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Bastien Montagne authoredBastien Montagne authored
add_mesh_3d_function_surface.py 16.54 KiB
# ##### 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'}