add_mesh_extra_objects/add_mesh_3d_function_surface.py

   1 # SPDX-License-Identifier: GPL-2.0-or-later
   2
   3 # Original by Buerbaum Martin (Pontiac), Elod Csirmaz
   4
   5 import bpy
   6 import math
   7 import numpy
   8 from mathutils import *
   9 from math import *
  10 from bpy.types import Operator
  11 from bpy.props import (
  12         StringProperty,
  13         IntProperty,
  14         FloatProperty,
  15         BoolProperty,
  16         )
  17
  18
  19 # List of safe functions for eval()
  20 safe_list = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh',
  21     'degrees', 'e', 'exp', 'fabs', 'floor', 'fmod', 'frexp', 'hypot',
  22     'ldexp', 'log', 'log10', 'modf', 'pi', 'pow', 'radians',
  23     'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'gcd']
  24
  25 # Use the list to filter the local namespace
  26 safe_dict = dict((k, globals().get(k, None)) for k in safe_list)
  27 safe_dict['math'] = math
  28 safe_dict['numpy'] = safe_dict['np'] = numpy
  29 safe_dict['lcm'] = numpy.lcm
  30 safe_dict['max'] = max
  31 safe_dict['min'] = min
  32
  33
  34 # Stores the values of a list of properties and the
  35 # operator id in a property group ('recall_op') inside the object
  36 # Could (in theory) be used for non-objects.
  37 # Note: Replaces any existing property group with the same name!
  38 # ob ... Object to store the properties in
  39 # op ... The operator that should be used
  40 # op_args ... A dictionary with valid Blender
  41 #             properties (operator arguments/parameters)
  42
  43
  44 # Create a new mesh (object) from verts/edges/faces
  45 # verts/edges/faces ... List of vertices/edges/faces for the
  46 #                       new mesh (as used in from_pydata)
  47 # name ... Name of the new mesh (& object)
  48
  49 def create_mesh_object(context, verts, edges, faces, name):
  50
  51     # Create new mesh
  52     mesh = bpy.data.meshes.new(name)
  53
  54     # Make a mesh from a list of verts/edges/faces
  55     mesh.from_pydata(verts, edges, faces)
  56
  57     # Update mesh geometry after adding stuff
  58     mesh.update()
  59
  60     from bpy_extras import object_utils
  61     return object_utils.object_data_add(context, mesh, operator=None)
  62
  63
  64 # A very simple "bridge" tool
  65
  66 def createFaces(vertIdx1, vertIdx2, closed=False, flipped=False):
  67     faces = []
  68
  69     if not vertIdx1 or not vertIdx2:
  70         return None
  71
  72     if len(vertIdx1) < 2 and len(vertIdx2) < 2:
  73         return None
  74
  75     fan = False
  76     if (len(vertIdx1) != len(vertIdx2)):
  77         if (len(vertIdx1) == 1 and len(vertIdx2) > 1):
  78             fan = True
  79         else:
  80             return None
  81
  82     total = len(vertIdx2)
  83
  84     if closed:
  85         # Bridge the start with the end
  86         if flipped:
  87             face = [
  88                 vertIdx1[0],
  89                 vertIdx2[0],
  90                 vertIdx2[total - 1]]
  91             if not fan:
  92                 face.append(vertIdx1[total - 1])
  93             faces.append(face)
  94
  95         else:
  96             face = [vertIdx2[0], vertIdx1[0]]
  97             if not fan:
  98                 face.append(vertIdx1[total - 1])
  99             face.append(vertIdx2[total - 1])
 100             faces.append(face)
 101
 102     # Bridge the rest of the faces
 103     for num in range(total - 1):
 104         if flipped:
 105             if fan:
 106                 face = [vertIdx2[num], vertIdx1[0], vertIdx2[num + 1]]
 107             else:
 108                 face = [vertIdx2[num], vertIdx1[num],
 109                     vertIdx1[num + 1], vertIdx2[num + 1]]
 110             faces.append(face)
 111         else:
 112             if fan:
 113                 face = [vertIdx1[0], vertIdx2[num], vertIdx2[num + 1]]
 114             else:
 115                 face = [vertIdx1[num], vertIdx2[num],
 116                     vertIdx2[num + 1], vertIdx1[num + 1]]
 117             faces.append(face)
 118
 119     return faces
 120
 121
 122 class AddZFunctionSurface(Operator):
 123     bl_idname = "mesh.primitive_z_function_surface"
 124     bl_label = "Add Z Function Surface"
 125     bl_description = "Add a surface defined defined by a function z=f(x,y)"
 126     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 127
 128     equation: StringProperty(
 129                 name="Z Equation",
