add_mesh_extra_objects/add_mesh_3d_function_surface.py

   1 # GPL # original by Buerbaum Martin (Pontiac), Elod Csirmaz
   2
   3 import bpy
   4 from mathutils import *
   5 from math import *
   6 from bpy.types import Operator
   7 from bpy.props import (
   8         StringProperty,
   9         IntProperty,
  10         FloatProperty,
  11         BoolProperty,
  12         )
  13
  14
  15 # List of safe functions for eval()
  16 safe_list = ['math', 'acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh',
  17     'degrees', 'e', 'exp', 'fabs', 'floor', 'fmod', 'frexp', 'hypot',
  18     'ldexp', 'log', 'log10', 'modf', 'pi', 'pow', 'radians',
  19     'sin', 'sinh', 'sqrt', 'tan', 'tanh']
  20
  21 # Use the list to filter the local namespace
  22 safe_dict = dict((k, globals().get(k, None)) for k in safe_list)
  23
  24
  25 # Stores the values of a list of properties and the
  26 # operator id in a property group ('recall_op') inside the object
  27 # Could (in theory) be used for non-objects.
  28 # Note: Replaces any existing property group with the same name!
  29 # ob ... Object to store the properties in
  30 # op ... The operator that should be used
  31 # op_args ... A dictionary with valid Blender
  32 #             properties (operator arguments/parameters)
  33
  34
  35 # Create a new mesh (object) from verts/edges/faces
  36 # verts/edges/faces ... List of vertices/edges/faces for the
  37 #                       new mesh (as used in from_pydata)
  38 # name ... Name of the new mesh (& object)
  39
  40 def create_mesh_object(context, verts, edges, faces, name):
  41
  42     # Create new mesh
  43     mesh = bpy.data.meshes.new(name)
  44
  45     # Make a mesh from a list of verts/edges/faces
  46     mesh.from_pydata(verts, edges, faces)
  47
  48     # Update mesh geometry after adding stuff
  49     mesh.update()
  50
  51     from bpy_extras import object_utils
  52     return object_utils.object_data_add(context, mesh, operator=None)
  53
  54
  55 # A very simple "bridge" tool
  56
  57 def createFaces(vertIdx1, vertIdx2, closed=False, flipped=False):
  58     faces = []
  59
  60     if not vertIdx1 or not vertIdx2:
  61         return None
  62
  63     if len(vertIdx1) < 2 and len(vertIdx2) < 2:
  64         return None
  65
  66     fan = False
  67     if (len(vertIdx1) != len(vertIdx2)):
  68         if (len(vertIdx1) == 1 and len(vertIdx2) > 1):
  69             fan = True
  70         else:
  71             return None
  72
  73     total = len(vertIdx2)
  74
  75     if closed:
  76         # Bridge the start with the end
  77         if flipped:
  78             face = [
  79                 vertIdx1[0],
  80                 vertIdx2[0],
  81                 vertIdx2[total - 1]]
  82             if not fan:
  83                 face.append(vertIdx1[total - 1])
  84             faces.append(face)
  85
  86         else:
  87             face = [vertIdx2[0], vertIdx1[0]]
  88             if not fan:
  89                 face.append(vertIdx1[total - 1])
  90             face.append(vertIdx2[total - 1])
  91             faces.append(face)
  92
  93     # Bridge the rest of the faces
  94     for num in range(total - 1):
  95         if flipped:
  96             if fan:
  97                 face = [vertIdx2[num], vertIdx1[0], vertIdx2[num + 1]]
  98             else:
  99                 face = [vertIdx2[num], vertIdx1[num],
 100                     vertIdx1[num + 1], vertIdx2[num + 1]]
 101             faces.append(face)
 102         else:
 103             if fan:
 104                 face = [vertIdx1[0], vertIdx2[num], vertIdx2[num + 1]]
 105             else:
 106                 face = [vertIdx1[num], vertIdx2[num],
 107                     vertIdx2[num + 1], vertIdx1[num + 1]]
 108             faces.append(face)
 109
 110     return faces
 111
 112
 113 class AddZFunctionSurface(Operator):
 114     bl_idname = "mesh.primitive_z_function_surface"
 115     bl_label = "Add Z Function Surface"
 116     bl_description = "Add a surface defined defined by a function z=f(x,y)"
 117     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 118
 119     equation: StringProperty(
 120                 name="Z Equation",
 121                 description="Equation for z=f(x,y)",
 122                 default="1 - ( x**2 + y**2 )"
 123                 )
 124     div_x: IntProperty(
 125                 name="X Subdivisions",
 126                 description="Number of vertices in x direction",
 127                 default=16,
 128                 min=3,
 129                 max=256
 130                 )
 131     div_y: IntProperty(
 132                 name="Y Subdivisions",
 133                 description="Number of vertices in y direction",
 134                 default=16,
 135                 min=3,
 136                 max=256
 137                 )
 138     size_x: FloatProperty(
 139                 name="X Size",
 140                 description="Size of the x axis",
 141                 default=2.0,
 142                 min=0.01,
 143                 max=100.0,
 144                 unit="LENGTH"
 145                 )
 146     size_y: FloatProperty(
 147                 name="Y Size",
 148                 description="Size of the y axis",
 149                 default=2.0,
 150                 min=0.01,
 151                 max=100.0,
 152                 unit="LENGTH"
 153                 )
 154
 155     def execute(self, context):
 156         equation = self.equation
 157         div_x = self.div_x
 158         div_y = self.div_y
 159         size_x = self.size_x
