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mesh_looptools.py
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mesh_looptools.py
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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 #####
bl_info = {
"name": "LoopTools",
"author": "Bart Crouch",
"version": (4, 6, 7),
"blender": (2, 72, 2),
"location": "View3D > Toolbar and View3D > Specials (W-key)",
"warning": "",
"description": "Mesh modelling toolkit. Several tools to aid modelling",
"wiki_url": "https://wiki.blender.org/index.php/Extensions:2.6/Py/"
"Scripts/Modeling/LoopTools",
"category": "Mesh",
}
import bmesh
import bpy
import collections
import mathutils
import math
from bpy_extras import view3d_utils
from bpy.types import (
Operator,
Menu,
Panel,
PropertyGroup,
AddonPreferences,
)
from bpy.props import (
BoolProperty,
EnumProperty,
FloatProperty,
IntProperty,
PointerProperty,
StringProperty,
)
# ########################################
# ##### General functions ################
# ########################################
# used by all tools to improve speed on reruns Unlink
looptools_cache = {}
def get_grease_pencil(object, context):
gp = object.grease_pencil
if not gp:
gp = context.scene.grease_pencil
return gp
# force a full recalculation next time
def cache_delete(tool):
if tool in looptools_cache:
del looptools_cache[tool]
# check cache for stored information
def cache_read(tool, object, bm, input_method, boundaries):
# current tool not cached yet
if tool not in looptools_cache:
return(False, False, False, False, False)
# check if selected object didn't change
if object.name != looptools_cache[tool]["object"]:
return(False, False, False, False, False)
# check if input didn't change
if input_method != looptools_cache[tool]["input_method"]:
return(False, False, False, False, False)
if boundaries != looptools_cache[tool]["boundaries"]:
return(False, False, False, False, False)
modifiers = [mod.name for mod in object.modifiers if mod.show_viewport and
mod.type == 'MIRROR']
if modifiers != looptools_cache[tool]["modifiers"]:
return(False, False, False, False, False)
input = [v.index for v in bm.verts if v.select and not v.hide]
if input != looptools_cache[tool]["input"]:
return(False, False, False, False, False)
# reading values
single_loops = looptools_cache[tool]["single_loops"]
loops = looptools_cache[tool]["loops"]
derived = looptools_cache[tool]["derived"]
mapping = looptools_cache[tool]["mapping"]
return(True, single_loops, loops, derived, mapping)
# store information in the cache
def cache_write(tool, object, bm, input_method, boundaries, single_loops,
loops, derived, mapping):
# clear cache of current tool
if tool in looptools_cache:
del looptools_cache[tool]
# prepare values to be saved to cache
input = [v.index for v in bm.verts if v.select and not v.hide]
modifiers = [mod.name for mod in object.modifiers if mod.show_viewport and
mod.type == 'MIRROR']
# update cache
looptools_cache[tool] = {"input": input, "object": object.name,
"input_method": input_method, "boundaries": boundaries,
"single_loops": single_loops, "loops": loops,
"derived": derived, "mapping": mapping, "modifiers": modifiers}
# calculates natural cubic splines through all given knots
def calculate_cubic_splines(bm_mod, tknots, knots):
# hack for circular loops
if knots[0] == knots[-1] and len(knots) > 1:
circular = True
k_new1 = []
for k in range(-1, -5, -1):
if k - 1 < -len(knots):
k += len(knots)
k_new1.append(knots[k - 1])
k_new2 = []
for k in range(4):
if k + 1 > len(knots) - 1:
k -= len(knots)
k_new2.append(knots[k + 1])
for k in k_new1:
knots.insert(0, k)
for k in k_new2:
knots.append(k)
t_new1 = []
total1 = 0
for t in range(-1, -5, -1):
