add_mesh_extra_objects/add_mesh_3d_function_surface.py

   1 # SPDX-FileCopyrightText: 2010-2022 Blender Foundation
   2 #
   3 # SPDX-License-Identifier: GPL-2.0-or-later
   4
   5 # Original by Buerbaum Martin (Pontiac), Elod Csirmaz
   6
   7 import bpy
   8 import math
   9 import numpy
  10 from mathutils import *
  11 from math import *
  12 from bpy.types import Operator
  13 from bpy.props import (
  14         StringProperty,
  15         IntProperty,
  16         FloatProperty,
  17         BoolProperty,
  18         )
  19
  20
  21 # List of safe functions for eval()
  22 safe_list = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh',
  23     'degrees', 'e', 'exp', 'fabs', 'floor', 'fmod', 'frexp', 'hypot',
  24     'ldexp', 'log', 'log10', 'modf', 'pi', 'pow', 'radians',
  25     'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'gcd']
  26
  27 # Use the list to filter the local namespace
  28 safe_dict = dict((k, globals().get(k, None)) for k in safe_list)
  29 safe_dict['math'] = math
  30 safe_dict['numpy'] = safe_dict['np'] = numpy
  31 safe_dict['lcm'] = numpy.lcm
  32 safe_dict['max'] = max
  33 safe_dict['min'] = min
  34
  35
  36 # Stores the values of a list of properties and the
  37 # operator id in a property group ('recall_op') inside the object
  38 # Could (in theory) be used for non-objects.
  39 # Note: Replaces any existing property group with the same name!
  40 # ob ... Object to store the properties in
  41 # op ... The operator that should be used
  42 # op_args ... A dictionary with valid Blender
  43 #             properties (operator arguments/parameters)
  44
  45
  46 # Create a new mesh (object) from verts/edges/faces
  47 # verts/edges/faces ... List of vertices/edges/faces for the
  48 #                       new mesh (as used in from_pydata)
  49 # name ... Name of the new mesh (& object)
  50
  51 def create_mesh_object(context, verts, edges, faces, name):
  52
  53     # Create new mesh
  54     mesh = bpy.data.meshes.new(name)
  55
  56     # Make a mesh from a list of verts/edges/faces
  57     mesh.from_pydata(verts, edges, faces)
  58
  59     # Update mesh geometry after adding stuff
  60     mesh.update()
  61
  62     from bpy_extras import object_utils
  63     return object_utils.object_data_add(context, mesh, operator=None)
  64
  65
  66 # A very simple "bridge" tool
  67
  68 def createFaces(vertIdx1, vertIdx2, closed=False, flipped=False):
  69     faces = []
  70
  71     if not vertIdx1 or not vertIdx2:
  72         return None
  73
  74     if len(vertIdx1) < 2 and len(vertIdx2) < 2:
  75         return None
  76
  77     fan = False
  78     if (len(vertIdx1) != len(vertIdx2)):
  79         if (len(vertIdx1) == 1 and len(vertIdx2) > 1):
  80             fan = True
  81         else:
  82             return None
  83
  84     total = len(vertIdx2)
  85
  86     if closed:
  87         # Bridge the start with the end
  88         if flipped:
  89             face = [
  90                 vertIdx1[0],
  91                 vertIdx2[0],
  92                 vertIdx2[total - 1]]
  93             if not fan:
  94                 face.append(vertIdx1[total - 1])
  95             faces.append(face)
  96
  97         else:
  98             face = [vertIdx2[0], vertIdx1[0]]
  99             if not fan:
 100                 face.append(vertIdx1[total - 1])
 101             face.append(vertIdx2[total - 1])
 102             faces.append(face)
 103
 104     # Bridge the rest of the faces
 105     for num in range(total - 1):
 106         if flipped:
 107             if fan:
 108                 face = [vertIdx2[num], vertIdx1[0], vertIdx2[num + 1]]
 109             else:
 110                 face = [vertIdx2[num], vertIdx1[num],
 111                     vertIdx1[num + 1], vertIdx2[num + 1]]
 112             faces.append(face)
 113         else:
 114             if fan:
 115                 face = [vertIdx1[0], vertIdx2[num], vertIdx2[num + 1]]
 116             else:
 117                 face = [vertIdx1[num], vertIdx2[num],
 118                     vertIdx2[num + 1], vertIdx1[num + 1]]
 119             faces.append(face)
 120
 121     return faces
 122
 123
 124 class AddZFunctionSurface(Operator):
 125     bl_idname = "mesh.primitive_z_function_surface"
 126     bl_label = "Add Z Function Surface"
 127     bl_description = "Add a surface defined defined by a function z=f(x,y)"
 128     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 129
 130     equation: StringProperty(
