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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",
"location": "View3D > Sidebar > Edit Tab / Edit Mode Context Menu",
"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.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_strokes(self, context):
looptools = context.window_manager.looptools
if looptools.gstretch_use_guide == "Annotation":
try:
strokes = bpy.data.grease_pencils[0].layers.active.active_frame.strokes
return True
except:
self.report({'WARNING'}, "active Annotation strokes not found")
return False
if looptools.gstretch_use_guide == "GPencil" and not looptools.gstretch_guide == None:
try:
strokes = looptools.gstretch_guide.data.layers.active.active_frame.strokes
return True
except:
self.report({'WARNING'}, "active GPencil strokes not found")
return False
else:
return False
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# 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"]
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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']
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_new2 = []
for k in range(4):
if k + 1 > len(knots) - 1:
k -= len(knots)
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
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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:
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])
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)
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]
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return(splines)
# calculates linear splines through all given knots
def calculate_linear_splines(bm_mod, tknots, knots):
splines = []
a = bm_mod.verts[knots[i]].co
b = bm_mod.verts[knots[i + 1]].co
d = b - a
u = tknots[i + 1] - t
splines.append([a, d, t, u]) # [locStart, locDif, tStart, tDif]
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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]]
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# calculating the center of masss
com = mathutils.Vector()
for loc in locs:
com += loc
com /= len(locs)
x, y, z = com
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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
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# calculating the normal to the plane
normal = False
try:
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))
normal = mathutils.Vector((0.0, 1.0, 0.0))
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):
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
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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()
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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))
normal = object.matrix_world.inverted().to_euler().to_matrix() @ \
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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[:])
splines = calculate_linear_splines(bm_mod, tknots, knots[:])
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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:
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continue
# passed all tests, loop is valid
valid_loops.append([loop, circular])
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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)
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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)
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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)
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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)
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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)
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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])
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return(vert_verts)
# return the edgekey ([v1.index, v2.index]) of a bmesh edge
def edgekey(edge):
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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, input):
# get mesh with modifiers applied
derived, bm_mod = get_derived_bmesh(object, bm)
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# 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)
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# if only selected loops are needed, we're done
if input == 'selected':
return(derived, bm_mod, loops)
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# elif input == 'all':
loops = get_parallel_loops(bm_mod, loops)
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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)
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# find loops consisting of connected selected edges
loops = []
while len(vert_verts) > 0:
loop = [iter(vert_verts.keys()).__next__()]
growing = True
flipped = False
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# 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
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# 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]
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loops.append(loop)
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return(loops)
# get the derived mesh data, if there is a mirror modifier
def get_derived_bmesh(object, bm):
# 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()
depsgraph = bpy.context.evaluated_depsgraph_get()
object_eval = object.evaluated_get(depsgraph)
mesh_mod = object_eval.to_mesh()
bm_mod.from_mesh(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
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bm_mod.verts.ensure_lookup_table()
bm_mod.edges.ensure_lookup_table()
bm_mod.faces.ensure_lookup_table()
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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)