if t - 1 < -len(tknots):
t += len(tknots)
total1 += tknots[t] - tknots[t - 1]
t_new1.append(tknots[0] - total1)
t_new2 = []
total2 = 0
for t in range(4):
if t + 1 > len(tknots) - 1:
t -= len(tknots)
total2 += tknots[t + 1] - tknots[t]
t_new2.append(tknots[-1] + total2)
for t in t_new1:
tknots.insert(0, t)
for t in t_new2:
tknots.append(t)
else:
circular = False
# end of hack
n = len(knots)
if n < 2:
return False
x = tknots[:]
locs = [bm_mod.verts[k].co[:] for k in knots]
result = []
for j in range(3):
a = []
for i in locs:
a.append(i[j])
h = []
for i in range(n - 1):
if x[i + 1] - x[i] == 0:
h.append(1e-8)
else:
h.append(x[i + 1] - x[i])
q = [False]
for i in range(1, n - 1):
q.append(3 / h[i] * (a[i + 1] - a[i]) - 3 / h[i - 1] * (a[i] - a[i - 1]))
l = [1.0]
u = [0.0]
z = [0.0]
for i in range(1, n - 1):
l.append(2 * (x[i + 1] - x[i - 1]) - h[i - 1] * u[i - 1])
if l[i] == 0:
l[i] = 1e-8
u.append(h[i] / l[i])
z.append((q[i] - h[i - 1] * z[i - 1]) / l[i])
l.append(1.0)
z.append(0.0)
b = [False for i in range(n - 1)]
c = [False for i in range(n)]
d = [False for i in range(n - 1)]
c[n - 1] = 0.0
for i in range(n - 2, -1, -1):
c[i] = z[i] - u[i] * c[i + 1]
b[i] = (a[i + 1] - a[i]) / h[i] - h[i] * (c[i + 1] + 2 * c[i]) / 3
d[i] = (c[i + 1] - c[i]) / (3 * h[i])
for i in range(n - 1):
result.append([a[i], b[i], c[i], d[i], x[i]])
splines = []
for i in range(len(knots) - 1):
splines.append([result[i], result[i + n - 1], result[i + (n - 1) * 2]])
if circular: # cleaning up after hack
knots = knots[4:-4]
tknots = tknots[4:-4]
return(splines)
# calculates linear splines through all given knots
def calculate_linear_splines(bm_mod, tknots, knots):
splines = []
for i in range(len(knots) - 1):
a = bm_mod.verts[knots[i]].co
b = bm_mod.verts[knots[i + 1]].co
d = b - a
t = tknots[i]
u = tknots[i + 1] - t
splines.append([a, d, t, u]) # [locStart, locDif, tStart, tDif]
return(splines)
# calculate a best-fit plane to the given vertices
def calculate_plane(bm_mod, loop, method="best_fit", object=False):
# getting the vertex locations
locs = [bm_mod.verts[v].co.copy() for v in loop[0]]
# calculating the center of masss
com = mathutils.Vector()
for loc in locs:
com += loc
com /= len(locs)
x, y, z = com
if method == 'best_fit':
# creating the covariance matrix
mat = mathutils.Matrix(((0.0, 0.0, 0.0),
(0.0, 0.0, 0.0),
(0.0, 0.0, 0.0),
))
for loc in locs:
mat[0][0] += (loc[0] - x) ** 2
mat[1][0] += (loc[0] - x) * (loc[1] - y)
mat[2][0] += (loc[0] - x) * (loc[2] - z)
mat[0][1] += (loc[1] - y) * (loc[0] - x)
mat[1][1] += (loc[1] - y) ** 2
mat[2][1] += (loc[1] - y) * (loc[2] - z)
mat[0][2] += (loc[2] - z) * (loc[0] - x)
mat[1][2] += (loc[2] - z) * (loc[1] - y)
mat[2][2] += (loc[2] - z) ** 2
# calculating the normal to the plane
normal = False
try:
mat = matrix_invert(mat)
except:
ax = 2
if math.fabs(sum(mat[0])) < math.fabs(sum(mat[1])):
if math.fabs(sum(mat[0])) < math.fabs(sum(mat[2])):
ax = 0
elif math.fabs(sum(mat[1])) < math.fabs(sum(mat[2])):
ax = 1
if ax == 0:
normal = mathutils.Vector((1.0, 0.0, 0.0))
elif ax == 1:
normal = mathutils.Vector((0.0, 1.0, 0.0))
else:
normal = mathutils.Vector((0.0, 0.0, 1.0))
if not normal:
# warning! this is different from .normalize()
itermax = 500
vec2 = mathutils.Vector((1.0, 1.0, 1.0))
for i in range(itermax):
vec = vec2
vec2 = mat * vec
if vec2.length != 0:
vec2 /= vec2.length
if vec2 == vec:
break
if vec2.length == 0:
vec2 = mathutils.Vector((1.0, 1.0, 1.0))
normal = vec2
elif method == 'normal':
# averaging the vertex normals
v_normals = [bm_mod.verts[v].normal for v in loop[0]]
normal = mathutils.Vector()
for v_normal in v_normals:
normal += v_normal
normal /= len(v_normals)
normal.normalize()
elif method == 'view':