 131                 name="Z Equation",
 132                 description="Equation for z=f(x,y)",
 133                 default="1 - ( x**2 + y**2 )"
 134                 )
 135     div_x: IntProperty(
 136                 name="X Subdivisions",
 137                 description="Number of vertices in x direction",
 138                 default=16,
 139                 min=3,
 140                 max=256
 141                 )
 142     div_y: IntProperty(
 143                 name="Y Subdivisions",
 144                 description="Number of vertices in y direction",
 145                 default=16,
 146                 min=3,
 147                 max=256
 148                 )
 149     size_x: FloatProperty(
 150                 name="X Size",
 151                 description="Size of the x axis",
 152                 default=2.0,
 153                 min=0.01,
 154                 max=100.0,
 155                 unit="LENGTH"
 156                 )
 157     size_y: FloatProperty(
 158                 name="Y Size",
 159                 description="Size of the y axis",
 160                 default=2.0,
 161                 min=0.01,
 162                 max=100.0,
 163                 unit="LENGTH"
 164                 )
 165
 166     def execute(self, context):
 167         equation = self.equation
 168         div_x = self.div_x
 169         div_y = self.div_y
 170         size_x = self.size_x
 171         size_y = self.size_y
 172
 173         verts = []
 174         faces = []
 175
 176         delta_x = size_x / (div_x - 1)
 177         delta_y = size_y / (div_y - 1)
 178         start_x = -(size_x / 2.0)
 179         start_y = -(size_y / 2.0)
 180
 181         edgeloop_prev = []
 182
 183         if equation:
 184             try:
 185                 expr_args = (
 186                     compile(equation, __file__, 'eval'),
 187                     {"__builtins__": None},
 188                     safe_dict)
 189             except:
 190                 import traceback
 191                 # WARNING is used to prevent the constant pop-up spam
 192                 self.report({'WARNING'},
 193                             "Error parsing expression: {} "
 194                             "(Check the console for more info)".format(equation))
 195                 print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 196
 197                 return {'CANCELLED'}
 198
 199             for row_x in range(div_x):
 200                 edgeloop_cur = []
 201                 x = start_x + row_x * delta_x
 202
 203                 for row_y in range(div_y):
 204                     y = start_y + row_y * delta_y
 205                     z = 0.0
 206
 207                     safe_dict['x'] = x
 208                     safe_dict['y'] = y
 209
 210                     # Try to evaluate the equation.
 211                     try:
 212                         z = float(eval(*expr_args))
 213                     except:
 214                         import traceback
 215                         self.report({'WARNING'},
 216                                     "Error evaluating expression: {} "
 217                                     "(Check the console for more info)".format(equation))
 218                         print("\n[Add Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 219
 220                         return {'CANCELLED'}
 221
 222                     edgeloop_cur.append(len(verts))
 223                     verts.append((x, y, z))
 224
 225                 if len(edgeloop_prev) > 0:
 226                     faces_row = createFaces(edgeloop_prev, edgeloop_cur)
 227                     faces.extend(faces_row)
 228
 229                 edgeloop_prev = edgeloop_cur
 230
 231             base = create_mesh_object(context, verts, [], faces, "Z Function")
 232         else:
 233             self.report({'WARNING'}, "Z Equation - No expression is given")
 234
 235             return {'CANCELLED'}
 236
 237         return {'FINISHED'}
 238
 239
 240 def xyz_function_surface_faces(self, x_eq, y_eq, z_eq,
 241             range_u_min, range_u_max, range_u_step, wrap_u,
 242             range_v_min, range_v_max, range_v_step, wrap_v,
 243             a_eq, b_eq, c_eq, f_eq, g_eq, h_eq, n, close_v):
 244
 245     verts = []
 246     faces = []
 247
 248     # Distance of each step in Blender Units
 249     uStep = (range_u_max - range_u_min) / range_u_step
 250     vStep = (range_v_max - range_v_min) / range_v_step
 251
 252     # Number of steps in the vertex creation loops.