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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]
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# 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]
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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 not in verts:
verts.append(v)
break
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# 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
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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])))
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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
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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])
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# find parallel loops
while len(newloops) > 0:
side_a = []
side_b = []
for i in newloops[-1]:
i = tuple(i)
forbidden_side = False
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# 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
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if has_branches:
# weird input with branches
break
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newloops.pop(-1)
sides = []
if side_a:
sides.append(side_a)
if side_b:
sides.append(side_b)
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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)
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# input contains branches, only return selected loop
if has_branches:
return(loops)
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# change edgeloops into normal loops
loops = []
for edgeloop in all_edgeloops:
loop = []
# grow loop by comparing vertices between consecutive edge-keys
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])
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return(loops)
# gather initial data
def initialise():
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)
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bm.verts.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.faces.ensure_lookup_table()
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return(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
orient_slot = bpy.context.scene.transform_orientation_slots[0]
custom = orient_slot.custom_orientation
mat = custom.matrix.to_4x4().inverted() @ object.matrix_world.copy()
elif orient_slot.type == 'LOCAL':
elif orient_slot.type == 'VIEW':
mat = bpy.context.region_data.view_matrix.copy() @ \
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]
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
new_loc = loc * (influence / 100) + \
bm.verts[index].co * ((100 - influence) / 100)
bm.normal_update()
object.data.update()
bm.verts.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.faces.ensure_lookup_table()
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# 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():
# update editmesh cached data
obj = bpy.context.active_object
if obj.mode == 'EDIT':
bmesh.update_edit_mesh(obj.data, loop_triangles=True, destructive=True)
# ########################################
# ##### 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]
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for j in range(3):
a = []
for i in coordinates:
a.append(float(i[j]))
h = []
for i in range(3):
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)
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# 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 = []
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# 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))
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# 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
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# 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)]
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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 = []
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for i, line in enumerate(lines):
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,
v2 = max_vert_index
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]])
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prev_verts = next_verts[:]
prev_vert_indices = next_vert_indices[:]
next_verts = []
next_vert_indices = []
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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
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# 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)
for i, loop in enumerate([loop1, loop2]):
for vertex in loop:
if bm.verts[vertex].co == centers[i]:
# prevent zero-length vectors in angle comparisons
centers[i] += mathutils.Vector((0.01, 0, 0))
break
center1, center2 = centers
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# calculate the normals of the virtual planes that the loops are on
normals = []
normal_plurity = False
for i, loop in enumerate([loop1, loop2]):
# covariance matrix
mat = mathutils.Matrix(((0.0, 0.0, 0.0),
(0.0, 0.0, 0.0),
(0.0, 0.0, 0.0)))
x, y, z = centers[i]
for loc in [bm.verts[vertex].co for vertex in loop]:
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
# plane normal
normal = False
if sum(mat[0]) < 1e-6 or sum(mat[1]) < 1e-6 or sum(mat[2]) < 1e-6:
normal_plurity = True
try:
mat.invert()
except:
if sum(mat[0]) == 0:
normal = mathutils.Vector((1.0, 0.0, 0.0))
elif sum(mat[1]) == 0:
normal = mathutils.Vector((0.0, 1.0, 0.0))
elif sum(mat[2]) == 0:
normal = mathutils.Vector((0.0, 0.0, 1.0))
if not normal:
# warning! this is different from .normalize()
itermax = 500
iter = 0
vec = mathutils.Vector((1.0, 1.0, 1.0))
while vec != vec2 and iter < itermax:
iter += 1
if vec2.length != 0:
vec2 /= vec2.length
if vec2.length == 0:
vec2 = mathutils.Vector((1.0, 1.0, 1.0))
