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+# add_mesh_twisted_torus.py Copyright (C) 2009-2010, Paulo Gomes
+# tuga3d {at} gmail {dot} com
+# add twisted torus to the blender 2.50 add->mesh menu
+# ***** 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+#
+# ***** END GPL LICENCE BLOCK *****
+
+"""
+
+Usage:
+
+* Launch from Add Mesh menu
+
+* Modify parameters as desired or keep defaults
+
+"""
+
+bl_addon_info = {
+ 'name': 'Add Mesh: Twisted Torus',
+ 'author': 'Paulo_Gomes',
+ 'version': '0.11',
+ 'blender': (2, 5, 3),
+ 'location': 'View3D > Add > Mesh ',
+ 'description': 'Adds a mesh Twisted Torus to the Add Mesh menu',
+ 'warning': '', # used for warning icon and text in addons panel
+ 'wiki_url': 'http://wiki.blender.org/index.php/Extensions:2.5/Py/' \
+ 'Scripts/Add_Mesh/Add_Twisted_Torus',
+ 'tracker_url': 'https://projects.blender.org/tracker/index.php?'\
+ 'func=detail&aid=21622&group_id=153&atid=469',
+ 'category': 'Add Mesh'}
+
+import bpy
+from bpy.props import *
+
+import mathutils
+from mathutils import *
+from math import cos, sin, pi
+
+# calculates the matrix for the new object
+# depending on user pref
+def align_matrix(context):
+ loc = TranslationMatrix(context.scene.cursor_location)
+ obj_align = context.user_preferences.edit.object_align
+ if (context.space_data.type == 'VIEW_3D'
+ and obj_align == 'VIEW'):
+ rot = context.space_data.region_3d.view_matrix.rotation_part().invert().resize4x4()
+ else:
+ rot = Matrix()
+ align_matrix = loc * rot
+ return align_matrix
+
+
+# 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).
+# edit ... Replace existing mesh data.
+# Note: Using "edit" will destroy/delete existing mesh data.
+def create_mesh_object(context, verts, edges, faces, name, edit, align_matrix):
+ scene = context.scene
+ obj_act = scene.objects.active
+
+ # Can't edit anything, unless we have an active obj.
+ if edit and not obj_act:
+ return None
+
+ # 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()
+
+ # Deselect all objects.
+ bpy.ops.object.select_all(action='DESELECT')
+
+ if edit:
+ # Replace geometry of existing object
+
+ # Use the active obj and select it.
+ ob_new = obj_act
+ ob_new.select = True
+
+ if obj_act.mode == 'OBJECT':
+ # Get existing mesh datablock.
+ old_mesh = ob_new.data
+
+ # Set object data to nothing
+ ob_new.data = None
+
+ # Clear users of existing mesh datablock.
+ old_mesh.user_clear()
+
+ # Remove old mesh datablock if no users are left.
+ if (old_mesh.users == 0):
+ bpy.data.meshes.remove(old_mesh)
+
+ # Assign new mesh datablock.
+ ob_new.data = mesh
+
+ 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.select = True
+
+ # Place the object at the 3D cursor location.
+ # apply viewRotaion
+ ob_new.matrix_world = align_matrix
+
+ 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.select = 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')
+
+ ob_new = obj_act
+
+ else:
+ # We are in ObjectMode.
+ # Make the new object the active one.
+ scene.objects.active = ob_new
+
+ return ob_new
+
+
+# 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
+
+
+def add_twisted_torus(major_rad, minor_rad, major_seg, minor_seg, twists):
+ PI_2 = pi * 2.0
+ z_axis = (0.0, 0.0, 1.0)
+
+ verts = []
+ faces = []
+
+ edgeloop_prev = []
+ for major_index in range(major_seg):
+ quat = Quaternion(z_axis, (major_index / major_seg) * PI_2)
+ rot_twists = PI_2 * major_index / major_seg * twists
+
+ edgeloop = []
+
+ # Create section ring
+ for minor_index in range(minor_seg):
+ angle = (PI_2 * minor_index / minor_seg) + rot_twists
+
+ vec = Vector((
+ major_rad + (cos(angle) * minor_rad),
+ 0.0,
+ sin(angle) * minor_rad))
+ vec = vec * quat
+
+ edgeloop.append(len(verts))
+ verts.append(vec)
+
+ # Remember very first edgeloop.