 253     # Number of steps is the number of faces
 254     #   => Number of points is +1 unless wrapped.
 255     uRange = range_u_step + 1
 256     vRange = range_v_step + 1
 257
 258     if wrap_u:
 259         uRange = uRange - 1
 260
 261     if wrap_v:
 262         vRange = vRange - 1
 263
 264     try:
 265         expr_args_x = (
 266             compile(x_eq, __file__.replace(".py", "_x.py"), 'eval'),
 267             {"__builtins__": None},
 268             safe_dict)
 269         expr_args_y = (
 270             compile(y_eq, __file__.replace(".py", "_y.py"), 'eval'),
 271             {"__builtins__": None},
 272             safe_dict)
 273         expr_args_z = (
 274             compile(z_eq, __file__.replace(".py", "_z.py"), 'eval'),
 275             {"__builtins__": None},
 276             safe_dict)
 277         expr_args_a = (
 278             compile(a_eq, __file__.replace(".py", "_a.py"), 'eval'),
 279             {"__builtins__": None},
 280             safe_dict)
 281         expr_args_b = (
 282             compile(b_eq, __file__.replace(".py", "_b.py"), 'eval'),
 283             {"__builtins__": None},
 284             safe_dict)
 285         expr_args_c = (
 286             compile(c_eq, __file__.replace(".py", "_c.py"), 'eval'),
 287             {"__builtins__": None},
 288             safe_dict)
 289         expr_args_f = (
 290             compile(f_eq, __file__.replace(".py", "_f.py"), 'eval'),
 291             {"__builtins__": None},
 292             safe_dict)
 293         expr_args_g = (
 294             compile(g_eq, __file__.replace(".py", "_g.py"), 'eval'),
 295             {"__builtins__": None},
 296             safe_dict)
 297         expr_args_h = (
 298             compile(h_eq, __file__.replace(".py", "_h.py"), 'eval'),
 299             {"__builtins__": None},
 300             safe_dict)
 301     except:
 302         import traceback
 303         self.report({'WARNING'}, "Error parsing expression(s) - "
 304                     "Check the console for more info")
 305         print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 306         return [], []
 307
 308     for vN in range(vRange):
 309         v = range_v_min + (vN * vStep)
 310
 311         for uN in range(uRange):
 312             u = range_u_min + (uN * uStep)
 313
 314             safe_dict['u'] = u
 315             safe_dict['v'] = v
 316
 317             safe_dict['n'] = n
 318
 319             # Try to evaluate the equations.
