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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 bpy
def line_point_side_v2(l1, l2, pt):
return (((l1[0] - pt[0]) * (l2[1] - pt[1])) -
((l2[0] - pt[0]) * (l1[1] - pt[1])))
def shell_angle_to_dist(angle):
from math import cos
return 1.0 if (angle < 0.0001) else abs(1.0 / cos(angle))
def vis_curve_object():
scene = bpy.data.scenes[0] # weak!
cu = bpy.data.curves.new(name="Line", type='CURVE')
ob = bpy.data.objects.new(name="Test", object_data=cu)
ob.layers = [True] * 20
base = scene.objects.link(ob)
return ob
def vis_curve_spline(p1, h1, p2, h2):
ob = vis_curve_object()
spline = ob.data.splines.new(type='BEZIER')
spline.bezier_points.add(1)
spline.bezier_points[0].co = p1.to_3d()
spline.bezier_points[1].co = p2.to_3d()
spline.bezier_points[0].handle_right = h1.to_3d()
spline.bezier_points[1].handle_left = h2.to_3d()
def vis_circle_object(co, rad=1.0):
import math
scene = bpy.data.scenes[0] # weak!
ob = bpy.data.objects.new(name="Circle", object_data=None)
ob.rotation_euler.x = math.pi / 2
ob.location = co.to_3d()
ob.empty_draw_size = rad
ob.layers = [True] * 20
base = scene.objects.link(ob)
return ob
def visualize_line(p1, p2, p3=None, rad=None):
pair = p1.to_3d(), p2.to_3d()
ob = vis_curve_object()
spline = ob.data.splines.new(type='POLY')
spline.points.add(1)
for co, v in zip((pair), spline.points):
v.co.xyz = co
if p3:
spline = ob.data.splines.new(type='POLY')
spline.points[0].co.xyz = p3.to_3d()
print(rad)
if rad is not None:
vis_circle_object(p3, rad)
def treat_points(points,
double_limit=0.0001,
):
# first remove doubles
tot_len = 0.0
if double_limit != 0.0:
i = len(points) - 1
while i > 0:
length = (points[i] - points[i - 1]).length
if length < double_limit:
del points[i]
if i >= len(points):
i -= 1
else:
tot_len += length
i -= 1
return tot_len
def solve_curvature_2d(p1, p2, n1, n2, fac, fallback):
""" Add a nice circular curvature on
"""
from mathutils import Vector
from mathutils.geometry import (barycentric_transform,
intersect_line_line,
intersect_point_line,
)
p1_a = p1 + n1
p2_a = p2 - n2
isect = intersect_line_line(p1.to_3d(),
p1_a.to_3d(),
p2.to_3d(),
p2_a.to_3d(),
)
if isect:
corner = isect[0]
else:
corner = None
if corner:
corner = corner.xy
p1_first_order = p1.lerp(corner, fac)
p2_first_order = corner.lerp(p2, fac)
co = p1_first_order.lerp(p2_first_order, fac)
return co.xy
else:
# cant interpolate. just return interpolated value
return fallback.copy() # p1.lerp(p2, fac)
def points_to_bezier(points_orig,
double_limit=0.0001,
kink_tolerance=0.25,
bezier_tolerance=0.1, # error distance, scale dependant
subdiv=8,
angle_span=0.95, # 1.0 tries to evaluate splines of 180d
):
import math
from mathutils import Vector
class Point(object):
__slots__ = ("co",
"angle",
"no",
"is_joint",
"next",
"prev",
)
def __init__(self, co):
self.co = co
self.is_joint = False
def calc_angle(self):
if self.prev is None or self.next is None:
self.angle = 0.0
else:
va = self.co - self.prev.co
vb = self.next.co - self.co
self.angle = va.angle(vb, 0.0)
# XXX 2D
if line_point_side_v2(self.prev.co,
self.co,
self.next.co,
) < 0.0:
self.angle = -self.angle
def angle_diff(self):
""" use for detecting joints, detect difference in angle from
surrounding points.
