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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 #####
# <pep8 compliant>
import itertools
from . import is_
from .fake_entities import ArcEntity
from mathutils import Vector, Matrix, Euler, Color
from math import pi, radians, floor, ceil, degrees
from copy import deepcopy
class ShortVec(Vector):
def __str__(self):
return "Vec" + str((round(self.x, 2), round(self.y, 2), round(self.z, 2)))
def __repr__(self):
return self.__str__()
def bspline_to_cubic(do, en, curve, errors=None):
"""
do: an instance of Do()
en: a DXF entity
curve: Blender geometry data of type "CURVE"
inserts knots until every knot has multiplicity of 3; returns new spline controlpoints
if degree of the spline is > 3 "None" is returned
"""
def clean_knots():
start = knots[:degree + 1]
end = knots[-degree - 1:]
if start.count(start[0]) < degree + 1:
maxa = max(start)
for i in range(degree + 1):
knots[i] = maxa
if end.count(end[0]) < degree + 1:
mina = min(end)
lenk = len(knots)
for i in range(lenk - degree - 1, lenk):
knots[i] = mina
def insert_knot(t, k, p):
""" http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS-knot-insert.html """
def a(t, ui, uip):
if uip == ui:
print("zero!")
return 0
return (t - ui) / (uip - ui)
new_spline = spline.copy()
for pp in range(p, 1, -1):
i = k - pp + 1
ai = a(t, knots[i], knots[i + p])
new_spline[i] = (1 - ai) * spline[i - 1] + ai * spline[i]
ai = a(t, knots[k], knots[k + p])
new_spline.insert(k, (1 - ai) * spline[k - 1] + ai * spline[k % len(spline)])
knots.insert(k, t)
return new_spline
knots = list(en.knots)
spline = [ShortVec(cp) for cp in en.controlpoints]
degree = len(knots) - len(spline) - 1
if degree <= 3:
clean_knots()
k = 1
st = 1
while k < len(knots) - 1:
t = knots[k]
multilen = knots[st:-st].count(t)
if multilen < degree:
before = multilen
while multilen < degree:
spline = insert_knot(t, k, degree)
multilen += 1
k += 1
k += before
else:
k += degree
if degree <= 2:
return quad_to_cube(spline)
# the ugly truth
if len(spline) % 3 == 0:
spline.append([spline[-1]])
errors.add("Cubic spline: Something went wrong with knot insertion")
return spline
def quad_to_cube(spline):
"""
spline: list of (x,y,z)-tuples)
Converts quad bezier to cubic bezier curve.
"""
s = []
for i, p in enumerate(spline):
if i % 2 == 1:
before = Vector(spline[i - 1])
after = Vector(spline[(i + 1) % len(spline)])
s.append(before + 2 / 3 * (Vector(p) - before))
s.append(after + 2 / 3 * (Vector(p) - after))
else:
s.append(p)
# degree == 1
if len(spline) == 2:
s.append(spline[-1])
return s
def bulge_to_arc(point, next, bulge):
"""
point: start point of segment in lwpolyline
next: end point of segment in lwpolyline
bulge: number between 0 and 1
Converts a bulge of lwpolyline to an arc with a bulge describing the amount of how much a straight segment should
be bended to an arc. With the bulge one can find the center point of the arc that replaces the segment.
"""
rot = Matrix(((0, -1, 0), (1, 0, 0), (0, 0, 1)))
section = next - point
section_length = section.length / 2
direction = -bulge / abs(bulge)
correction = 1
sagitta_len = section_length * abs(bulge)
radius = (sagitta_len**2 + section_length**2) / (2 * sagitta_len)
if sagitta_len < radius:
cosagitta_len = radius - sagitta_len
else:
cosagitta_len = sagitta_len - radius
direction *= -1
correction *= -1
center = point + section / 2 + section.normalized() * cosagitta_len * rot * direction
cp = point - center
cn = next - center
cr = cp.to_3d().cross(cn.to_3d()) * correction
start = Vector((1, 0))
if cr[2] > 0:
angdir = 0
startangle = -start.angle_signed(cp.to_2d())
endangle = -start.angle_signed(cn.to_2d())
else:
angdir = 1
startangle = start.angle_signed(cp.to_2d())
endangle = start.angle_signed(cn.to_2d())
return ArcEntity(startangle, endangle, center.to_3d(), radius, angdir)
def bulgepoly_to_cubic(do, lwpolyline):
"""
do: instance of Do()
lwpolyline: DXF entity of type polyline
Bulges define how much a straight segment of a polyline should be transformed to an arc. Hence do.arc() is called
for segments with a bulge and all segments are being connected to a cubic bezier curve in the end.
