff.
v0.3.5 - createFaces can now "Flip" faces and create fan/star like faces.
v0.3.4 - Updated store_recall_properties, apply_object_align
    and create_mesh_object.
    Changed how recall data is stored.
v0.3.3 - API change Mathutils -> mathutils (r557)
v0.3.2 - Various fixes&streamlining by ideasman42/Campbell Barton.
    r544 Compile expressions for faster execution
    r544 Use operator reports for errors too
    r544 Avoid type checks by converting to a float, errors
    converting to a float are reported too.
    Fixed an error Campbell overlooked (appending tuples to an
    array, not single values) Thamnks for the report wild_doogy.
    Added 'description' field, updated 'wiki_url'.
    Made the script PEP8 compatible again.
v0.3.1 - Use hidden "edit" property for "recall" operator.
    Bugfix: Z Function was mixing up div_x and div_y
v0.3 - X,Y,Z Function Surface (by Ed Mackey & tuga3d).
    Renamed old function to "Z Function Surface".
    Align the geometry to the view if the user preference says so.
    Store recall properties in newly created object.
v0.2.3 - Use bl_info for Add-On information.
v0.2.2 - Fixed Add-On registration text.
v0.2.1 - Fixed some new API stuff.
    Mainly we now have the register/unregister functions.
    Also the new() function for objects now accepts a mesh object.
    Changed the script so it can be managed from the "Add-Ons" tab
    in the user preferences.
    Added dummy "PLUGIN" icon.
    Corrected FSF address.
    Clean up of tooltips.
v0.2 - Added security check for eval() function
    Check return value of eval() for complex numbers.
v0.1.1 - Use 'CANCELLED' return value when failing.
    Updated web links.
v0.1 - Initial revision.
More Links:
http://gitorious.org/blender-scripts/blender-3d-function-surface
http://blenderartists.org/forum/showthread.php?t=179043
"""
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'}

    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'}

    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'}