"""
if self.prev is None or self.next is None:
return 0.0
else:
if (self.angle > self.prev.angle and
self.angle > self.next.angle):
return abs(self.angle - self.prev.angle) / math.pi
else:
return 0.0
def angle_filter(self):
tot = 1
a = self.angle
if self.prev:
tot += 1
a += self.prev.angle
if self.next:
tot += 1
a += self.next.angle
a = a / tot
return 0.0 if abs(a) < 0.01 else a
def calc_normal(self):
v1 = v2 = None
if self.prev and not self.prev.is_joint:
v1 = (self.co - self.prev.co).normalized()
if self.next and not self.next.is_joint:
v2 = (self.next.co - self.co).normalized()
if v1 and v2:
self.no = (v1 + v2).normalized()
elif v1:
self.no = v1
elif v2:
self.no = v2
else:
print("Warning, assigning dummy normal")
self.no = Vector(0, 1)
class Spline(object):
__slots__ = ("points",
"handle_left",
"handle_right",
"next",
"prev",
)
def __init__(self, points):
self.points = points
def link_points(self):
if hasattr(self.points[0], "prev"):
raise Exception("already linked")
p_prev = None
for p in self.points:
p.prev = p_prev
p_prev = p
p_prev = None
for p in reversed(self.points):
p.next = p_prev
p_prev = p
def split(self, i, is_joint=False):
prev = self.prev
next = self.next
if is_joint:
self.points[i].is_joint = True
# share a point
spline_a = Spline(self.points[:i + 1])
spline_b = Spline(self.points[i:])
# invalidate self, dont reuse!
self.points = None
spline_a.next = spline_b
spline_b.prev = spline_a
spline_a.prev = prev
spline_b.next = next
if prev:
prev.next = spline_a
if next:
next.prev = spline_b
return spline_a, spline_b
def calc_angle(self):
for p in self.points:
p.calc_angle()
def calc_normal(self):
for p in self.points:
p.calc_normal()
def calc_all(self):
self.link_points()
self.calc_angle()
self.calc_normal()
def total_angle(self):
return abs(sum((p.angle for p in self.points)))
def redistribute(self, segment_length, smooth=False):
if len(self.points) == 1:
return
from mathutils.geometry import intersect_line_sphere_2d
p_line = p = self.points[0]
points = [(p.co.copy(), p.co.copy())]
p = p.next
def point_add(co, p=None):
co = co.copy()
co_smooth = co.copy()
if smooth:
if p is None:
pass # works ok but no smoothing
elif (p.prev.no - p.no).length < 0.001:
pass # normals are too similar, paralelle
elif (p.angle > 0.0) != (p.prev.angle > 0.0):
pass
else:
# visualize_line(p.co, p.co + p.no)
# this assumes co is on the line
fac = ((p.prev.co - co).length /
(p.prev.co - p.co).length)
assert(fac >= 0.0 and fac <= 1.0)
co_smooth = solve_curvature_2d(p.prev.co,
p.co,
p.prev.no,
p.no,
fac,
co,
)
points.append((co, co_smooth))
def point_step(p):
if p.is_joint or p.next is None:
point_add(p.co)
return None
else:
return p.next
print("START")
while p:
# we want the first pont past the segment size
#if p.is_joint:
# vis_circle_object(p.co)
length = (points[-1][0] - p.co).length
if abs(length - segment_length) < 0.00001:
# close enough to be considered on the circle bounds
point_add(p.co)
p_line = p
p = point_step(p)
elif length < segment_length:
p = point_step(p)
else:
# the point is further then the segment width
p_start = points[-1][0] if p.prev is p_line else p.prev.co
if (p_start - points[-1][0]).length > segment_length:
raise Exception("eek2")
if (p.co - points[-1][0]).length < segment_length:
raise Exception("eek3")
# print(p_start, p.co, points[-1][0], segment_length)
i1, i2 = intersect_line_sphere_2d(p_start,
p.co,
points[-1][0],
segment_length,
)
# print()
# print(i1, i2)
# assert(i1 is not None)
if i1 is not None:
point_add(i1, p)
p_line = p.prev
elif i2:
raise Exception("err")
elif i1 is None and i2 is None:
visualize_line(p_start,
p.co,
points[-1][0],
segment_length,
)
# XXX FIXME
# raise Exception("BAD!s")
point_add(p.co)
p_line = p
p = point_step(p)
joint = self.points[0].is_joint, self.points[-1].is_joint
self.points = [Point(p[1]) for p in points]
self.points[0].is_joint, self.points[-1].is_joint = joint
self.calc_all()
# raise Exception("END")
def intersect_line(self, l1, l2, reverse=False):
from mathutils.geometry import (intersect_point_line,
)
if reverse:
p_first = self.points[-2]
point_iter = reversed(self.points[:-1])
else:
p_first = self.points[1]
point_iter = self.points[1:]
side = (line_point_side_v2(l1, l2, p_first.co) < 0.0)
ok = False
for p_apex in point_iter:
if (line_point_side_v2(l1,
l2,
p_apex.co,
) < 0.0) != side:
if reverse:
p_apex_other = p_apex.next
else:
p_apex_other = p_apex.prev
# find the exact point on the line between the apex and
# the middle
p_test_1 = intersect_point_line(p_apex.co,
l1,
l2)[0].xy
p_test_2 = intersect_point_line(p_apex_other.co,
l1,
l2)[0].xy
w1 = (p_test_1 - p_apex.co).length
w2 = (p_test_2 - p_apex_other.co).length
#assert(w1 + w2 != 0)
#try:
fac = w1 / (w1 + w2)
#except ZeroDivisionError:
# fac = 0.5
assert(fac >= 0.0 and fac <= 1.0)
p_apex_co = p_apex.co.lerp(p_apex_other.co, fac)
p_apex_no = p_apex.no.lerp(p_apex_other.no, fac)
p_apex_no.normalize()
# visualize_line(p_mid.to_3d(), corner.to_3d())
# visualize_line(p_apex.co.to_3d(), p_apex_co.to_3d())
return p_apex_co, p_apex_no, p_apex
# intersection not found
return None, None, None
def bezier_solve(self):
""" Calculate bezier handles,
assume the splines have been broken up.
"""
from mathutils.geometry import (intersect_point_line,
intersect_line_line,
)
# get a line
p1 = self.points[0]
p2 = self.points[-1]
# ------
# take 2
p_vec = (p2.co - p1.co).normalized()
# vector between line and point directions
l1_no = (p1.no + p_vec).normalized()
l2_no = ((-p2.no) - p_vec).normalized()
l1_co = p1.co + l1_no
l2_co = p2.co + l2_no
# visualize_line(p1.co, l1_co)
# visualize_line(p2.co, l2_co)
line_ix_p1_co, line_ix_p1_no, line_ix_p1 = \
self.intersect_line(p1.co,
l1_co,
)
line_ix_p2_co, line_ix_p2_no, line_ix_p2 = \
self.intersect_line(p2.co,
l2_co,
reverse=True,
)
if line_ix_p1_co is None:
line_ix_p1_co, line_ix_p1_no, line_ix_p1 = \
p1.next.co, p1.next.no, p1.next
if line_ix_p2_co is None:
line_ix_p2_co, line_ix_p2_no, line_ix_p2 = \
p2.prev.co, p2.prev.no, p2.prev
# vis_circle_object(line_ix_p1_co)
# vis_circle_object(line_ix_p2_co)
l1_max = 0.0
p1_apex_co = None
p = self.points[1]
while p and (not p.is_joint) and p != line_ix_p1:
ix = intersect_point_line(p.co, p1.co, l1_co)[0].xy
length = (ix - p.co).length
if length > l1_max:
l1_max = length
p1_apex_co = p.co
p = p.next
l2_max = 0.0
p2_apex_co = None
p = self.points[-2]
while p and (not p.is_joint) and p != line_ix_p2:
ix = intersect_point_line(p.co, p2.co, l2_co)[0].xy
length = (ix - p.co).length
if length > l2_max:
l2_max = length
p2_apex_co = p.co
p = p.prev
if p1_apex_co is None:
p1_apex_co = p1.next.co
if p2_apex_co is None:
p2_apex_co = p2.prev.co
l1_tan = (p1.no - p1.no.project(l1_no)).normalized()
l2_tan = -(p2.no - p2.no.project(l2_no)).normalized()
# values are good!
#~ visualize_line(p1.co, p1.co + l1_tan)
#~ visualize_line(p2.co, p2.co + l2_tan)
#~ visualize_line(p1.co, p1.co + l1_no)
#~ visualize_line(p2.co, p2.co + l2_no)