 130                 description="Equation for z=f(x,y)",
 131                 default="1 - ( x**2 + y**2 )"
 132                 )
 133     div_x: IntProperty(
 134                 name="X Subdivisions",
 135                 description="Number of vertices in x direction",
 136                 default=16,
 137                 min=3,
 138                 max=256
 139                 )
 140     div_y: IntProperty(
 141                 name="Y Subdivisions",
 142                 description="Number of vertices in y direction",
 143                 default=16,
 144                 min=3,
 145                 max=256
 146                 )
 147     size_x: FloatProperty(
 148                 name="X Size",
 149                 description="Size of the x axis",
 150                 default=2.0,
 151                 min=0.01,
 152                 max=100.0,
 153                 unit="LENGTH"
 154                 )
 155     size_y: FloatProperty(
 156                 name="Y Size",
 157                 description="Size of the y axis",
 158                 default=2.0,
 159                 min=0.01,
 160                 max=100.0,
 161                 unit="LENGTH"
 162                 )
 163
 164     def execute(self, context):
 165         equation = self.equation
 166         div_x = self.div_x
 167         div_y = self.div_y
 168         size_x = self.size_x
 169         size_y = self.size_y
 170
 171         verts = []
 172         faces = []
 173
 174         delta_x = size_x / (div_x - 1)
 175         delta_y = size_y / (div_y - 1)
 176         start_x = -(size_x / 2.0)
 177         start_y = -(size_y / 2.0)
 178
 179         edgeloop_prev = []
 180
 181         if equation:
 182             try:
 183                 expr_args = (
 184                     compile(equation, __file__, 'eval'),
 185                     {"__builtins__": None},
 186                     safe_dict)
 187             except:
 188                 import traceback
 189                 # WARNING is used to prevent the constant pop-up spam
 190                 self.report({'WARNING'},
 191                             "Error parsing expression: {} "
 192                             "(Check the console for more info)".format(equation))
 193                 print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 194
 195                 return {'CANCELLED'}
 196
 197             for row_x in range(div_x):
 198                 edgeloop_cur = []
 199                 x = start_x + row_x * delta_x
 200
 201                 for row_y in range(div_y):
 202                     y = start_y + row_y * delta_y
 203                     z = 0.0
 204
 205                     safe_dict['x'] = x
 206                     safe_dict['y'] = y
 207
 208                     # Try to evaluate the equation.
 209                     try:
 210                         z = float(eval(*expr_args))
 211                     except:
 212                         import traceback
 213                         self.report({'WARNING'},
 214                                     "Error evaluating expression: {} "
 215                                     "(Check the console for more info)".format(equation))
 216                         print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 217
 218                         return {'CANCELLED'}
 219
 220                     edgeloop_cur.append(len(verts))
 221                     verts.append((x, y, z))
 222
 223                 if len(edgeloop_prev) > 0:
 224                     faces_row = createFaces(edgeloop_prev, edgeloop_cur)
 225                     faces.extend(faces_row)
 226
 227                 edgeloop_prev = edgeloop_cur
 228
 229             base = create_mesh_object(context, verts, [], faces, "Z Function")
 230         else:
 231             self.report({'WARNING'}, "Z Equation - No expression is given")
 232
 233             return {'CANCELLED'}
 234
 235         return {'FINISHED'}
 236
 237
 238 def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
 239             range_u_min, range_u_max, range_u_step, wrap_u,
 240             range_v_min, range_v_max, range_v_step, wrap_v,
 241             a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v):
 242
 243     verts = []
 244     faces = []
 245
 246     # Distance of each step in Blender Units
 247     uStep = (range_u_max - range_u_min) / range_u_step
 248     vStep = (range_v_max - range_v_min) / range_v_step
 249
 250     # Number of steps in the vertex creation loops.