normal = vec2
normals.append(normal)
# have plane normals face in the same direction (maximum angle: 90 degrees)
if ((center1 + normals[0]) - center2).length < \
((center1 - normals[0]) - center2).length:
normals[0].negate()
if ((center2 + normals[1]) - center1).length > \
((center2 - normals[1]) - center1).length:
normals[1].negate()
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# rotation matrix, representing the difference between the plane normals
axis = normals[0].cross(normals[1])
axis = mathutils.Vector([loc if abs(loc) > 1e-8 else 0 for loc in axis])
if axis.angle(mathutils.Vector((0, 0, 1)), 0) > 1.5707964:
axis.negate()
angle = normals[0].dot(normals[1])
rotation_matrix = mathutils.Matrix.Rotation(angle, 4, axis)
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# if circular, rotate loops so they are aligned
if circular:
# make sure loop1 is the circular one (or both are circular)
if loop2_circular and not loop1_circular:
loop1_circular, loop2_circular = True, False
loop1, loop2 = loop2, loop1
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# match start vertex of loop1 with loop2
target_vector = bm.verts[loop2[0]].co - center2
dif_angles = [[(rotation_matrix @ (bm.verts[vertex].co - center1)
).angle(target_vector, 0), False, i] for
i, vertex in enumerate(loop1)]
dif_angles.sort()
if len(loop1) != len(loop2):
angle_limit = dif_angles[0][0] * 1.2 # 20% margin
dif_angles = [
[(bm.verts[loop2[0]].co -
bm.verts[loop1[index]].co).length, angle, index] for
angle, distance, index in dif_angles if angle <= angle_limit
]
dif_angles.sort()
loop1 = loop1[dif_angles[0][2]:] + loop1[:dif_angles[0][2]]
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# have both loops face the same way
if normal_plurity and not circular:
second_to_first, second_to_second, second_to_last = [
(bm.verts[loop1[1]].co - center1).angle(
bm.verts[loop2[i]].co - center2) for i in [0, 1, -1]
]
last_to_first, last_to_second = [
(bm.verts[loop1[-1]].co -
center1).angle(bm.verts[loop2[i]].co - center2) for
i in [0, 1]
]
if (min(last_to_first, last_to_second) * 1.1 < min(second_to_first,
second_to_second)) or (loop2_circular and second_to_last * 1.1 <
min(second_to_first, second_to_second)):
loop1.reverse()
if circular:
loop1 = [loop1[-1]] + loop1[:-1]
else:
angle = (bm.verts[loop1[0]].co - center1).\
cross(bm.verts[loop1[1]].co - center1).angle(normals[0], 0)
target_angle = (bm.verts[loop2[0]].co - center2).\
cross(bm.verts[loop2[1]].co - center2).angle(normals[1], 0)
limit = 1.5707964 # 0.5*pi, 90 degrees
if not ((angle > limit and target_angle > limit) or
(angle < limit and target_angle < limit)):
loop1.reverse()
if circular:
loop1 = [loop1[-1]] + loop1[:-1]
elif normals[0].angle(normals[1]) > limit:
loop1.reverse()
if circular:
loop1 = [loop1[-1]] + loop1[:-1]
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# both loops have the same length
if len(loop1) == len(loop2):
# manual override
if twist:
if abs(twist) < len(loop1):
loop1 = loop1[twist:] + loop1[:twist]
if reverse:
loop1.reverse()
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lines.append([loop1[0], loop2[0]])
for i in range(1, len(loop1)):
lines.append([loop1[i], loop2[i]])
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# loops of different lengths
else:
# make loop1 longest loop
if len(loop2) > len(loop1):
loop1, loop2 = loop2, loop1
loop1_circular, loop2_circular = loop2_circular, loop1_circular
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# manual override
if twist:
if abs(twist) < len(loop1):
loop1 = loop1[twist:] + loop1[:twist]
if reverse:
loop1.reverse()
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# shortest angle difference doesn't always give correct start vertex
if loop1_circular and not loop2_circular:
shifting = 1
while shifting:
if len(loop1) - shifting < len(loop2):
shifting = False
break
(rotation_matrix @ (bm.verts[loop1[-1]].co - center1)).angle(
(bm.verts[loop2[i]].co - center2), 0) for i in [-1, 0]
]
if to_first < to_last:
loop1 = [loop1[-1]] + loop1[:-1]
shifting += 1
else:
shifting = False
break
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# basic shortest side first
if mode == 'basic':
lines.append([loop1[0], loop2[0]])
for i in range(1, len(loop1)):
if i >= len(loop2) - 1:
# triangles
lines.append([loop1[i], loop2[-1]])
else:
# quads
lines.append([loop1[i], loop2[i]])
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# shortest edge algorithm
lines.append([loop1[0], loop2[0]])
prev_vert2 = 0
if prev_vert2 == len(loop2) - 1 and not loop2_circular:
# force triangles, reached end of loop2
tri, quad = 0, 1
elif prev_vert2 == len(loop2) - 1 and loop2_circular:
# at end of loop2, but circular, so check with first vert
tri, quad = [(bm.verts[loop1[i + 1]].co -
bm.verts[loop2[j]].co).length
for j in [prev_vert2, 0]]
circle_full = 2
elif len(loop1) - 1 - i == len(loop2) - 1 - prev_vert2 and \
not circle_full:
# force quads, otherwise won't make it to end of loop2
tri, quad = 1, 0
else:
# calculate if tri or quad gives shortest edge
tri, quad = [(bm.verts[loop1[i + 1]].co -
bm.verts[loop2[j]].co).length
for j in range(prev_vert2, prev_vert2 + 2)]
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# triangle
if tri < quad:
lines.append([loop1[i + 1], loop2[prev_vert2]])
if circle_full == 2:
circle_full = False
# quad
elif not circle_full:
lines.append([loop1[i + 1], loop2[prev_vert2 + 1]])
prev_vert2 += 1
# quad to first vertex of loop2
else:
lines.append([loop1[i + 1], loop2[0]])
prev_vert2 = 0
circle_full = True
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# final face for circular loops
if loop1_circular and loop2_circular:
lines.append([loop1[0], loop2[0]])
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return(lines)
# calculate number of segments needed
def bridge_calculate_segments(bm, lines, loops, segments):
# return if amount of segments is set by user
if segments != 0:
return segments
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average_edge_length = [
(bm.verts[vertex].co -
bm.verts[loop[0][i + 1]].co).length for loop in loops for
i, vertex in enumerate(loop[0][:-1])
]
# closing edges of circular loops
average_edge_length += [
(bm.verts[loop[0][-1]].co -
bm.verts[loop[0][0]].co).length for loop in loops if loop[1]
]
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# average lengths
average_edge_length = sum(average_edge_length) / len(average_edge_length)
average_bridge_length = sum(
[(bm.verts[v1].co -
bm.verts[v2].co).length for v1, v2 in lines]
) / len(lines)
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segments = max(1, round(average_bridge_length / average_edge_length))
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return(segments)
# return dictionary with vertex index as key, and the normal vector as value
def bridge_calculate_virtual_vertex_normals(bm, lines, loops, edge_faces,
edgekey_to_edge):
if not edge_faces: # interpolation isn't set to cubic
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# pity reduce() isn't one of the basic functions in python anymore
def average_vector_dictionary(dic):
for key, vectors in dic.items():
# if type(vectors) == type([]) and len(vectors) > 1:
if len(vectors) > 1:
average = mathutils.Vector()
for vector in vectors:
average += vector
average /= len(vectors)
dic[key] = [average]
return dic
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# get all edges of the loop
edges = [
[edgekey_to_edge[tuple(sorted([loops[j][0][i],
loops[j][0][i + 1]]))] for i in range(len(loops[j][0]) - 1)] for
j in [0, 1]
]
edges = edges[0] + edges[1]
for j in [0, 1]:
edges.append(edgekey_to_edge[tuple(sorted([loops[j][0][0],
loops[j][0][-1]]))])
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"""
calculation based on face topology (assign edge-normals to vertices)
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edge_normal = face_normal x edge_vector
vertex_normal = average(edge_normals)
"""
vertex_normals = dict([(vertex, []) for vertex in loops[0][0] + loops[1][0]])
for edge in edges:
faces = edge_faces[edgekey(edge)] # valid faces connected to edge
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if faces:
# get edge coordinates
v1, v2 = [bm.verts[edgekey(edge)[i]].co for i in [0, 1]]
edge_vector = v1 - v2
if edge_vector.length < 1e-4:
# zero-length edge, vertices at same location
continue
edge_center = (v1 + v2) / 2
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# average face coordinates, if connected to more than 1 valid face
if len(faces) > 1:
face_normal = mathutils.Vector()
face_center = mathutils.Vector()
for face in faces:
face_normal += face.normal
face_center += face.calc_center_median()
face_normal /= len(faces)
face_center /= len(faces)
else:
face_normal = faces[0].normal
face_center = faces[0].calc_center_median()
if face_normal.length < 1e-4:
# faces with a surface of 0 have no face normal
continue
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# calculate virtual edge normal
edge_normal = edge_vector.cross(face_normal)
edge_normal.length = 0.01
if (face_center - (edge_center + edge_normal)).length > \
(face_center - (edge_center - edge_normal)).length:
# make normal face the correct way
edge_normal.negate()
edge_normal.normalize()
# add virtual edge normal as entry for both vertices it connects
for vertex in edgekey(edge):
vertex_normals[vertex].append(edge_normal)
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"""
calculation based on connection with other loop (vertex focused method)
- used for vertices that aren't connected to any valid faces
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plane_normal = edge_vector x connection_vector
vertex_normal = plane_normal x edge_vector
"""
vertices = [
vertex for vertex, normal in vertex_normals.items() if not normal
]
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if vertices:
# edge vectors connected to vertices
edge_vectors = dict([[vertex, []] for vertex in vertices])
for edge in edges:
for v in edgekey(edge):
if v in edge_vectors:
edge_vector = bm.verts[edgekey(edge)[0]].co - \
bm.verts[edgekey(edge)[1]].co
if edge_vector.length < 1e-4:
# zero-length edge, vertices at same location
continue
edge_vectors[v].append(edge_vector)
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# connection vectors between vertices of both loops
connection_vectors = dict([[vertex, []] for vertex in vertices])
connections = dict([[vertex, []] for vertex in vertices])
for v1, v2 in lines:
if v1 in connection_vectors or v2 in connection_vectors:
new_vector = bm.verts[v1].co - bm.verts[v2].co
if new_vector.length < 1e-4:
# zero-length connection vector,
# vertices in different loops at same location
continue
if v1 in connection_vectors:
connection_vectors[v1].append(new_vector)
connections[v1].append(v2)
if v2 in connection_vectors:
connection_vectors[v2].append(new_vector)
connections[v2].append(v1)
connection_vectors = average_vector_dictionary(connection_vectors)
connection_vectors = dict(
[[vertex, vector[0]] if vector else
[vertex, []] for vertex, vector in connection_vectors.items()]
)
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for vertex, values in edge_vectors.items():
# vertex normal doesn't matter, just assign a random vector to it
if not connection_vectors[vertex]:
vertex_normals[vertex] = [mathutils.Vector((1, 0, 0))]
continue
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# calculate to what location the vertex is connected,
# used to determine what way to flip the normal
connected_center = mathutils.Vector()
for v in connections[vertex]:
connected_center += bm.verts[v].co
if len(connections[vertex]) > 1:
connected_center /= len(connections[vertex])
if len(connections[vertex]) == 0:
# shouldn't be possible, but better safe than sorry
vertex_normals[vertex] = [mathutils.Vector((1, 0, 0))]