 160         size_y = self.size_y
 161
 162         verts = []
 163         faces = []
 164
 165         delta_x = size_x / (div_x - 1)
 166         delta_y = size_y / (div_y - 1)
 167         start_x = -(size_x / 2.0)
 168         start_y = -(size_y / 2.0)
 169
 170         edgeloop_prev = []
 171
 172         if equation:
 173             try:
 174                 expr_args = (
 175                     compile(equation, __file__, 'eval'),
 176                     {"__builtins__": None},
 177                     safe_dict)
 178             except:
 179                 import traceback
 180                 # WARNING is used to prevent the constant pop-up spam
 181                 self.report({'WARNING'},
 182                             "Error parsing expression: {} "
 183                             "(Check the console for more info)".format(equation))
 184                 print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 185
 186                 return {'CANCELLED'}
 187
 188             for row_x in range(div_x):
 189                 edgeloop_cur = []
 190                 x = start_x + row_x * delta_x
 191
 192                 for row_y in range(div_y):
 193                     y = start_y + row_y * delta_y
 194                     z = 0.0
 195
 196                     safe_dict['x'] = x
 197                     safe_dict['y'] = y
 198
 199                     # Try to evaluate the equation.
 200                     try:
 201                         z = float(eval(*expr_args))
 202                     except:
 203                         import traceback
 204                         self.report({'WARNING'},
 205                                     "Error evaluating expression: {} "
 206                                     "(Check the console for more info)".format(equation))
 207                         print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 208
 209                         return {'CANCELLED'}
 210
 211                     edgeloop_cur.append(len(verts))
 212                     verts.append((x, y, z))
 213
 214                 if len(edgeloop_prev) > 0:
 215                     faces_row = createFaces(edgeloop_prev, edgeloop_cur)
 216                     faces.extend(faces_row)
 217
 218                 edgeloop_prev = edgeloop_cur
 219
 220             base = create_mesh_object(context, verts, [], faces, "Z Function")
 221         else:
 222             self.report({'WARNING'}, "Z Equation - No expression is given")
 223
 224             return {'CANCELLED'}
 225
 226         return {'FINISHED'}
 227
 228
 229 def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
 230             range_u_min, range_u_max, range_u_step, wrap_u,
 231             range_v_min, range_v_max, range_v_step, wrap_v,
 232             a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v):
 233
 234     verts = []
 235     faces = []
 236
 237     # Distance of each step in Blender Units
 238     uStep = (range_u_max - range_u_min) / range_u_step
 239     vStep = (range_v_max - range_v_min) / range_v_step
 240
 241     # Number of steps in the vertex creation loops.
 242     # Number of steps is the number of faces
 243     #   => Number of points is +1 unless wrapped.
 244     uRange = range_u_step + 1
 245     vRange = range_v_step + 1
 246
 247     if wrap_u:
 248         uRange = uRange - 1
 249
 250     if wrap_v:
 251         vRange = vRange - 1
 252
 253     try:
 254         expr_args_x = (
 255             compile(x_eq, __file__.replace(".py", "_x.py"), 'eval'),
 256             {"__builtins__": None},
 257             safe_dict)
 258         expr_args_y = (
 259             compile(y_eq, __file__.replace(".py", "_y.py"), 'eval'),
 260             {"__builtins__": None},
 261             safe_dict)
 262         expr_args_z = (
 263             compile(z_eq, __file__.replace(".py", "_z.py"), 'eval'),
 264             {"__builtins__": None},
 265             safe_dict)
 266         expr_args_a = (
 267             compile(a_eq, __file__.replace(".py", "_a.py"), 'eval'),
 268             {"__builtins__": None},
 269             safe_dict)
 270         expr_args_b = (
 271             compile(b_eq, __file__.replace(".py", "_b.py"), 'eval'),
 272             {"__builtins__": None},
 273             safe_dict)
 274         expr_args_c = (
 275             compile(c_eq, __file__.replace(".py", "_c.py"), 'eval'),
 276             {"__builtins__": None},
 277             safe_dict)
 278         expr_args_f = (
 279             compile(f_eq, __file__.replace(".py", "_f.py"), 'eval'),
 280             {"__builtins__": None},
 281             safe_dict)
 282         expr_args_g = (
 283             compile(g_eq, __file__.replace(".py", "_g.py"), 'eval'),
 284             {"__builtins__": None},
 285             safe_dict)
 286         expr_args_h = (
 287             compile(h_eq, __file__.replace(".py", "_h.py"), 'eval'),
 288             {"__builtins__": None},
 289             safe_dict)
 290     except:
 291         import traceback
 292         self.report({'WARNING'}, "Error parsing expression(s) - "
 293                     "Check the console for more info")
 294         print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 295         return [], []
 296
 297     for vN in range(vRange):
 298         v = range_v_min + (vN * vStep)
 299
 300         for uN in range(uRange):
 301             u = range_u_min + (uN * uStep)
 302
 303             safe_dict['u'] = u
 304             safe_dict['v'] = v
 305
 306             safe_dict['n'] = n
 307
 308             # Try to evaluate the equations.