 251     # Number of steps is the number of faces
 252     #   => Number of points is +1 unless wrapped.
 253     uRange = range_u_step + 1
 254     vRange = range_v_step + 1
 255
 256     if wrap_u:
 257         uRange = uRange - 1
 258
 259     if wrap_v:
 260         vRange = vRange - 1
 261
 262     try:
 263         expr_args_x = (
 264             compile(x_eq, __file__.replace(".py", "_x.py"), 'eval'),
 265             {"__builtins__": None},
 266             safe_dict)
 267         expr_args_y = (
 268             compile(y_eq, __file__.replace(".py", "_y.py"), 'eval'),
 269             {"__builtins__": None},
 270             safe_dict)
 271         expr_args_z = (
 272             compile(z_eq, __file__.replace(".py", "_z.py"), 'eval'),
 273             {"__builtins__": None},
 274             safe_dict)
 275         expr_args_a = (
 276             compile(a_eq, __file__.replace(".py", "_a.py"), 'eval'),
 277             {"__builtins__": None},
 278             safe_dict)
 279         expr_args_b = (
 280             compile(b_eq, __file__.replace(".py", "_b.py"), 'eval'),
 281             {"__builtins__": None},
 282             safe_dict)
 283         expr_args_c = (
 284             compile(c_eq, __file__.replace(".py", "_c.py"), 'eval'),
 285             {"__builtins__": None},
 286             safe_dict)
 287         expr_args_f = (
 288             compile(f_eq, __file__.replace(".py", "_f.py"), 'eval'),
 289             {"__builtins__": None},
 290             safe_dict)
 291         expr_args_g = (
 292             compile(g_eq, __file__.replace(".py", "_g.py"), 'eval'),
 293             {"__builtins__": None},
 294             safe_dict)
 295         expr_args_h = (
 296             compile(h_eq, __file__.replace(".py", "_h.py"), 'eval'),
 297             {"__builtins__": None},
 298             safe_dict)
 299     except:
 300         import traceback
 301         self.report({'WARNING'}, "Error parsing expression(s) - "
 302                     "Check the console for more info")
 303         print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 304         return [], []
 305
 306     for vN in range(vRange):
 307         v = range_v_min + (vN * vStep)
 308
 309         for uN in range(uRange):
 310             u = range_u_min + (uN * uStep)
 311
 312             safe_dict['u'] = u
 313             safe_dict['v'] = v
 314
 315             safe_dict['n'] = n
 316
 317             # Try to evaluate the equations.