continue
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# can't do proper calculations, because of zero-length vector
if not values:
if (connected_center - (bm.verts[vertex].co +
connection_vectors[vertex])).length < (connected_center -
(bm.verts[vertex].co - connection_vectors[vertex])).length:
connection_vectors[vertex].negate()
vertex_normals[vertex] = [connection_vectors[vertex].normalized()]
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# calculate vertex normals using edge-vectors,
# connection-vectors and the derived plane normal
for edge_vector in values:
plane_normal = edge_vector.cross(connection_vectors[vertex])
vertex_normal = edge_vector.cross(plane_normal)
vertex_normal.length = 0.1
if (connected_center - (bm.verts[vertex].co +
vertex_normal)).length < (connected_center -
(bm.verts[vertex].co - vertex_normal)).length:
# make normal face the correct way
vertex_normal.negate()
vertex_normal.normalize()
vertex_normals[vertex].append(vertex_normal)
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# average virtual vertex normals, based on all edges it's connected to
vertex_normals = average_vector_dictionary(vertex_normals)
vertex_normals = dict([[vertex, vector[0]] for vertex, vector in vertex_normals.items()])
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return(vertex_normals)
# add vertices to mesh
def bridge_create_vertices(bm, vertices):
for i in range(len(vertices)):
bm.verts.new(vertices[i])
# add faces to mesh
def bridge_create_faces(object, bm, faces, twist):
# have the normal point the correct way
if twist < 0:
[face.reverse() for face in faces]
faces = [face[2:] + face[:2] if face[0] == face[1] else face for face in faces]
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# eekadoodle prevention
for i in range(len(faces)):
if not faces[i][-1]:
if faces[i][0] == faces[i][-1]:
faces[i] = [faces[i][1], faces[i][2], faces[i][3], faces[i][1]]
else:
faces[i] = [faces[i][-1]] + faces[i][:-1]
# result of converting from pre-bmesh period
if faces[i][-1] == faces[i][-2]:
faces[i] = faces[i][:-1]
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for i in range(len(faces)):
new_faces.append(bm.faces.new([bm.verts[v] for v in faces[i]]))
bm.normal_update()
object.data.update(calc_edges=True) # calc_edges prevents memory-corruption
bm.verts.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.faces.ensure_lookup_table()
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# calculate input loops
def bridge_get_input(bm):
# create list of internal edges, which should be skipped
eks_of_selected_faces = [
item for sublist in [face_edgekeys(face) for
face in bm.faces if face.select and not face.hide] for item in sublist
]
edge_count = {}
for ek in eks_of_selected_faces:
if ek in edge_count:
edge_count[ek] += 1
else:
edge_count[ek] = 1
internal_edges = [ek for ek in edge_count if edge_count[ek] > 1]
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# sort correct edges into loops
selected_edges = [
edgekey(edge) for edge in bm.edges if edge.select and
not edge.hide and edgekey(edge) not in internal_edges
]
loops = get_connected_selections(selected_edges)
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return(loops)
# return values needed by the bridge operator
def bridge_initialise(bm, interpolation):
if interpolation == 'cubic':
# dict with edge-key as key and list of connected valid faces as value
face_blacklist = [
face.index for face in bm.faces if face.select or
face.hide
]
edge_faces = dict(
[[edgekey(edge), []] for edge in bm.edges if not edge.hide]
)
for face in bm.faces:
if face.index in face_blacklist:
continue
for key in face_edgekeys(face):
edge_faces[key].append(face)
# dictionary with the edge-key as key and edge as value
edgekey_to_edge = dict(
[[edgekey(edge), edge] for edge in bm.edges if edge.select and not edge.hide]
)
else:
edge_faces = False
edgekey_to_edge = False
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# selected faces input
old_selected_faces = [
face.index for face in bm.faces if face.select and not face.hide
]
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# find out if faces created by bridging should be smoothed
smooth = False
if bm.faces:
if sum([face.smooth for face in bm.faces]) / len(bm.faces) >= 0.5:
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return(edge_faces, edgekey_to_edge, old_selected_faces, smooth)
# return a string with the input method
def bridge_input_method(loft, loft_loop):
method = ""
if loft:
if loft_loop:
method = "Loft loop"
else:
method = "Loft no-loop"
else:
method = "Bridge"
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return(method)
# match up loops in pairs, used for multi-input bridging
def bridge_match_loops(bm, loops):
# calculate average loop normals and centers
normals = []
centers = []
for vertices, circular in loops:
normal = mathutils.Vector()
center = mathutils.Vector()
for vertex in vertices:
normal += bm.verts[vertex].normal
center += bm.verts[vertex].co
normals.append(normal / len(vertices) / 10)
centers.append(center / len(vertices))
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# possible matches if loop normals are faced towards the center
# of the other loop
matches = dict([[i, []] for i in range(len(loops))])
matches_amount = 0
for i in range(len(loops) + 1):
for j in range(i + 1, len(loops)):
if (centers[i] - centers[j]).length > \
(centers[i] - (centers[j] + normals[j])).length and \
(centers[j] - centers[i]).length > \
(centers[j] - (centers[i] + normals[i])).length:
matches_amount += 1
matches[i].append([(centers[i] - centers[j]).length, i, j])
matches[j].append([(centers[i] - centers[j]).length, j, i])
# if no loops face each other, just make matches between all the loops
if matches_amount == 0:
for i in range(len(loops) + 1):
for j in range(i + 1, len(loops)):
matches[i].append([(centers[i] - centers[j]).length, i, j])