 320             try:
 321                 safe_dict['a'] = float(eval(*expr_args_a))
 322                 safe_dict['b'] = float(eval(*expr_args_b))
 323                 safe_dict['c'] = float(eval(*expr_args_c))
 324                 safe_dict['f'] = float(eval(*expr_args_f))
 325                 safe_dict['g'] = float(eval(*expr_args_g))
 326                 safe_dict['h'] = float(eval(*expr_args_h))
 327
 328                 verts.append((
 329                     float(eval(*expr_args_x)),
 330                     float(eval(*expr_args_y)),
 331                     float(eval(*expr_args_z))))
 332             except:
 333                 import traceback
 334                 self.report({'WARNING'}, "Error evaluating expression(s) - "
 335                              "Check the console for more info")
 336                 print("\n[Add X, Y, Z Function Surface]:\n\n", traceback.format_exc(limit=1))
 337                 return [], []
 338
 339     for vN in range(range_v_step):
 340         vNext = vN + 1
 341
 342         if wrap_v and (vNext >= vRange):
 343             vNext = 0
 344
 345         for uN in range(range_u_step):
 346             uNext = uN + 1
 347
 348             if wrap_u and (uNext >= uRange):
 349                 uNext = 0
 350
 351             faces.append([(vNext * uRange) + uNext,
 352                 (vNext * uRange) + uN,
 353                 (vN * uRange) + uN,
 354                 (vN * uRange) + uNext])
 355
 356     if close_v and wrap_u and (not wrap_v):
 357         for uN in range(1, range_u_step - 1):
 358             faces.append([
 359                 range_u_step - 1,
 360                 range_u_step - 1 - uN,
 361                 range_u_step - 2 - uN])
 362             faces.append([
 363                 range_v_step * uRange,
 364                 range_v_step * uRange + uN,
 365                 range_v_step * uRange + uN + 1])
 366
 367     return verts, faces
 368
 369
 370 # Original Script "Parametric.py" by Ed Mackey.
 371 # -> http://www.blinken.com/blender-plugins.php
 372 # Partly converted for Blender 2.5 by tuga3d.
 373 #
 374 # Sphere:
 375 # x = sin(2*pi*u)*sin(pi*v)
 376 # y = cos(2*pi*u)*sin(pi*v)
 377 # z = cos(pi*v)
 378 # u_min = v_min = 0
 379 # u_max = v_max = 1
 380 #
 381 # "Snail shell"
 382 # x = 1.2**v*(sin(u)**2 *sin(v))
 383 # y = 1.2**v*(sin(u)*cos(u))
 384 # z = 1.2**v*(sin(u)**2 *cos(v))
 385 # u_min = 0
 386 # u_max = pi
 387 # v_min = -pi/4,
 388 # v max = 5*pi/2
 389
 390 class AddXYZFunctionSurface(Operator):
 391     bl_idname = "mesh.primitive_xyz_function_surface"
 392     bl_label = "Add X, Y, Z Function Surface"
 393     bl_description = ("Add a surface defined defined by 3 functions:\n"
 394                       "x=F1(u,v), y=F2(u,v) and z=F3(u,v)")
 395     bl_options = {'REGISTER', 'UNDO', 'PRESET'}
 396
 397     x_eq: StringProperty(
 398                 name="X equation",
 399                 description="Equation for x=F(u,v). "
 400                             "Also available: n, a, b, c, f, g, h",
 401                 default="cos(v)*(1+cos(u))*sin(v/8)"
 402                 )
 403     y_eq: StringProperty(
 404                 name="Y equation",
 405                 description="Equation for y=F(u,v). "
 406                             "Also available: n, a, b, c, f, g, h",
 407                 default="sin(u)*sin(v/8)+cos(v/8)*1.5"
 408                 )
 409     z_eq: StringProperty(
 410                 name="Z equation",
 411                 description="Equation for z=F(u,v). "
 412                             "Also available: n, a, b, c, f, g, h",
 413                 default="sin(v)*(1+cos(u))*sin(v/8)"
 414                 )
 415     range_u_min: FloatProperty(
 416                 name="U min",
 417                 description="Minimum U value. Lower boundary of U range",
 418                 min=-100.00,
 419                 max=0.00,
 420                 default=0.00
 421                 )
 422     range_u_max: FloatProperty(
 423                 name="U max",
 424                 description="Maximum U value. Upper boundary of U range",
 425                 min=0.00,
 426                 max=100.00,
 427                 default=2 * pi
 428                 )
 429     range_u_step: IntProperty(
 430                 name="U step",
 431                 description="U Subdivisions",
 432                 min=1,
 433                 max=1024,
 434                 default=32
 435                 )
 436     wrap_u: BoolProperty(
 437                 name="U wrap",
 438                 description="U Wrap around",
 439                 default=True
 440                 )
 441     range_v_min: FloatProperty(
 442                 name="V min",
 443                 description="Minimum V value. Lower boundary of V range",
