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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 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()
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(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,
p1_a,
p2,
p2_a,
)
if isect:
corner = isect[0].lerp(isect[1], 0.5)
else:
corner = None
if corner:
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
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=0.02, # 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)
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 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((0.0, 1, 0.0))
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
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(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(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()
def bezier_solve_(self):
""" Calculate bezier handles,
assume the splines have been broken up.
http://polymathprogrammer.com/
"""
p1 = self.points[0]
p2 = self.points[-1]
line_ix_p1 = self.points[len(self.points) // 3]
line_ix_p2 = self.points[int((len(self.points) / 3) * 2)]
u = 1 / 3
v = 2 / 3
p0x, p0y, p0z = p1.co
p1x, p1y, p1z = line_ix_p1.co
p2x, p2y, p2z = line_ix_p2.co
p3x, p3y, p3z = p2.co
ui = 1.0 - u
vi = 1.0 - v
u_p3 = u * u * u
v_p3 = v * v * v
ui_p3 = ui * ui * ui
vi_p3 = vi * vi * vi
# --- snip
q1 = Vector()
q2 = Vector()
pos = Vector(), Vector(), Vector(), Vector()
a = 3.0 * ui * ui * u
b = 3.0 * ui * u * u
c = 3.0 * vi * vi * v
d = 3.0 * vi * v * v
det = a * d - b * c
if det == 0.0:
assert(0)
return 0
q1.x = p1x - (ui_p3 * p0x + u_p3 * p3x)
q1.y = p1y - (ui_p3 * p0y + u_p3 * p3y)
q1.z = p1z - (ui_p3 * p0z + u_p3 * p3z)
q2.x = p2x - (vi_p3 * p0x + v_p3 * p3x)
q2.y = p2y - (vi_p3 * p0y + v_p3 * p3y)
q2.z = p2z - (vi_p3 * p0z + v_p3 * p3z)
pos[1].x = (d * q1.x - b * q2.x) / det
pos[1].y = (d * q1.y - b * q2.y) / det
pos[1].z = (d * q1.z - b * q2.z) / det
pos[2].x = ((-c) * q1.x + a * q2.x) / det
pos[2].y = ((-c) * q1.y + a * q2.y) / det
pos[2].z = ((-c) * q1.z + a * q2.z) / det
self.handle_left = pos[1]
self.handle_right = pos[2]
def bezier_solve(self):
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)
# picking 1/2 and 2/3'rds works best
line_ix_p1 = self.points[int(len(self.points) * (1.0 / 3.0))]
line_ix_p1_co, line_ix_p1_no = line_ix_p1.co, line_ix_p1.no
line_ix_p2 = self.points[int(len(self.points) * (2.0 / 3.0))]
line_ix_p2_co, line_ix_p2_no = line_ix_p2.co, line_ix_p2.no
# used to seek for the upper most point but this gives mostly
# as good results
p1_apex_co = self.points[int(len(self.points) * (1.0 / 3.0) * 0.75)].co
p2_apex_co = self.points[int(len(self.points) * (1.0 - (1.0 / 3.0) * 0.75))].co
l1_tan = (p1.no - p1.no.project(l1_no)).normalized()
l2_tan = -(p2.no - p2.no.project(l2_no)).normalized()
# 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.cross(p2.no).cross(p_vec).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 * p1.no.angle(l2_no_ref) / (pi * 1.0)
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
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, error_max=-1.0, test_count=16):
from mathutils.geometry import interpolate_bezier
test_points = interpolate_bezier(self.points[0].co,
self.handle_left,
self.handle_right,
self.points[-1].co,
test_count,
)
from mathutils.geometry import intersect_point_line
error = 0.0
# this is a rough method measuring the error but should be ok
# TODO. dont test against every single point.
for co in test_points:
co = co
# 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
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 / test_count
if error_max != -1.0 and error > error_max:
return True
if error_max != -1.0:
return False
else:
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:
assert(s.prev == s_prev)
if s_prev:
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.xyz = 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 + (pt.co - hr))
elif s_prev:
pt = s_prev.points[-1]
hl = s_prev.handle_right
hr = (pt.co + (pt.co - hl))
else:
assert(0)
bp.co.xyz = pt.co
bp.handle_left.xyz = hl
bp.handle_right.xyz = 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()
# higher quality but not really needed
'''
curve.redistribute(segment_length / 4.0, smooth=True)
curve.redistribute(segment_length, smooth=False)
'''
curve.redistribute(segment_length, smooth=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(bezier_tolerance))[1]
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__":
bpy.ops.wm.open_mainfile(filepath="/root/curve_test2.blend")
ob = bpy.data.objects["Curve"]
points = [p.co.xyz 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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