matches[j].append([(centers[i] - centers[j]).length, j, i])
for key, value in matches.items():
value.sort()
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# matches based on distance between centers and number of vertices in loops
new_order = []
for loop_index in range(len(loops)):
if loop_index in new_order:
continue
loop_matches = matches[loop_index]
if not loop_matches:
continue
shortest_distance = loop_matches[0][0]
shortest_distance *= 1.1
loop_matches = [
[abs(len(loops[loop_index][0]) -
len(loops[loop[2]][0])), loop[0], loop[1], loop[2]] for loop in
loop_matches if loop[0] < shortest_distance
]
loop_matches.sort()
for match in loop_matches:
if match[3] not in new_order:
new_order += [loop_index, match[3]]
break
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# reorder loops based on matches
if len(new_order) >= 2:
loops = [loops[i] for i in new_order]
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return(loops)
# remove old_selected_faces
def bridge_remove_internal_faces(bm, old_selected_faces):
# collect bmesh faces and internal bmesh edges
remove_faces = [bm.faces[face] for face in old_selected_faces]
edges = collections.Counter(
[edge.index for face in remove_faces for edge in face.edges]
)
remove_edges = [bm.edges[edge] for edge in edges if edges[edge] > 1]
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# remove internal faces and edges
for face in remove_faces:
bm.faces.remove(face)
for edge in remove_edges:
bm.edges.remove(edge)
bm.faces.ensure_lookup_table()
bm.edges.ensure_lookup_table()
bm.verts.ensure_lookup_table()
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# update list of internal faces that are flagged for removal
def bridge_save_unused_faces(bm, old_selected_faces, loops):
# key: vertex index, value: lists of selected faces using it
vertex_to_face = dict([[i, []] for i in range(len(bm.verts))])
[[vertex_to_face[vertex.index].append(face) for vertex in
bm.faces[face].verts] for face in old_selected_faces]
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# group selected faces that are connected
groups = []
grouped_faces = []
for face in old_selected_faces:
if face in grouped_faces:
continue
grouped_faces.append(face)
group = [face]
new_faces = [face]
while new_faces:
grow_face = new_faces[0]
for vertex in bm.faces[grow_face].verts:
vertex_face_group = [
face for face in vertex_to_face[vertex.index] if
face not in grouped_faces
]
new_faces += vertex_face_group
grouped_faces += vertex_face_group
group += vertex_face_group
new_faces.pop(0)
groups.append(group)
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# key: vertex index, value: True/False (is it in a loop that is used)
used_vertices = dict([[i, 0] for i in range(len(bm.verts))])
for loop in loops:
for vertex in loop[0]:
used_vertices[vertex] = True
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# check if group is bridged, if not remove faces from internal faces list
for group in groups:
used = False
for face in group:
if used:
break
for vertex in bm.faces[face].verts:
if used_vertices[vertex.index]:
used = True
break
if not used:
for face in group:
old_selected_faces.remove(face)
# add the newly created faces to the selection
def bridge_select_new_faces(new_faces, smooth):
for face in new_faces:
face.select_set(True)
face.smooth = smooth
# sort loops, so they are connected in the correct order when lofting
def bridge_sort_loops(bm, loops, loft_loop):
# simplify loops to single points, and prepare for pathfinding
x, y, z = [
[sum([bm.verts[i].co[j] for i in loop[0]]) /
len(loop[0]) for loop in loops] for j in range(3)
]
nodes = [mathutils.Vector((x[i], y[i], z[i])) for i in range(len(loops))]
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active_node = 0
open = [i for i in range(1, len(loops))]
# connect node to path, that is shortest to active_node
while len(open) > 0:
distances = [(nodes[active_node] - nodes[i]).length for i in open]
active_node = open[distances.index(min(distances))]
open.remove(active_node)
path.append([active_node, min(distances)])
# check if we didn't start in the middle of the path
for i in range(2, len(path)):
if (nodes[path[i][0]] - nodes[0]).length < path[i][1]:
temp = path[:i]
path.reverse()
path = path[:-i] + temp
break
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# reorder loops
loops = [loops[i[0]] for i in path]
# if requested, duplicate first loop at last position, so loft can loop
if loft_loop:
loops = loops + [loops[0]]
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return(loops)
# remapping old indices to new position in list
def bridge_update_old_selection(bm, old_selected_faces):
"""
old_indices = old_selected_faces[:]
old_selected_faces = []
for i, face in enumerate(bm.faces):
if face.index in old_indices:
old_selected_faces.append(i)
"""
old_selected_faces = [
i for i, face in enumerate(bm.faces) if face.index in old_selected_faces
]
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return(old_selected_faces)
# ########################################
# ##### Circle functions #################
# ########################################
# convert 3d coordinates to 2d coordinates on plane
def circle_3d_to_2d(bm_mod, loop, com, normal):
# project vertices onto the plane
verts = [bm_mod.verts[v] for v in loop[0]]
verts_projected = [[v.co - (v.co - com).dot(normal) * normal, v.index]
for v in verts]
# calculate two vectors (p and q) along the plane
m = mathutils.Vector((normal[0] + 1.0, normal[1], normal[2]))
p = m - (m.dot(normal) * normal)
m = mathutils.Vector((normal[0], normal[1] + 1.0, normal[2]))
p = m - (m.dot(normal) * normal)
q = p.cross(normal)
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# change to 2d coordinates using perpendicular projection
locs_2d = []
for loc, vert in verts_projected:
vloc = loc - com
x = p.dot(vloc) / p.dot(p)
y = q.dot(vloc) / q.dot(q)
locs_2d.append([x, y, vert])
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return(locs_2d, p, q)