 444                 min=-100.00,
 445                 max=0.00,
 446                 default=0.00
 447                 )
 448     range_v_max: FloatProperty(
 449                 name="V max",
 450                 description="Maximum V value. Upper boundary of V range",
 451                 min=0.00,
 452                 max=100.00,
 453                 default=4 * pi
 454                 )
 455     range_v_step: IntProperty(
 456                 name="V step",
 457                 description="V Subdivisions",
 458                 min=1,
 459                 max=1024,
 460                 default=128
 461                 )
 462     wrap_v: BoolProperty(
 463                 name="V wrap",
 464                 description="V Wrap around",
 465                 default=False
 466                 )
 467     close_v: BoolProperty(
 468                 name="Close V",
 469                 description="Create faces for first and last "
 470                             "V values (only if U is wrapped)",
 471                 default=False
 472                 )
 473     n_eq: IntProperty(
 474                 name="Number of objects (n=0..N-1)",
 475                 description="The parameter n will be the index "
 476                             "of the current object, 0 to N-1",
 477                 min=1,
 478                 max=100,
 479                 default=1
 480                 )
 481     a_eq: StringProperty(
 482                 name="A helper function",
 483                 description="Equation for a=F(u,v). Also available: n",
 484                 default="0"
 485                 )
 486     b_eq: StringProperty(
 487                 name="B helper function",
 488                 description="Equation for b=F(u,v). Also available: n",
 489                 default="0"
 490                 )
 491     c_eq: StringProperty(
 492                 name="C helper function",
 493                 description="Equation for c=F(u,v). Also available: n",
 494                 default="0"
 495                 )
 496     f_eq: StringProperty(
 497                 name="F helper function",
 498                 description="Equation for f=F(u,v). Also available: n, a, b, c",
 499                 default="0"
 500                 )
 501     g_eq: StringProperty(
 502                 name="G helper function",
 503                 description="Equation for g=F(u,v). Also available: n, a, b, c",
 504                 default="0"
 505                 )
 506     h_eq: StringProperty(
 507                 name="H helper function",
 508                 description="Equation for h=F(u,v). Also available: n, a, b, c",
 509                 default="0"
 510                 )
 511     show_wire : BoolProperty(
 512             name="Show wireframe",
 513             default=True,
 514             description="Add the object’s wireframe over solid drawing"
 515             )
 516     edit_mode : BoolProperty(
 517             name="Show in edit mode",
 518             default=True,
 519             description="Show in edit mode"
 520             )
 521
 522     def execute(self, context):
 523         for n in range(0, self.n_eq):
 524             verts, faces = xyz_function_surface_faces(
 525                                 self,
 526                                 self.x_eq,
 527                                 self.y_eq,
 528                                 self.z_eq,
 529                                 self.range_u_min,
 530                                 self.range_u_max,
 531                                 self.range_u_step,
 532                                 self.wrap_u,
 533                                 self.range_v_min,
 534                                 self.range_v_max,
 535                                 self.range_v_step,
 536                                 self.wrap_v,
 537                                 self.a_eq,
 538                                 self.b_eq,
 539                                 self.c_eq,
 540                                 self.f_eq,
 541                                 self.g_eq,
 542                                 self.h_eq,
 543                                 n,
 544                                 self.close_v
 545                                 )
 546             if not verts:
 547                 return {'CANCELLED'}
 548
 549             obj = create_mesh_object(context, verts, [], faces, "XYZ Function")
 550
 551         if self.show_wire:
 552             context.active_object.show_wire = True
 553         else:
 554             context.active_object.show_wire = False
 555
 556         if self.edit_mode:
 557             bpy.ops.object.mode_set(mode = 'EDIT')
 558         else:
 559             bpy.ops.object.mode_set(mode = 'OBJECT')
 560
 561         return {'FINISHED'}