# calculate view normal
rotation = bpy.context.space_data.region_3d.view_matrix.to_3x3().\
inverted()
normal = rotation * mathutils.Vector((0.0, 0.0, 1.0))
if object:
normal = object.matrix_world.inverted().to_euler().to_matrix() * \
normal
return(com, normal)
# calculate splines based on given interpolation method (controller function)
def calculate_splines(interpolation, bm_mod, tknots, knots):
if interpolation == 'cubic':
splines = calculate_cubic_splines(bm_mod, tknots, knots[:])
else: # interpolations == 'linear'
splines = calculate_linear_splines(bm_mod, tknots, knots[:])
return(splines)
# check loops and only return valid ones
def check_loops(loops, mapping, bm_mod):
valid_loops = []
for loop, circular in loops:
# loop needs to have at least 3 vertices
if len(loop) < 3:
continue
# loop needs at least 1 vertex in the original, non-mirrored mesh
if mapping:
all_virtual = True
for vert in loop:
if mapping[vert] > -1:
all_virtual = False
break
if all_virtual:
continue
# vertices can not all be at the same location
stacked = True
for i in range(len(loop) - 1):
if (bm_mod.verts[loop[i]].co - bm_mod.verts[loop[i + 1]].co).length > 1e-6:
stacked = False
break
if stacked:
continue
# passed all tests, loop is valid
valid_loops.append([loop, circular])
return(valid_loops)
# input: bmesh, output: dict with the edge-key as key and face-index as value
def dict_edge_faces(bm):
edge_faces = dict([[edgekey(edge), []] for edge in bm.edges if not edge.hide])
for face in bm.faces:
if face.hide:
continue
for key in face_edgekeys(face):
edge_faces[key].append(face.index)
return(edge_faces)
# input: bmesh (edge-faces optional), output: dict with face-face connections
def dict_face_faces(bm, edge_faces=False):
if not edge_faces:
edge_faces = dict_edge_faces(bm)
connected_faces = dict([[face.index, []] for face in bm.faces if not face.hide])
for face in bm.faces:
if face.hide:
continue
for edge_key in face_edgekeys(face):
for connected_face in edge_faces[edge_key]:
if connected_face == face.index:
continue
connected_faces[face.index].append(connected_face)
return(connected_faces)
# input: bmesh, output: dict with the vert index as key and edge-keys as value
def dict_vert_edges(bm):
vert_edges = dict([[v.index, []] for v in bm.verts if not v.hide])
for edge in bm.edges:
if edge.hide:
continue
ek = edgekey(edge)
for vert in ek:
vert_edges[vert].append(ek)
return(vert_edges)
# input: bmesh, output: dict with the vert index as key and face index as value
def dict_vert_faces(bm):
vert_faces = dict([[v.index, []] for v in bm.verts if not v.hide])
for face in bm.faces:
if not face.hide:
for vert in face.verts:
vert_faces[vert.index].append(face.index)
return(vert_faces)
# input: list of edge-keys, output: dictionary with vertex-vertex connections
def dict_vert_verts(edge_keys):
# create connection data
vert_verts = {}
for ek in edge_keys:
for i in range(2):
if ek[i] in vert_verts:
vert_verts[ek[i]].append(ek[1 - i])
else:
vert_verts[ek[i]] = [ek[1 - i]]
return(vert_verts)
# return the edgekey ([v1.index, v2.index]) of a bmesh edge
def edgekey(edge):
return(tuple(sorted([edge.verts[0].index, edge.verts[1].index])))
# returns the edgekeys of a bmesh face
def face_edgekeys(face):
return([tuple(sorted([edge.verts[0].index, edge.verts[1].index])) for edge in face.edges])
# calculate input loops
def get_connected_input(object, bm, scene, input):
# get mesh with modifiers applied
derived, bm_mod = get_derived_bmesh(object, bm, scene)
# calculate selected loops
edge_keys = [edgekey(edge) for edge in bm_mod.edges if edge.select and not edge.hide]
loops = get_connected_selections(edge_keys)
# if only selected loops are needed, we're done
if input == 'selected':
return(derived, bm_mod, loops)