Reference: http://www.afralisp.net/archive/lisp/Bulges1.htm
"""
def handle_segment(last, point, bulge):
if bulge != 0 and (point - last).length != 0:
arc = bulge_to_arc(last, point, bulge)
cubic_bezier = do.arc(arc, None, aunits=1, angdir=arc.angdir, angbase=0)
else:
la = last.to_3d()
po = point.to_3d()
section = point - last
cubic_bezier = [la, la + section * 1 / 3, la + section * 2 / 3, po]
return cubic_bezier
points = lwpolyline.points
bulges = lwpolyline.bulge
lenpo = len(points)
spline = []
for i in range(1, lenpo):
spline += handle_segment(Vector(points[i - 1]), Vector(points[i]), bulges[i - 1])[:-1]
if lwpolyline.is_closed:
spline += handle_segment(Vector(points[-1]), Vector(points[0]), bulges[-1])
else:
spline.append(points[-1])
return spline
def bulgepoly_to_lenlist(lwpolyline):
"""
returns a list with the segment lengths of a lwpolyline
"""
def handle_segment(last, point, bulge):
seglen = (point - last).length
if bulge != 0 and seglen != 0:
arc = bulge_to_arc(last, point, bulge)
if arc.startangle > arc.endangle:
arc.endangle += 2 * pi
angle = arc.endangle - arc.startangle
lenlist.append(abs(arc.radius * angle))
else:
lenlist.append(seglen)
points = lwpolyline.points
bulges = lwpolyline.bulge
lenpo = len(points)
lenlist = []
for i in range(1, lenpo):
handle_segment(Vector(points[i - 1][:2]), Vector(points[i][:2]), bulges[i - 1])
if lwpolyline.is_closed:
handle_segment(Vector(points[-1][:2]), Vector(points[0][:2]), bulges[-1])
return lenlist
def extrusion_to_matrix(entity):
"""
Converts an extrusion vector to a rotation matrix that denotes the transformation between world coordinate system
and the entity's own coordinate system (described by the extrusion vector).
"""
def arbitrary_x_axis(extrusion_normal):
world_y = Vector((0, 1, 0))
world_z = Vector((0, 0, 1))
if abs(extrusion_normal[0]) < 1 / 64 and abs(extrusion_normal[1]) < 1 / 64:
a_x = world_y.cross(extrusion_normal)
else:
a_x = world_z.cross(extrusion_normal)
a_x.normalize()
return a_x, extrusion_normal.cross(a_x)
az = Vector(entity.extrusion)
ax, ay = arbitrary_x_axis(az)
ax4 = ax.to_4d()
ay4 = ay.to_4d()
az4 = az.to_4d()
ax4[3] = 0
ay4[3] = 0
az4[3] = 0
translation = Vector((0, 0, 0, 1))
if hasattr(entity, "elevation"):
if type(entity.elevation) is tuple:
translation = Vector(entity.elevation).to_4d()
else:
translation = (az * entity.elevation).to_4d()
return Matrix((ax4, ay4, az4, translation)).transposed()
def split_by_width(entity):
"""
Used to split a curve (polyline, lwpolyline) into smaller segments if their width is varying in the overall curve.
"""
class WidthTuple:
def __init__(self, w):
self.w1 = w[0]
self.w2 = w[1]
def __eq__(self, other):
return self.w1 == other.w1 and self.w2 == other.w2 and self.w1 == self.w2
if is_.varying_width(entity):
entities = []
en_template = deepcopy(entity)
en_template.points = []
en_template.bulge = []
en_template.width = []
en_template.tangents = []
en_template.is_closed = False
i = 0
for pair, same_width in itertools.groupby(entity.width, key=lambda w: WidthTuple(w)):
en = deepcopy(en_template)
for segment in same_width:
en.points.append(entity.points[i])
en.points.append(entity.points[(i + 1) % len(entity.points)])
en.bulge.append(entity.bulge[i])
en.width.append(entity.width[i])
i += 1
entities.append(en)
if not entity.is_closed:
entities.pop(-1)
return entities
else:
return [entity]
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