 309             try:
 310                 safe_dict['a'] = float(eval(*expr_args_a))
 311                 safe_dict['b'] = float(eval(*expr_args_b))
 312                 safe_dict['c'] = float(eval(*expr_args_c))
 313                 safe_dict['f'] = float(eval(*expr_args_f))
 314                 safe_dict['g'] = float(eval(*expr_args_g))
 315                 safe_dict['h'] = float(eval(*expr_args_h))
 316
 317                 verts.append((
 318                     float(eval(*expr_args_x)),
 319                     float(eval(*expr_args_y)),
 320                     float(eval(*expr_args_z))))
 321             except:
 322                 import traceback
 323                 self.report({'WARNING'}, "Error evaluating expression(s) - "
 324                              "Check the console for more info")
 325                 print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 326                 return [], []
 327
 328     for vN in range(range_v_step):
 329         vNext = vN + 1
 330
 331         if wrap_v and (vNext >= vRange):
 332             vNext = 0
 333
 334         for uN in range(range_u_step):
 335             uNext = uN + 1
 336
 337             if wrap_u and (uNext >= uRange):
 338                 uNext = 0
 339
 340             faces.append([(vNext * uRange) + uNext,
 341                 (vNext * uRange) + uN,
 342                 (vN * uRange) + uN,
 343                 (vN * uRange) + uNext])
 344
 345     if close_v and wrap_u and (not wrap_v):
 346         for uN in range(1, range_u_step - 1):
 347             faces.append([
 348                 range_u_step - 1,
 349                 range_u_step - 1 - uN,
 350                 range_u_step - 2 - uN])
 351             faces.append([
 352                 range_v_step * uRange,
 353                 range_v_step * uRange + uN,
 354                 range_v_step * uRange + uN + 1])
 355
 356     return verts, faces
 357
 358
 359 # Original Script "Parametric.py" by Ed Mackey.
 360 # -> http://www.blinken.com/blender-plugins.php
 361 # Partly converted for Blender 2.5 by tuga3d.
 362 #
 363 # Sphere:
 364 # x = sin(2*pi*u)*sin(pi*v)
 365 # y = cos(2*pi*u)*sin(pi*v)
 366 # z = cos(pi*v)
 367 # u_min = v_min = 0
 368 # u_max = v_max = 1
 369 #
 370 # "Snail shell"
 371 # x = 1.2**v*(sin(u)**2 *sin(v))
 372 # y = 1.2**v*(sin(u)*cos(u))
 373 # z = 1.2**v*(sin(u)**2 *cos(v))
 374 # u_min = 0
 375 # u_max = pi
 376 # v_min = -pi/4,
 377 # v max = 5*pi/2
 378
 379 class AddXYZFunctionSurface(Operator):
 380     bl_idname = "mesh.primitive_xyz_function_surface"
 381     bl_label = "Add X, Y, Z Function Surface"
 382     bl_description = ("Add a surface defined defined by 3 functions:\n"
 383                       "x=F1(u,v), y=F2(u,v) and z=F3(u,v)")
 384     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 385
 386     x_eq: StringProperty(
 387                 name="X equation",
 388                 description="Equation for x=F(u,v). "
 389                             "Also available: n, a, b, c, f, g, h",
 390                 default="cos(v)*(1+cos(u))*sin(v/8)"
 391                 )
 392     y_eq: StringProperty(
 393                 name="Y equation",
 394                 description="Equation for y=F(u,v). "
 395                             "Also available: n, a, b, c, f, g, h",
 396                 default="sin(u)*sin(v/8)+cos(v/8)*1.5"
 397                 )
 398     z_eq: StringProperty(
 399                 name="Z equation",
 400                 description="Equation for z=F(u,v). "
 401                             "Also available: n, a, b, c, f, g, h",
 402                 default="sin(v)*(1+cos(u))*sin(v/8)"
 403                 )
 404     range_u_min: FloatProperty(
 405                 name="U min",
 406                 description="Minimum U value. Lower boundary of U range",
 407                 min=-100.00,
 408                 max=0.00,
 409                 default=0.00
 410                 )
 411     range_u_max: FloatProperty(
 412                 name="U max",
 413                 description="Maximum U value. Upper boundary of U range",
 414                 min=0.00,
 415                 max=100.00,
 416                 default=2 * pi
 417                 )
 418     range_u_step: IntProperty(
 419                 name="U step",
 420                 description="U Subdivisions",
 421                 min=1,
 422                 max=1024,
 423                 default=32
 424                 )
 425     wrap_u: BoolProperty(
 426                 name="U wrap",
 427                 description="U Wrap around",
 428                 default=True
 429                 )
 430     range_v_min: FloatProperty(
 431                 name="V min",
 432                 description="Minimum V value. Lower boundary of V range",