# elif input == 'all':
loops = get_parallel_loops(bm_mod, loops)
return(derived, bm_mod, loops)
# sorts all edge-keys into a list of loops
def get_connected_selections(edge_keys):
# create connection data
vert_verts = dict_vert_verts(edge_keys)
# find loops consisting of connected selected edges
loops = []
while len(vert_verts) > 0:
loop = [iter(vert_verts.keys()).__next__()]
growing = True
flipped = False
# extend loop
while growing:
# no more connection data for current vertex
if loop[-1] not in vert_verts:
if not flipped:
loop.reverse()
flipped = True
else:
growing = False
else:
extended = False
for i, next_vert in enumerate(vert_verts[loop[-1]]):
if next_vert not in loop:
vert_verts[loop[-1]].pop(i)
if len(vert_verts[loop[-1]]) == 0:
del vert_verts[loop[-1]]
# remove connection both ways
if next_vert in vert_verts:
if len(vert_verts[next_vert]) == 1:
del vert_verts[next_vert]
else:
vert_verts[next_vert].remove(loop[-1])
loop.append(next_vert)
extended = True
break
if not extended:
# found one end of the loop, continue with next
if not flipped:
loop.reverse()
flipped = True
# found both ends of the loop, stop growing
else:
growing = False
# check if loop is circular
if loop[0] in vert_verts:
if loop[-1] in vert_verts[loop[0]]:
# is circular
if len(vert_verts[loop[0]]) == 1:
del vert_verts[loop[0]]
else:
vert_verts[loop[0]].remove(loop[-1])
if len(vert_verts[loop[-1]]) == 1:
del vert_verts[loop[-1]]
else:
vert_verts[loop[-1]].remove(loop[0])
loop = [loop, True]
else:
# not circular
loop = [loop, False]
else:
# not circular
loop = [loop, False]
loops.append(loop)
return(loops)
# get the derived mesh data, if there is a mirror modifier
def get_derived_bmesh(object, bm, scene):
# check for mirror modifiers
if 'MIRROR' in [mod.type for mod in object.modifiers if mod.show_viewport]:
derived = True
# disable other modifiers
show_viewport = [mod.name for mod in object.modifiers if mod.show_viewport]
for mod in object.modifiers:
if mod.type != 'MIRROR':
mod.show_viewport = False
# get derived mesh
bm_mod = bmesh.new()
mesh_mod = object.to_mesh(scene, True, 'PREVIEW')
bm_mod.from_mesh(mesh_mod)
bpy.context.blend_data.meshes.remove(mesh_mod)
# re-enable other modifiers
for mod_name in show_viewport:
object.modifiers[mod_name].show_viewport = True
# no mirror modifiers, so no derived mesh necessary
else:
derived = False
bm_mod = bm
bm_mod.verts.ensure_lookup_table()
bm_mod.edges.ensure_lookup_table()
bm_mod.faces.ensure_lookup_table()
return(derived, bm_mod)
# return a mapping of derived indices to indices
def get_mapping(derived, bm, bm_mod, single_vertices, full_search, loops):
if not derived:
return(False)
if full_search:
verts = [v for v in bm.verts if not v.hide]
else:
verts = [v for v in bm.verts if v.select and not v.hide]
# non-selected vertices around single vertices also need to be mapped
if single_vertices:
mapping = dict([[vert, -1] for vert in single_vertices])
verts_mod = [bm_mod.verts[vert] for vert in single_vertices]
for v in verts:
for v_mod in verts_mod:
if (v.co - v_mod.co).length < 1e-6:
mapping[v_mod.index] = v.index
break
real_singles = [v_real for v_real in mapping.values() if v_real > -1]
verts_indices = [vert.index for vert in verts]
for face in [face for face in bm.faces if not face.select and not face.hide]:
for vert in face.verts:
if vert.index in real_singles:
for v in face.verts:
if v.index not in verts_indices:
if v not in verts:
verts.append(v)
break
# create mapping of derived indices to indices
mapping = dict([[vert, -1] for loop in loops for vert in loop[0]])
if single_vertices:
for single in single_vertices:
mapping[single] = -1
verts_mod = [bm_mod.verts[i] for i in mapping.keys()]
for v in verts:
for v_mod in verts_mod:
if (v.co - v_mod.co).length < 1e-6:
mapping[v_mod.index] = v.index
verts_mod.remove(v_mod)
break
return(mapping)
# calculate the determinant of a matrix
def matrix_determinant(m):
determinant = m[0][0] * m[1][1] * m[2][2] + m[0][1] * m[1][2] * m[2][0] \
+ m[0][2] * m[1][0] * m[2][1] - m[0][2] * m[1][1] * m[2][0] \
- m[0][1] * m[1][0] * m[2][2] - m[0][0] * m[1][2] * m[2][1]
return(determinant)
# custom matrix inversion, to provide higher precision than the built-in one
def matrix_invert(m):
r = mathutils.Matrix((
(m[1][1] * m[2][2] - m[1][2] * m[2][1], m[0][2] * m[2][1] - m[0][1] * m[2][2],
m[0][1] * m[1][2] - m[0][2] * m[1][1]),
(m[1][2] * m[2][0] - m[1][0] * m[2][2], m[0][0] * m[2][2] - m[0][2] * m[2][0],
m[0][2] * m[1][0] - m[0][0] * m[1][2]),
(m[1][0] * m[2][1] - m[1][1] * m[2][0], m[0][1] * m[2][0] - m[0][0] * m[2][1],
m[0][0] * m[1][1] - m[0][1] * m[1][0])))
return (r * (1 / matrix_determinant(m)))
# returns a list of all loops parallel to the input, input included
def get_parallel_loops(bm_mod, loops):
# get required dictionaries
edge_faces = dict_edge_faces(bm_mod)
connected_faces = dict_face_faces(bm_mod, edge_faces)
# turn vertex loops into edge loops
edgeloops = []
for loop in loops:
edgeloop = [[sorted([loop[0][i], loop[0][i + 1]]) for i in
range(len(loop[0]) - 1)], loop[1]]
if loop[1]: # circular
edgeloop[0].append(sorted([loop[0][-1], loop[0][0]]))
edgeloops.append(edgeloop[:])
# variables to keep track while iterating
all_edgeloops = []
has_branches = False
for loop in edgeloops:
# initialise with original loop
all_edgeloops.append(loop[0])
newloops = [loop[0]]
verts_used = []
for edge in loop[0]:
if edge[0] not in verts_used:
verts_used.append(edge[0])
if edge[1] not in verts_used:
verts_used.append(edge[1])
# find parallel loops
while len(newloops) > 0:
side_a = []
side_b = []
for i in newloops[-1]:
i = tuple(i)
forbidden_side = False
if i not in edge_faces:
# weird input with branches
has_branches = True
break
for face in edge_faces[i]:
if len(side_a) == 0 and forbidden_side != "a":
side_a.append(face)
if forbidden_side:
break
forbidden_side = "a"
continue
elif side_a[-1] in connected_faces[face] and \
forbidden_side != "a":
side_a.append(face)
if forbidden_side:
break
forbidden_side = "a"
continue
if len(side_b) == 0 and forbidden_side != "b":
side_b.append(face)
if forbidden_side:
break
forbidden_side = "b"
continue
elif side_b[-1] in connected_faces[face] and \
forbidden_side != "b":
side_b.append(face)
if forbidden_side:
break
forbidden_side = "b"
continue
if has_branches:
# weird input with branches
break
newloops.pop(-1)
sides = []
if side_a:
sides.append(side_a)
if side_b:
sides.append(side_b)
for side in sides:
extraloop = []
for fi in side:
for key in face_edgekeys(bm_mod.faces[fi]):
if key[0] not in verts_used and key[1] not in \
verts_used:
extraloop.append(key)
break
if extraloop:
for key in extraloop:
for new_vert in key:
if new_vert not in verts_used:
verts_used.append(new_vert)
newloops.append(extraloop)
all_edgeloops.append(extraloop)
# input contains branches, only return selected loop
if has_branches:
return(loops)
# change edgeloops into normal loops
loops = []
for edgeloop in all_edgeloops:
loop = []
# grow loop by comparing vertices between consecutive edge-keys
for i in range(len(edgeloop) - 1):
for vert in range(2):
if edgeloop[i][vert] in edgeloop[i + 1]:
loop.append(edgeloop[i][vert])
break
if loop:
# add starting vertex
for vert in range(2):
if edgeloop[0][vert] != loop[0]:
loop = [edgeloop[0][vert]] + loop
break
# add ending vertex
for vert in range(2):
if edgeloop[-1][vert] != loop[-1]:
loop.append(edgeloop[-1][vert])
break
# check if loop is circular
if loop[0] == loop[-1]:
circular = True
