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# ##### 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 #####
import bpy
from Mathutils import *
from math import *
from bpy.props import *
bl_addon_info = {
'name': 'Add Mesh: 3D Function Surfaces',
'author': 'Buerbaum Martin (Pontiac)',
'version': '0.3.1',
'blender': (2, 5, 3),
'location': 'View3D > Add > Mesh > Z Function Surface &' \
' XYZ Function Surface',
'description': 'Create Objects using Math Formulas',
'url': 'http://wiki.blender.org/index.php/Extensions:2.5/Py/' \
'Scripts/Add_Mesh/Add_3d_Function_Surface',
'category': 'Add Mesh'}
# More Links:
# http://gitorious.org/blender-scripts/blender-3d-function-surface
# http://blenderartists.org/forum/showthread.php?t=179043
__bpydoc__ = """
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 = f(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 = f(u,v)
y = f(u,v)
z = f(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:
v0.3.1 - 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_addon_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.
"""
# 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 in a
# property group (named like the operator) in the object.
# Always replaces any existing property group with the same name!
# @todo: Should we do this in EDIT Mode? Sounds dangerous.
def obj_store_recall_properties(ob, op, prop_list):
if ob and op and prop_list:
#print("Storing recall data for operator: " + op.bl_idname) # DEBUG
# Store new recall properties.
prop_list['recall_op'] = op.bl_idname
ob['recall'] = prop_list
# Apply view rotation to objects if "Align To" for new objects
# was set to "VIEW" in the User Preference.
def apply_view_rotation(context, ob):
align = bpy.context.user_preferences.edit.object_align
if (context.space_data.type == 'VIEW_3D'
and align == 'VIEW'):
view3d = context.space_data
region = view3d.region_3d
viewMatrix = region.view_matrix
rot = viewMatrix.rotation_part()
ob.rotation_euler = rot.invert().to_euler()
def createFaces(vertIdx1, vertIdx2, ring):
'''
A very simple "bridge" tool.
Connects two equally long vertex-loops with faces and
returns a list of the new faces.
Parameters
vertIdx1 ... List of vertex indices of the first loop.
vertIdx2 ... List of vertex indices of the second loop.
'''
faces = []
if (len(vertIdx1) != len(vertIdx2)) or (len(vertIdx1) < 2):
return None
total = len(vertIdx1)
if (ring):
# Bridge the start with the end.
faces.append([vertIdx2[0], vertIdx1[0],
vertIdx1[total - 1], vertIdx2[total - 1]])
# Bridge the rest of the faces.
for num in range(total - 1):
faces.append([vertIdx1[num], vertIdx2[num],
vertIdx2[num + 1], vertIdx1[num + 1]])
return faces
def createObject(context, verts, faces, name, edit):
'''Creates Meshes & Objects for the given lists of vertices and faces.'''
scene = context.scene
# Create new mesh
mesh = bpy.data.meshes.new(name)
# Add the geometry to the mesh.
#mesh.add_geometry(len(verts), 0, len(faces))
#mesh.verts.foreach_set("co", unpack_list(verts))
#mesh.faces.foreach_set("verts_raw", unpack_face_list(faces))
# To quote the documentation:
# "Make a mesh from a list of verts/edges/faces Until we have a nicer
# way to make geometry, use this."
# http://www.blender.org/documentation/250PythonDoc/
# bpy.types.Mesh.html#bpy.types.Mesh.from_pydata
mesh.from_pydata(verts, [], faces)
# Deselect all objects.
bpy.ops.object.select_all(action='DESELECT')
# Update mesh geometry after adding stuff.
mesh.update()
if edit:
# Recreate geometry of existing object
obj_act = context.active_object
ob_new = obj_act
bpy.ops.object.mode_set(mode='EDIT')
bpy.ops.mesh.select_all(action='SELECT')
bpy.ops.mesh.delete(type='VERT')
bpy.ops.object.mode_set(mode='OBJECT')
ob_new.data = mesh
ob_new.selected = True
else:
# Create new object
ob_new = bpy.data.objects.new(name, mesh)
# Link new object to the given scene and select it.
scene.objects.link(ob_new)
ob_new.selected = True
# Place the object at the 3D cursor location.
ob_new.location = scene.cursor_location
obj_act = scene.objects.active
apply_view_rotation(context, ob_new)
if obj_act and obj_act.mode == 'EDIT':
if not edit:
# We are in EditMode, switch to ObjectMode.
bpy.ops.object.mode_set(mode='OBJECT')
# Select the active object as well.
obj_act.selected = True
# Apply location of new object.
scene.update()
# Join new object into the active.
bpy.ops.object.join()
# Switching back to EditMode.
bpy.ops.object.mode_set(mode='EDIT')
else:
# We are in ObjectMode.
# Make the new object the active one.
scene.objects.active = ob_new
return ob_new
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'}
# edit - Whether to add or update.
edit = BoolProperty(name="",
description="",
default=False,
options={'HIDDEN'})
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):
edit = self.properties.edit
equation = self.properties.equation
div_x = self.properties.div_x
div_y = self.properties.div_y
size_x = self.properties.size_x
size_y = self.properties.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, False)
faces.extend(faces_row)
edgeloop_prev = edgeloop_cur
obj = createObject(context, verts, faces, "Z Function", edit)
# Store 'recall' properties in the object.
recall_prop_list = {
"edit": True,
"equation": equation,
"div_x": div_x,
"div_y": div_y,
"size_x": size_x,
"size_y": size_y}
obj_store_recall_properties(obj, self, recall_prop_list)
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):
verts = []
faces = []
uStep = (range_u_max - range_u_min) / range_u_step
vStep = (range_v_max - range_v_min) / range_v_step
uRange = range_u_step
if range_u_step == 0:
uRange = uRange + 1
vRange = range_v_step
if range_v_step == 0:
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)
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
# Try to evaluate the equation.
try:
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(1, range_v_step + 1):
vThis = vN
if (vThis >= vRange):
if wrap_v:
vThis = 0
else:
continue
for uN in range(1, range_u_step + 1):
uThis = uN
if (uThis >= uRange):
if wrap_u:
uThis = 0
else:
continue
faces.append([(vThis * uRange) + uThis,
(vThis * uRange) + uN - 1,
((vN - 1) * uRange) + uN - 1,
((vN - 1) * uRange) + uThis])
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=f(u,v), y=f(u,v) and z=f(u,v)'''
bl_idname = "mesh.primitive_xyz_function_surface"
bl_label = "Add X,Y,Z Function Surface"
bl_options = {'REGISTER', 'UNDO'}
# edit - Whether to add or update.
edit = BoolProperty(name="",
description="",
default=False,
options={'HIDDEN'})
x_eq = StringProperty(name="X Equation",
description="Equation for x=f(u,v)",
default="1.2**v*(sin(u)**2 *sin(v))")
y_eq = StringProperty(name="Y Equation",
description="Equation for y=f(u,v)",
default="1.2**v*(sin(u)*cos(u))")
z_eq = StringProperty(name="Z Equation",
description="Equation for z=f(u,v)",
default="1.2**v*(sin(u)**2 *cos(v))")
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=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=-pi / 4)
range_v_max = FloatProperty(name="V max",
description="Maximum V value. Upper boundary of V range.",
min=0.00,
max=100.00,
default=5 * pi / 2)
range_v_step = IntProperty(name="V step",
description="V Subdivisions",
min=1,
max=1024,
default=32)
wrap_v = BoolProperty(name="V wrap",
description="V Wrap around",
default=False)
def execute(self, context):
props = self.properties
verts, faces = xyz_function_surface_faces(
self,
props.x_eq,
props.y_eq,
props.z_eq,
props.range_u_min,
props.range_u_max,
props.range_u_step,
props.wrap_u,
props.range_v_min,
props.range_v_max,
props.range_v_step,
props.wrap_v)
if not verts:
return {'CANCELLED'}
obj = createObject(context, verts, faces, "XYZ Function", props.edit)
# Store 'recall' properties in the object.
recall_prop_list = {
"edit": True,
"x_eq": props.x_eq,
"y_eq": props.y_eq,
"z_eq": props.z_eq,
"range_u_min": props.range_u_min,
"range_u_max": props.range_u_max,
"range_u_step": props.range_u_step,
"wrap_u": props.wrap_u,
"range_v_min": props.range_v_min,
"range_v_max": props.range_v_max,
"range_v_step": props.range_v_step,
"wrap_v": props.wrap_v}
obj_store_recall_properties(obj, self, recall_prop_list)
return {'FINISHED'}
################################
import space_info
# Define "3D Function Surface" menu
menu_func_z = (lambda self, context: self.layout.operator(
AddZFunctionSurface.bl_idname,
text="Z Function Surface",
icon="PLUGIN"))
menu_func_xyz = (lambda self, context: self.layout.operator(
AddXYZFunctionSurface.bl_idname,
text="X,Y,Z Function Surface",
icon="PLUGIN"))
def register():
# Register the operators/menus.
bpy.types.register(AddZFunctionSurface)
bpy.types.register(AddXYZFunctionSurface)
# Add menus to the "Add Mesh" menu
space_info.INFO_MT_mesh_add.append(menu_func_z)
space_info.INFO_MT_mesh_add.append(menu_func_xyz)
def unregister():
# Unregister the operators/menus.
bpy.types.unregister(AddZFunctionSurface)
bpy.types.unregister(AddXYZFunctionSurface)
# Remove menus from the "Add Mesh" menu.
space_info.INFO_MT_mesh_add.remove(menu_func_z)
space_info.INFO_MT_mesh_add.remove(menu_func_xyz)
if __name__ == "__main__":
register()
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