 318             try:
 319                 safe_dict['a'] = float(eval(*expr_args_a))
 320                 safe_dict['b'] = float(eval(*expr_args_b))
 321                 safe_dict['c'] = float(eval(*expr_args_c))
 322                 safe_dict['f'] = float(eval(*expr_args_f))
 323                 safe_dict['g'] = float(eval(*expr_args_g))
 324                 safe_dict['h'] = float(eval(*expr_args_h))
 325
 326                 verts.append((
 327                     float(eval(*expr_args_x)),
 328                     float(eval(*expr_args_y)),
 329                     float(eval(*expr_args_z))))
 330             except:
 331                 import traceback
 332                 self.report({'WARNING'}, "Error evaluating expression(s) - "
 333                              "Check the console for more info")
 334                 print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 335                 return [], []
 336
 337     for vN in range(range_v_step):
 338         vNext = vN + 1
 339
 340         if wrap_v and (vNext >= vRange):
 341             vNext = 0
 342
 343         for uN in range(range_u_step):
 344             uNext = uN + 1
 345
 346             if wrap_u and (uNext >= uRange):
 347                 uNext = 0
 348
 349             faces.append([(vNext * uRange) + uNext,
 350                 (vNext * uRange) + uN,
 351                 (vN * uRange) + uN,
 352                 (vN * uRange) + uNext])
 353
 354     if close_v and wrap_u and (not wrap_v):
 355         for uN in range(1, range_u_step - 1):
 356             faces.append([
 357                 range_u_step - 1,
 358                 range_u_step - 1 - uN,
 359                 range_u_step - 2 - uN])
 360             faces.append([
 361                 range_v_step * uRange,
 362                 range_v_step * uRange + uN,
 363                 range_v_step * uRange + uN + 1])
 364
 365     return verts, faces
 366
 367
 368 # Original Script "Parametric.py" by Ed Mackey.
 369 # -> http://www.blinken.com/blender-plugins.php
 370 # Partly converted for Blender 2.5 by tuga3d.
 371 #
 372 # Sphere:
 373 # x = sin(2*pi*u)*sin(pi*v)
 374 # y = cos(2*pi*u)*sin(pi*v)
 375 # z = cos(pi*v)
 376 # u_min = v_min = 0
 377 # u_max = v_max = 1
 378 #
 379 # "Snail shell"
 380 # x = 1.2**v*(sin(u)**2 *sin(v))
 381 # y = 1.2**v*(sin(u)*cos(u))
 382 # z = 1.2**v*(sin(u)**2 *cos(v))
 383 # u_min = 0
 384 # u_max = pi
 385 # v_min = -pi/4,
 386 # v max = 5*pi/2
 387
 388 class AddXYZFunctionSurface(Operator):
 389     bl_idname = "mesh.primitive_xyz_function_surface"
 390     bl_label = "Add X, Y, Z Function Surface"
 391     bl_description = ("Add a surface defined defined by 3 functions:\n"
 392                       "x=F1(u,v), y=F2(u,v) and z=F3(u,v)")
 393     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 394
 395     x_eq: StringProperty(
 396                 name="X equation",
 397                 description="Equation for x=F(u,v). "
 398                             "Also available: n, a, b, c, f, g, h",
 399                 default="cos(v)*(1+cos(u))*sin(v/8)"
 400                 )
 401     y_eq: StringProperty(
 402                 name="Y equation",
 403                 description="Equation for y=F(u,v). "
 404                             "Also available: n, a, b, c, f, g, h",
 405                 default="sin(u)*sin(v/8)+cos(v/8)*1.5"
 406                 )
 407     z_eq: StringProperty(
 408                 name="Z equation",
 409                 description="Equation for z=F(u,v). "
 410                             "Also available: n, a, b, c, f, g, h",
 411                 default="sin(v)*(1+cos(u))*sin(v/8)"
 412                 )
 413     range_u_min: FloatProperty(
 414                 name="U min",
 415                 description="Minimum U value. Lower boundary of U range",
 416                 min=-100.00,
 417                 max=0.00,
 418                 default=0.00
 419                 )
 420     range_u_max: FloatProperty(
 421                 name="U max",
 422                 description="Maximum U value. Upper boundary of U range",
 423                 min=0.00,
 424                 max=100.00,
 425                 default=2 * pi
 426                 )
 427     range_u_step: IntProperty(
 428                 name="U step",
 429                 description="U Subdivisions",
 430                 min=1,
 431                 max=1024,
 432                 default=32
 433                 )
 434     wrap_u: BoolProperty(
 435                 name="U wrap",
 436                 description="U Wrap around",
 437                 default=True
 438                 )
 439     range_v_min: FloatProperty(
 440                 name="V min",
 441                 description="Minimum V value. Lower boundary of V range",