loop = loop[:-1]
else:
circular = False
loops.append([loop, circular])
return(loops)
# gather initial data
def initialise():
global_undo = bpy.context.user_preferences.edit.use_global_undo
bpy.context.user_preferences.edit.use_global_undo = False
object = bpy.context.active_object
if 'MIRROR' in [mod.type for mod in object.modifiers if mod.show_viewport]:
# ensure that selection is synced for the derived mesh
bpy.ops.object.mode_set(mode='OBJECT')
bpy.ops.object.mode_set(mode='EDIT')
bm = bmesh.from_edit_mesh(object.data)
bm.verts.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.faces.ensure_lookup_table()
return(global_undo, object, bm)
# move the vertices to their new locations
def move_verts(object, bm, mapping, move, lock, influence):
if lock:
lock_x, lock_y, lock_z = lock
orientation = bpy.context.space_data.transform_orientation
custom = bpy.context.space_data.current_orientation
if custom:
mat = custom.matrix.to_4x4().inverted() * object.matrix_world.copy()
elif orientation == 'LOCAL':
mat = mathutils.Matrix.Identity(4)
elif orientation == 'VIEW':
mat = bpy.context.region_data.view_matrix.copy() * \
object.matrix_world.copy()
else: # orientation == 'GLOBAL'
mat = object.matrix_world.copy()
mat_inv = mat.inverted()
for loop in move:
for index, loc in loop:
if mapping:
if mapping[index] == -1:
continue
else:
index = mapping[index]
if lock:
delta = (loc - bm.verts[index].co) * mat_inv
if lock_x:
delta[0] = 0
if lock_y:
delta[1] = 0
if lock_z:
delta[2] = 0
delta = delta * mat
loc = bm.verts[index].co + delta
if influence < 0:
new_loc = loc
else:
new_loc = loc * (influence / 100) + \
bm.verts[index].co * ((100 - influence) / 100)
bm.verts[index].co = new_loc
bm.normal_update()
object.data.update()
bm.verts.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.faces.ensure_lookup_table()
# load custom tool settings
def settings_load(self):
lt = bpy.context.window_manager.looptools
tool = self.name.split()[0].lower()
keys = self.as_keywords().keys()
for key in keys:
setattr(self, key, getattr(lt, tool + "_" + key))
# store custom tool settings
def settings_write(self):
lt = bpy.context.window_manager.looptools
tool = self.name.split()[0].lower()
keys = self.as_keywords().keys()
for key in keys:
setattr(lt, tool + "_" + key, getattr(self, key))
# clean up and set settings back to original state
def terminate(global_undo):
# update editmesh cached data
obj = bpy.context.active_object
if obj.mode == 'EDIT':
bmesh.update_edit_mesh(obj.data, tessface=True, destructive=True)
bpy.context.user_preferences.edit.use_global_undo = global_undo
# ########################################
# ##### Bridge functions #################
# ########################################
# calculate a cubic spline through the middle section of 4 given coordinates
def bridge_calculate_cubic_spline(bm, coordinates):
result = []
x = [0, 1, 2, 3]
for j in range(3):
a = []
for i in coordinates:
a.append(float(i[j]))
h = []
for i in range(3):
h.append(x[i + 1] - x[i])
q = [False]
for i in range(1, 3):
q.append(3.0 / h[i] * (a[i + 1] - a[i]) - 3.0 / h[i - 1] * (a[i] - a[i - 1]))
l = [1.0]
u = [0.0]
z = [0.0]
for i in range(1, 3):
l.append(2.0 * (x[i + 1] - x[i - 1]) - h[i - 1] * u[i - 1])
u.append(h[i] / l[i])
z.append((q[i] - h[i - 1] * z[i - 1]) / l[i])
l.append(1.0)
z.append(0.0)
b = [False for i in range(3)]
c = [False for i in range(4)]
d = [False for i in range(3)]
c[3] = 0.0
for i in range(2, -1, -1):
c[i] = z[i] - u[i] * c[i + 1]
b[i] = (a[i + 1] - a[i]) / h[i] - h[i] * (c[i + 1] + 2.0 * c[i]) / 3.0
d[i] = (c[i + 1] - c[i]) / (3.0 * h[i])
for i in range(3):
result.append([a[i], b[i], c[i], d[i], x[i]])
spline = [result[1], result[4], result[7]]
return(spline)