 433                 min=-100.00,
 434                 max=0.00,
 435                 default=0.00
 436                 )
 437     range_v_max: FloatProperty(
 438                 name="V max",
 439                 description="Maximum V value. Upper boundary of V range",
 440                 min=0.00,
 441                 max=100.00,
 442                 default=4 * pi
 443                 )
 444     range_v_step: IntProperty(
 445                 name="V step",
 446                 description="V Subdivisions",
 447                 min=1,
 448                 max=1024,
 449                 default=128
 450                 )
 451     wrap_v: BoolProperty(
 452                 name="V wrap",
 453                 description="V Wrap around",
 454                 default=False
 455                 )
 456     close_v: BoolProperty(
 457                 name="Close V",
 458                 description="Create faces for first and last "
 459                             "V values (only if U is wrapped)",
 460                 default=False
 461                 )
 462     n_eq: IntProperty(
 463                 name="Number of objects (n=0..N-1)",
 464                 description="The parameter n will be the index "
 465                             "of the current object, 0 to N-1",
 466                 min=1,
 467                 max=100,
 468                 default=1
 469                 )
 470     a_eq: StringProperty(
 471                 name="A helper function",
 472                 description="Equation for a=F(u,v). Also available: n",
 473                 default="0"
 474                 )
 475     b_eq: StringProperty(
 476                 name="B helper function",
 477                 description="Equation for b=F(u,v). Also available: n",
 478                 default="0"
 479                 )
 480     c_eq: StringProperty(
 481                 name="C helper function",
 482                 description="Equation for c=F(u,v). Also available: n",
 483                 default="0"
 484                 )
 485     f_eq: StringProperty(
 486                 name="F helper function",
 487                 description="Equation for f=F(u,v). Also available: n, a, b, c",
 488                 default="0"
 489                 )
 490     g_eq: StringProperty(
 491                 name="G helper function",
 492                 description="Equation for g=F(u,v). Also available: n, a, b, c",
 493                 default="0"
 494                 )
 495     h_eq: StringProperty(
 496                 name="H helper function",
 497                 description="Equation for h=F(u,v). Also available: n, a, b, c",
 498                 default="0"
 499                 )
 500     show_wire : BoolProperty(
 501             name="Show wireframe",
 502             default=True,
 503             description="Add the object’s wireframe over solid drawing"
 504             )
 505     edit_mode : BoolProperty(
 506             name="Show in edit mode",
 507             default=True,
 508             description="Show in edit mode"
 509             )
 510
 511     def execute(self, context):
 512         for n in range(0, self.n_eq):
 513             verts, faces = xyz_function_surface_faces(
 514                                 self,
 515                                 self.x_eq,
 516                                 self.y_eq,
 517                                 self.z_eq,
 518                                 self.range_u_min,
 519                                 self.range_u_max,
 520                                 self.range_u_step,
 521                                 self.wrap_u,
 522                                 self.range_v_min,
 523                                 self.range_v_max,
 524                                 self.range_v_step,
 525                                 self.wrap_v,
 526                                 self.a_eq,
 527                                 self.b_eq,
 528                                 self.c_eq,
 529                                 self.f_eq,
 530                                 self.g_eq,
 531                                 self.h_eq,
 532                                 n,
 533                                 self.close_v
 534                                 )
 535             if not verts:
 536                 return {'CANCELLED'}
 537
 538             obj = create_mesh_object(context, verts, [], faces, "XYZ Function")
 539
 540             if self.show_wire:
 541                 obj.show_wire = True
 542
 543         if self.edit_mode:
 544             bpy.ops.object.mode_set(mode = 'EDIT')
 545         else:
 546             bpy.ops.object.mode_set(mode = 'OBJECT')
 547
 548         return {'FINISHED'}