 442                 min=-100.00,
 443                 max=0.00,
 444                 default=0.00
 445                 )
 446     range_v_max: FloatProperty(
 447                 name="V max",
 448                 description="Maximum V value. Upper boundary of V range",
 449                 min=0.00,
 450                 max=100.00,
 451                 default=4 * pi
 452                 )
 453     range_v_step: IntProperty(
 454                 name="V step",
 455                 description="V Subdivisions",
 456                 min=1,
 457                 max=1024,
 458                 default=128
 459                 )
 460     wrap_v: BoolProperty(
 461                 name="V wrap",
 462                 description="V Wrap around",
 463                 default=False
 464                 )
 465     close_v: BoolProperty(
 466                 name="Close V",
 467                 description="Create faces for first and last "
 468                             "V values (only if U is wrapped)",
 469                 default=False
 470                 )
 471     n_eq: IntProperty(
 472                 name="Number of objects (n=0..N-1)",
 473                 description="The parameter n will be the index "
 474                             "of the current object, 0 to N-1",
 475                 min=1,
 476                 max=100,
 477                 default=1
 478                 )
 479     a_eq: StringProperty(
 480                 name="A helper function",
 481                 description="Equation for a=F(u,v). Also available: n",
 482                 default="0"
 483                 )
 484     b_eq: StringProperty(
 485                 name="B helper function",
 486                 description="Equation for b=F(u,v). Also available: n",
 487                 default="0"
 488                 )
 489     c_eq: StringProperty(
 490                 name="C helper function",
 491                 description="Equation for c=F(u,v). Also available: n",
 492                 default="0"
 493                 )
 494     f_eq: StringProperty(
 495                 name="F helper function",
 496                 description="Equation for f=F(u,v). Also available: n, a, b, c",
 497                 default="0"
 498                 )
 499     g_eq: StringProperty(
 500                 name="G helper function",
 501                 description="Equation for g=F(u,v). Also available: n, a, b, c",
 502                 default="0"
 503                 )
 504     h_eq: StringProperty(
 505                 name="H helper function",
 506                 description="Equation for h=F(u,v). Also available: n, a, b, c",
 507                 default="0"
 508                 )
 509     show_wire : BoolProperty(
 510             name="Show wireframe",
 511             default=True,
 512             description="Add the object’s wireframe over solid drawing"
 513             )
 514     edit_mode : BoolProperty(
 515             name="Show in edit mode",
 516             default=True,
 517             description="Show in edit mode"
 518             )
 519
 520     def execute(self, context):
 521         for n in range(0, self.n_eq):
 522             verts, faces = xyz_function_surface_faces(
 523                                 self,
 524                                 self.x_eq,
 525                                 self.y_eq,
 526                                 self.z_eq,
 527                                 self.range_u_min,
 528                                 self.range_u_max,
 529                                 self.range_u_step,
 530                                 self.wrap_u,
 531                                 self.range_v_min,
 532                                 self.range_v_max,
 533                                 self.range_v_step,
 534                                 self.wrap_v,
 535                                 self.a_eq,
 536                                 self.b_eq,
 537                                 self.c_eq,
 538                                 self.f_eq,
 539                                 self.g_eq,
 540                                 self.h_eq,
 541                                 n,
 542                                 self.close_v
 543                                 )
 544             if not verts:
 545                 return {'CANCELLED'}
 546
 547             obj = create_mesh_object(context, verts, [], faces, "XYZ Function")
 548
 549         if self.show_wire:
 550             context.active_object.show_wire = True
 551         else:
 552             context.active_object.show_wire = False
 553
 554         if self.edit_mode:
 555             bpy.ops.object.mode_set(mode = 'EDIT')
 556         else:
 557             bpy.ops.object.mode_set(mode = 'OBJECT')
 558
 559         return {'FINISHED'}