# calculate bias based on the position of the other point allong
# the tangent.
# first need to reflect the second normal for angle comparison
# first fist need the reflection normal
no_ref = p_vec.to_3d().cross(p2.no.to_3d()).cross(p_vec.to_3d()).normalized()
l2_no_ref = p2.no.reflect(no_ref).normalized()
del no_ref
from math import pi
# This could be tweaked but seems to work well
fac_fac = (p1.co - p2.co).length * (0.5 / 0.75) * p1.no.angle(l2_no_ref) / pi
fac_1 = intersect_point_line(p2_apex_co, p1.co, p1.co + l1_tan)[1] * fac_fac
fac_2 = intersect_point_line(p1_apex_co, p2.co, p2.co + l2_tan)[1] * fac_fac
# TODO, scale the factors some useful way
h1_fac = ((p1.co - p1_apex_co).length / 0.75) - fac_1
h2_fac = ((p2.co - p2_apex_co).length / 0.75) - fac_2
h1 = p1.co + (p1.no * h1_fac)
h2 = p2.co - (p2.no * h2_fac)
self.handle_left = h1
self.handle_right = h2
'''
visualize_line(p1.co, p1_apex_co)
visualize_line(p1_apex_co, p2_apex_co)
visualize_line(p2.co, p2_apex_co)
visualize_line(p1.co, p2.co)
'''
def bezier_error(self):
from mathutils.geometry import interpolate_bezier
test_points = interpolate_bezier(self.points[0].co.to_3d(),
self.handle_left,
self.handle_right,
self.points[-1].co.to_3d(),
8,
)
from mathutils.geometry import intersect_point_line
error = 0.0
# this is a rough method measuring the error but should be good enough
# TODO. dont test against every single point.
for co in test_points:
co = co.xy
# initial values
co_best = self.points[0].co
length_best = (co - co_best).length
for p in self.points[1:]:
# dist to point
length = (co - p.co).length
if length < length_best:
length_best = length
co_best = p.co
p_ix, fac = intersect_point_line(co, p.co, p.prev.co)
p_ix = p_ix.xy
if fac >= 0.0 and fac <= 1.0:
length = (co - p_ix).length
if length < length_best:
length_best = length
co_best = p_ix
error += length_best
return error
class Curve(object):
__slots__ = ("splines",
)
def __init__(self, splines):
self.splines = splines
def link_splines(self):
s_prev = None
for s in self.splines:
s.prev = s_prev
s_perv = s
s_prev = None
for s in reversed(self.splines):
s.next = s_prev
s_perv = s
def calc_data(self):
for s in self.splines:
s.calc_all()
self.link_splines()
def split_func_map_point(self, func, is_joint=False):
""" func takes a point and returns true on split
return True if any splits are made.
"""
s_index = 0
s = self.splines[s_index]
while s:
assert(self.splines[s_index] == s)
for i, p in enumerate(s.points):
if i == 0 or i >= len(s.points) - 1:
continue
if func(p):
split_pair = s.split(i, is_joint=is_joint)
# keep list in sync
self.splines[s_index:s_index + 1] = split_pair
# advance on main while loop
s = split_pair[0]
assert(self.splines[s_index] == s)
break
s = s.next
s_index += 1
def split_func_spline(self, func, is_joint=False, recursive=False):
""" func takes a spline and returns the point index on split or -1
return True if any splits are made.
"""
s_index = 0
s = self.splines[s_index]
while s:
assert(self.splines[s_index] == s)
i = func(s)
if i != -1:
split_pair = s.split(i, is_joint=is_joint)
# keep list in sync
self.splines[s_index:s_index + 1] = split_pair
# advance on main while loop
s = split_pair[0]
assert(self.splines[s_index] == s)
if recursive:
continue
s = s.next
s_index += 1
def validate(self):
s_prev = None
iii = 0
for s in self.splines:
print(iii)
assert(s.prev == s_prev)
if s_prev:
print()
assert(s_prev.next == s)
s_prev = s
iii += 1
def redistribute(self, segment_length, smooth=False):
for s in self.splines:
s.redistribute(segment_length, smooth)
def to_blend_data(self):
""" Points to blender data, debugging only
"""
scene = bpy.data.scenes[0] # weak!