+ if major_index == 0:
+ edgeloop_first = edgeloop
+
+ # Bridge last with current ring
+ if edgeloop_prev:
+ f = createFaces(edgeloop_prev, edgeloop, closed=True)
+ faces.extend(f)
+
+ edgeloop_prev = edgeloop
+
+ # Bridge first and last ring
+ f = createFaces(edgeloop_prev, edgeloop_first, closed=True)
+ faces.extend(f)
+
+ return verts, faces
+
+
+class AddTwistedTorus(bpy.types.Operator):
+ '''Add a torus mesh'''
+ bl_idname = "mesh.primitive_twisted_torus_add"
+ bl_label = "Add Torus"
+ bl_options = {'REGISTER', 'UNDO'}
+
+ # edit - Whether to add or update.
+ edit = BoolProperty(name="",
+ description="",
+ default=False,
+ options={'HIDDEN'})
+ major_radius = FloatProperty(name="Major Radius",
+ description="Radius from the origin to the" \
+ " center of the cross section",
+ min=0.01,
+ max=100.0,
+ default=1.0)
+ minor_radius = FloatProperty(name="Minor Radius",
+ description="Radius of the torus' cross section",
+ min=0.01,
+ max=100.0,
+ default=0.25)
+ major_segments = IntProperty(name="Major Segments",
+ description="Number of segments for the main ring of the torus",
+ min=3,
+ max=256,
+ default=48)
+ minor_segments = IntProperty(name="Minor Segments",
+ description="Number of segments for the minor ring of the torus",
+ min=3,
+ max=256,
+ default=12)
+ twists = IntProperty(name="Twists",
+ description="Number of twists of the torus",
+ min=0,
+ max=256,
+ default=1)
+
+ use_abso = BoolProperty(name="Use Int+Ext Controls",
+ description="Use the Int / Ext controls for torus dimensions",
+ default=False)
+ abso_major_rad = FloatProperty(name="Exterior Radius",
+ description="Total Exterior Radius of the torus",
+ min=0.01,
+ max=100.0,
+ default=1.0)
+ abso_minor_rad = FloatProperty(name="Inside Radius",
+ description="Total Interior Radius of the torus",
+ min=0.01,
+ max=100.0,
+ default=0.5)
+ align_matrix = Matrix()
+
+ def execute(self, context):
+ props = self.properties
+
+ if props.use_abso == True:
+ extra_helper = (props.abso_major_rad - props.abso_minor_rad) * 0.5
+ props.major_radius = props.abso_minor_rad + extra_helper
+ props.minor_radius = extra_helper
+
+ verts, faces = add_twisted_torus(
+ props.major_radius,
+ props.minor_radius,
+ props.major_segments,
+ props.minor_segments,
+ props.twists)
+
+ # Actually create the mesh object from this geometry data.
+ obj = create_mesh_object(context, verts, [], faces, "TwistedTorus",
+ props.edit, self.align_matrix)
+
+ return {'FINISHED'}
+
+ def invoke(self, context, event):
+ self.align_matrix = align_matrix(context)
+ self.execute(context)
+ return {'FINISHED'}
+
+# Add to the menu
+menu_func = (lambda self,
+ context: self.layout.operator(AddTwistedTorus.bl_idname,
+ text="Twisted Torus", icon='MESH_DONUT'))
+
+
+def register():
+ bpy.types.register(AddTwistedTorus)
+ bpy.types.INFO_MT_mesh_add.append(menu_func)
+
+
+def unregister():
+ bpy.types.unregister(AddTwistedTorus)
+ bpy.types.INFO_MT_mesh_add.remove(menu_func)
+
+if __name__ == "__main__":
+ register()