# calculate a best-fit circle to the 2d locations on the plane
def circle_calculate_best_fit(locs_2d):
# initial guess
x0 = 0.0
y0 = 0.0
r = 1.0
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# calculate center and radius (non-linear least squares solution)
for iter in range(500):
jmat = []
k = []
for v in locs_2d:
d = (v[0] ** 2 - 2.0 * x0 * v[0] + v[1] ** 2 - 2.0 * y0 * v[1] + x0 ** 2 + y0 ** 2) ** 0.5
jmat.append([(x0 - v[0]) / d, (y0 - v[1]) / d, -1.0])
k.append(-(((v[0] - x0) ** 2 + (v[1] - y0) ** 2) ** 0.5 - r))
jmat2 = mathutils.Matrix(((0.0, 0.0, 0.0),
(0.0, 0.0, 0.0),
(0.0, 0.0, 0.0),
))
k2 = mathutils.Vector((0.0, 0.0, 0.0))
for i in range(len(jmat)):
k2 += mathutils.Vector(jmat[i]) * k[i]
jmat2[0][0] += jmat[i][0] ** 2
jmat2[1][0] += jmat[i][0] * jmat[i][1]
jmat2[2][0] += jmat[i][0] * jmat[i][2]
jmat2[1][1] += jmat[i][1] ** 2
jmat2[2][1] += jmat[i][1] * jmat[i][2]
jmat2[2][2] += jmat[i][2] ** 2
jmat2[0][1] = jmat2[1][0]
jmat2[0][2] = jmat2[2][0]
jmat2[1][2] = jmat2[2][1]
try:
jmat2.invert()
except:
pass
x0 += dx0
y0 += dy0
r += dr
# stop iterating if we're close enough to optimal solution
if abs(dx0) < 1e-6 and abs(dy0) < 1e-6 and abs(dr) < 1e-6:
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# return center of circle and radius
return(x0, y0, r)
# calculate circle so no vertices have to be moved away from the center
def circle_calculate_min_fit(locs_2d):
# center of circle
x0 = (min([i[0] for i in locs_2d]) + max([i[0] for i in locs_2d])) / 2.0
y0 = (min([i[1] for i in locs_2d]) + max([i[1] for i in locs_2d])) / 2.0
center = mathutils.Vector([x0, y0])
# radius of circle
r = min([(mathutils.Vector([i[0], i[1]]) - center).length for i in locs_2d])
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# return center of circle and radius
return(x0, y0, r)
# calculate the new locations of the vertices that need to be moved
def circle_calculate_verts(flatten, bm_mod, locs_2d, com, p, q, normal):
# changing 2d coordinates back to 3d coordinates
locs_3d = []
for loc in locs_2d:
locs_3d.append([loc[2], loc[0] * p + loc[1] * q + com])
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else: # project the locations on the existing mesh
vert_edges = dict_vert_edges(bm_mod)
vert_faces = dict_vert_faces(bm_mod)
faces = [f for f in bm_mod.faces if not f.hide]
rays = [normal, -normal]
new_locs = []
for loc in locs_3d:
projection = False
if bm_mod.verts[loc[0]].co == loc[1]: # vertex hasn't moved
projection = loc[1]
else:
dif = normal.angle(loc[1] - bm_mod.verts[loc[0]].co)
if -1e-6 < dif < 1e-6 or math.pi - 1e-6 < dif < math.pi + 1e-6:
# original location is already along projection normal
projection = bm_mod.verts[loc[0]].co
else:
# quick search through adjacent faces
for face in vert_faces[loc[0]]:
verts = [v.co for v in bm_mod.faces[face].verts]
v1, v2, v3 = verts
v4 = False
v1, v2, v3, v4 = verts[:4]
for ray in rays:
intersect = mathutils.geometry.\
intersect_ray_tri(v1, v2, v3, ray, loc[1])
if intersect:
projection = intersect
break
elif v4:
intersect = mathutils.geometry.\
intersect_ray_tri(v1, v3, v4, ray, loc[1])
if intersect:
projection = intersect
break
if projection:
break
if not projection:
# check if projection is on adjacent edges
for edgekey in vert_edges[loc[0]]:
line1 = bm_mod.verts[edgekey[0]].co
line2 = bm_mod.verts[edgekey[1]].co
intersect, dist = mathutils.geometry.intersect_point_line(
loc[1], line1, line2
)
if 1e-6 < dist < 1 - 1e-6:
projection = intersect
break
if not projection:
# full search through the entire mesh
hits = []
for face in faces:
verts = [v.co for v in face.verts]
v1, v2, v3 = verts
v4 = False
v1, v2, v3, v4 = verts[:4]
for ray in rays:
intersect = mathutils.geometry.intersect_ray_tri(
v1, v2, v3, ray, loc[1]
)
if intersect:
hits.append([(loc[1] - intersect).length,
intersect])
break
elif v4:
intersect = mathutils.geometry.intersect_ray_tri(
v1, v3, v4, ray, loc[1]
)
if intersect:
hits.append([(loc[1] - intersect).length,
intersect])
break
if len(hits) >= 1:
# if more than 1 hit with mesh, closest hit is new loc
hits.sort()
projection = hits[0][1]
if not projection:
# nothing to project on, remain at flat location
projection = loc[1]
new_locs.append([loc[0], projection])
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# return new positions of projected circle
return(new_locs)
# check loops and only return valid ones
def circle_check_loops(single_loops, loops, mapping, bm_mod):
valid_single_loops = {}
valid_loops = []
for i, [loop, circular] in enumerate(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
# loop has to be non-collinear
collinear = True
loc0 = mathutils.Vector(bm_mod.verts[loop[0]].co[:])
loc1 = mathutils.Vector(bm_mod.verts[loop[1]].co[:])
for v in loop[2:]:
locn = mathutils.Vector(bm_mod.verts[v].co[:])
if loc0 == loc1 or loc1 == locn:
loc0 = loc1
loc1 = locn
continue
d1 = loc1 - loc0
d2 = locn - loc1
if -1e-6 < d1.angle(d2, 0) < 1e-6:
loc0 = loc1
loc1 = locn
continue
collinear = False
break
if collinear:
continue
# passed all tests, loop is valid
valid_loops.append([loop, circular])
valid_single_loops[len(valid_loops) - 1] = single_loops[i]
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return(valid_single_loops, valid_loops)
# calculate the location of single input vertices that need to be flattened
def circle_flatten_singles(bm_mod, com, p, q, normal, single_loop):
new_locs = []
for vert in single_loop:
loc = mathutils.Vector(bm_mod.verts[vert].co[:])
new_locs.append([vert, loc - (loc - com).dot(normal) * normal])
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return(new_locs)
# calculate input loops
def circle_get_input(object, bm):
# get mesh with modifiers applied
derived, bm_mod = get_derived_bmesh(object, bm)
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# create list of edge-keys based on selection state
faces = False
for face in bm.faces:
if face.select and not face.hide:
faces = True
break
if faces:
# get selected, non-hidden , non-internal edge-keys
eks_selected = [
key for keys in [face_edgekeys(face) for face in
bm_mod.faces if face.select and not face.hide] for key in keys
]
edge_count = {}
for ek in eks_selected:
if ek in edge_count:
edge_count[ek] += 1
else:
edge_count[ek] = 1
edge_keys = [
edgekey(edge) for edge in bm_mod.edges if edge.select and
not edge.hide and edge_count.get(edgekey(edge), 1) == 1
]
else:
# no faces, so no internal edges either
edge_keys = [
edgekey(edge) for edge in bm_mod.edges if edge.select and not edge.hide
]
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# add edge-keys around single vertices
verts_connected = dict(
[[vert, 1] for edge in [edge for edge in
bm_mod.edges if edge.select and not edge.hide] for vert in
edgekey(edge)]
)
single_vertices = [
vert.index for vert in bm_mod.verts if
vert.select and not vert.hide and
not verts_connected.get(vert.index, False)
]
if single_vertices and len(bm.faces) > 0:
vert_to_single = dict(
[[v.index, []] for v in bm_mod.verts if not v.hide]
)
for face in [face for face in bm_mod.faces if not face.select and not face.hide]:
for vert in face.verts:
vert = vert.index
if vert in single_vertices:
for ek in face_edgekeys(face):
edge_keys.append(ek)
if vert not in vert_to_single[ek[0]]:
vert_to_single[ek[0]].append(vert)
if vert not in vert_to_single[ek[1]]:
vert_to_single[ek[1]].append(vert)
break
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# sort edge-keys into loops
loops = get_connected_selections(edge_keys)
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# find out to which loops the single vertices belong
single_loops = dict([[i, []] for i in range(len(loops))])
if single_vertices and len(bm.faces) > 0:
for i, [loop, circular] in enumerate(loops):
for vert in loop:
if vert_to_single[vert]:
for single in vert_to_single[vert]:
if single not in single_loops[i]:
single_loops[i].append(single)
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return(derived, bm_mod, single_vertices, single_loops, loops)
# recalculate positions based on the influence of the circle shape
def circle_influence_locs(locs_2d, new_locs_2d, influence):
for i in range(len(locs_2d)):
oldx, oldy, j = locs_2d[i]
newx, newy, k = new_locs_2d[i]
altx = newx * (influence / 100) + oldx * ((100 - influence) / 100)
alty = newy * (influence / 100) + oldy * ((100 - influence) / 100)
locs_2d[i] = [altx, alty, j]
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return(locs_2d)
# project 2d locations on circle, respecting distance relations between verts
def circle_project_non_regular(locs_2d, x0, y0, r):
for i in range(len(locs_2d)):
x, y, j = locs_2d[i]
loc = mathutils.Vector([x - x0, y - y0])
loc.length = r
locs_2d[i] = [loc[0], loc[1], j]
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return(locs_2d)
# project 2d locations on circle, with equal distance between all vertices
def circle_project_regular(locs_2d, x0, y0, r):
# find offset angle and circling direction
x, y, i = locs_2d[0]
loc = mathutils.Vector([x - x0, y - y0])
loc.length = r
offset_angle = loc.angle(mathutils.Vector([1.0, 0.0]), 0.0)
loca = mathutils.Vector([x - x0, y - y0, 0.0])
if loc[1] < -1e-6:
offset_angle *= -1
x, y, j = locs_2d[1]
locb = mathutils.Vector([x - x0, y - y0, 0.0])
if loca.cross(locb)[2] >= 0:
ccw = 1
else:
ccw = -1
# distribute vertices along the circle
for i in range(len(locs_2d)):
t = offset_angle + ccw * (i / len(locs_2d) * 2 * math.pi)
x = math.cos(t) * r
y = math.sin(t) * r
locs_2d[i] = [x, y, locs_2d[i][2]]
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return(locs_2d)
# shift loop, so the first vertex is closest to the center
def circle_shift_loop(bm_mod, loop, com):
verts, circular = loop
distances = [
[(bm_mod.verts[vert].co - com).length, i] for i, vert in enumerate(verts)
]
distances.sort()
shift = distances[0][1]
loop = [verts[shift:] + verts[:shift], circular]
CoDEmanX
committed
return(loop)
# ########################################
# ##### Curve functions ##################
# ########################################
# create lists with knots and points, all correctly sorted
def curve_calculate_knots(loop, verts_selected):
knots = [v for v in loop[0] if v in verts_selected]
points = loop[0][:]
# circular loop, potential for weird splines
if loop[1]:
offset = int(len(loop[0]) / 4)
kpos = []
for k in knots:
kpos.append(loop[0].index(k))
kdif = []
for i in range(len(kpos) - 1):
kdif.append(kpos[i + 1] - kpos[i])
kdif.append(len(loop[0]) - kpos[-1] + kpos[0])
kadd = []
for k in kdif:
if k > 2 * offset:
kadd.append([kdif.index(k), True])
# next 2 lines are optional, they insert
# an extra control point in small gaps
# kadd.append([kdif.index(k), False])
kins = []
krot = False
for k in kadd: # extra knots to be added
if k[1]: # big gap (break circular spline)
kpos = loop[0].index(knots[k[0]]) + offset
if kpos > len(loop[0]) - 1:
kpos -= len(loop[0])
kins.append([knots[k[0]], loop[0][kpos]])
kpos2 = k[0] + 1
kpos2 -= len(knots)
kpos2 = loop[0].index(knots[kpos2]) - offset
if kpos2 < 0:
kpos2 += len(loop[0])
kins.append([loop[0][kpos], loop[0][kpos2]])
krot = loop[0][kpos2]
else: # small gap (keep circular spline)
k1 = loop[0].index(knots[k[0]])
k2 = k[0] + 1
k2 -= len(knots)
k2 = loop[0].index(knots[k2])
if k2 < k1:
dif = len(loop[0]) - 1 - k1 + k2
else:
dif = k2 - k1
if kn > len(loop[0]) - 1:
kn -= len(loop[0])
kins.append([loop[0][k1], loop[0][kn]])
knots.insert(knots.index(j[0]) + 1, j[1])
knots.append(knots[0])
points = loop[0][loop[0].index(knots[0]):]
points += loop[0][0:loop[0].index(knots[0]) + 1]
else: # non-circular loop (broken by script)
krot = knots.index(krot)
knots = knots[krot:] + knots[0:krot]
if loop[0].index(knots[0]) > loop[0].index(knots[-1]):
points = loop[0][loop[0].index(knots[0]):]
points += loop[0][0:loop[0].index(knots[-1]) + 1]
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