for base in scene.object_bases:
base.select = False
cu = bpy.data.curves.new(name="Test", type='CURVE')
for s in self.splines:
spline = cu.splines.new(type='POLY')
spline.points.add(len(s.points) - 1)
for p, v in zip(s.points, spline.points):
v.co.xy = p.co
ob = bpy.data.objects.new(name="Test", object_data=cu)
ob.layers = [True] * 20
base = scene.objects.link(ob)
scene.objects.active = ob
base.select = True
# base.layers = [True] * 20
print(ob, "Done")
def to_blend_curve(self, cu=None, cu_matrix=None):
""" return new bezier spline datablock or add to an existing
"""
if not cu:
cu = bpy.data.curves.new(name="Curve", type='CURVE')
spline = cu.splines.new(type='BEZIER')
spline.bezier_points.add(len(self.splines))
s_prev = None
for i, bp in enumerate(spline.bezier_points):
if i < len(self.splines):
s = self.splines[i]
else:
s = None
if s_prev and s:
pt = s.points[0]
hl = s_prev.handle_right
hr = s.handle_left
elif s:
pt = s.points[0]
hr = s.handle_left
hl = (pt.co.xy + (pt.co.xy - hr.xy))
elif s_prev:
pt = s_prev.points[-1]
hl = s_prev.handle_right
hr = (pt.co.xy + (pt.co.xy - hl.xy))
else:
assert(0)
bp.co.xy = pt.co
bp.handle_left.xy = hl
bp.handle_right.xy = hr
handle_type = 'FREE'
if pt.is_joint == False or (s_prev and s) == False:
# XXX, this should not happen, but since it can
# at least dont allow allignment to break the curve output
if (pt.co - hl).angle(hr - pt.co, 0.0) < 0.1:
handle_type = 'ALIGNED'
bp.handle_left_type = bp.handle_right_type = handle_type
s_prev = s
scene = bpy.data.scenes[0] # weak!
ob = bpy.data.objects.new(name="Test", object_data=cu)
ob.layers = [True] * 20
base = scene.objects.link(ob)
scene.objects.active = ob
base.select = True
return cu
points = list(points_orig)
# remove doubles
tot_length = treat_points(points)
# calculate segment spacing
segment_length = (tot_length / len(points)) / subdiv
curve = Curve([Spline([Point(p) for p in points])])
curve.calc_data()
if kink_tolerance != 0.0:
pass
curve.split_func_map_point(lambda p: p.angle_diff() > kink_tolerance,
is_joint=True,
)
# return
# curve.validate()
curve.redistribute(segment_length / 4.0, smooth=True)
curve.redistribute(segment_length, smooth=False)
def swap_side(p):
angle = p.angle_filter()
if p.prev.prev is None:
swap_side.last = angle
else:
if (swap_side.last > 0.0) != (angle > 0.0):
if abs(p.angle) > 0.025:
swap_side.last = p.angle
return True
return False
#curve.split_func_map_point(lambda p: (p.angle_filter() >= 0) != \
# (p.prev.angle_filter() >= 0))
# curve.split_func_map_point(swap_side)
# now split based on total spline angle.
import math
angle_span_rad = angle_span * math.pi
curve.split_func_spline(lambda s:
len(s.points) // 2
if (s.total_angle() > angle_span_rad and
len(s.points) > 2)
else -1,
recursive=True,
)
# debug only!
# to test how good the bezier spline fitting is without corrections
'''
for s in curve.splines:
s.bezier_solve()
'''
# or recursively subdivide...
curve.split_func_spline(lambda s:
len(s.points) // 2
if ((s.bezier_solve(), s.bezier_error())[1] >
bezier_tolerance) and (len(s.points))
else -1,
recursive=True,
)
'''
for s in curve.splines:
s.bezier_solve()
print(s.bezier_error())
'''
# VISUALIZE
# curve.to_blend_data()
curve.to_blend_curve()
if __name__ == "__main__":
print("A")
bpy.ops.wm.open_mainfile(filepath="/root/curve_test1.blend")
ob = bpy.data.objects["Curve"]
points = [p.co.xy for s in ob.data.splines for p in s.points]
print("points_to_bezier 1")
points_to_bezier(points)
print("points_to_bezier 2")
bpy.ops.wm.save_as_mainfile(filepath="/root/curve_test_edit.blend",
copy=True)
print("done!")
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