# return a list with new vertex location vectors, a list with face vertex
# integers, and the highest vertex integer in the virtual mesh
def bridge_calculate_geometry(bm, lines, vertex_normals, segments,
interpolation, cubic_strength, min_width, max_vert_index):
new_verts = []
faces = []
# calculate location based on interpolation method
def get_location(line, segment, splines):
v1 = bm.verts[lines[line][0]].co
v2 = bm.verts[lines[line][1]].co
if interpolation == 'linear':
return v1 + (segment / segments) * (v2 - v1)
else: # interpolation == 'cubic'
m = (segment / segments)
ax, bx, cx, dx, tx = splines[line][0]
x = ax + bx * m + cx * m ** 2 + dx * m ** 3
ay, by, cy, dy, ty = splines[line][1]
y = ay + by * m + cy * m ** 2 + dy * m ** 3
az, bz, cz, dz, tz = splines[line][2]
z = az + bz * m + cz * m ** 2 + dz * m ** 3
return mathutils.Vector((x, y, z))
# no interpolation needed
if segments == 1:
for i, line in enumerate(lines):
if i < len(lines) - 1:
faces.append([line[0], lines[i + 1][0], lines[i + 1][1], line[1]])
# more than 1 segment, interpolate
else:
# calculate splines (if necessary) once, so no recalculations needed
if interpolation == 'cubic':
splines = []
for line in lines:
v1 = bm.verts[line[0]].co
v2 = bm.verts[line[1]].co
size = (v2 - v1).length * cubic_strength
splines.append(bridge_calculate_cubic_spline(bm,
[v1 + size * vertex_normals[line[0]], v1, v2,
v2 + size * vertex_normals[line[1]]]))
else:
splines = False
# create starting situation
virtual_width = [(bm.verts[lines[i][0]].co -
bm.verts[lines[i + 1][0]].co).length for i
in range(len(lines) - 1)]
new_verts = [get_location(0, seg, splines) for seg in range(1,
segments)]
first_line_indices = [i for i in range(max_vert_index + 1,
max_vert_index + segments)]
prev_verts = new_verts[:] # vertex locations of verts on previous line
prev_vert_indices = first_line_indices[:]
max_vert_index += segments - 1 # highest vertex index in virtual mesh
next_verts = [] # vertex locations of verts on current line
next_vert_indices = []
for i, line in enumerate(lines):
if i < len(lines) - 1:
v1 = line[0]
v2 = lines[i + 1][0]
end_face = True
for seg in range(1, segments):
loc1 = prev_verts[seg - 1]
loc2 = get_location(i + 1, seg, splines)
if (loc1 - loc2).length < (min_width / 100) * virtual_width[i] \
and line[1] == lines[i + 1][1]:
# triangle, no new vertex
faces.append([v1, v2, prev_vert_indices[seg - 1],
prev_vert_indices[seg - 1]])
next_verts += prev_verts[seg - 1:]
next_vert_indices += prev_vert_indices[seg - 1:]
end_face = False
break
else:
if i == len(lines) - 2 and lines[0] == lines[-1]:
# quad with first line, no new vertex
faces.append([v1, v2, first_line_indices[seg - 1],
prev_vert_indices[seg - 1]])
v2 = first_line_indices[seg - 1]
v1 = prev_vert_indices[seg - 1]
else:
# quad, add new vertex
max_vert_index += 1
faces.append([v1, v2, max_vert_index,
prev_vert_indices[seg - 1]])
v2 = max_vert_index
v1 = prev_vert_indices[seg - 1]
new_verts.append(loc2)
next_verts.append(loc2)
next_vert_indices.append(max_vert_index)
if end_face:
faces.append([v1, v2, lines[i + 1][1], line[1]])
prev_verts = next_verts[:]
prev_vert_indices = next_vert_indices[:]
next_verts = []
next_vert_indices = []
return(new_verts, faces, max_vert_index)
# calculate lines (list of lists, vertex indices) that are used for bridging
def bridge_calculate_lines(bm, loops, mode, twist, reverse):
lines = []
loop1, loop2 = [i[0] for i in loops]
loop1_circular, loop2_circular = [i[1] for i in loops]
circular = loop1_circular or loop2_circular
circle_full = False
# calculate loop centers
centers = []
for loop in [loop1, loop2]:
center = mathutils.Vector()
for vertex in loop:
center += bm.verts[vertex].co
center /= len(loop)
centers.append(center)