Skip to content
Snippets Groups Projects
Commit bc44f0fc authored by Campbell Barton's avatar Campbell Barton
Browse files

wip commit, basic bezier evaluation working, but still need to rewrite some parts of this script.

parent ebf413ee
No related branches found
No related tags found
No related merge requests found
Hide whitespace changes
Inline Side-by-side
Showing
with 827 additions and 0 deletions
modules/curve_utils.py
+ 827
− 0
View file @ bc44f0fc
......@@ -17,3 +17,830 @@
# ##### 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 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]
# since we have even spacing we can just pick the middle point
# p_mid = self.points[len(self.points) // 2]
# vec, fac = mathutils.geometry.intersect_point_line(m_mid, p1, p2)
# TODO, ensure < 180d curves
p1_a, p1_b = p1.co, p1.co + p1.no
p2_a, p2_b = p2.co, p2.co - p2.no
isect = intersect_line_line(p1_a.to_3d(),
p1_b.to_3d(),
p2_a.to_3d(),
p2_b.to_3d(),
)
if isect is None:
# if isect is None, the line is paralelle
# just add simple handles
self.bezier_h1 = p1.co.lerp(p2.co, 1.0 / 3.0)
self.bezier_h2 = p2.co.lerp(p1.co, 1.0 / 3.0)
return
corner = isect[0].xy
p_mid = p1.co.lerp(p2.co, 0.5)
dist_best = 10000000.0
p_best = None
side = (line_point_side_v2(p_mid, corner, p1.co) < 0.0)
ok = False
for p_apex in self.points:
if (line_point_side_v2(p_mid,
corner,
p_apex.co,
) < 0.0) != side:
# find the exact point on the line between the apex and
# the middle
p_test_1 = intersect_point_line(p_apex.co,
p_mid,
corner)[0].xy
p_test_2 = intersect_point_line(p_apex.prev.co,
p_mid,
corner)[0].xy
w1 = (p_test_1 - p_apex.co).length
w2 = (p_test_2 - p_apex.prev.co).length
fac = w1 / (w1 + w2)
p_apex_co = p_apex.co.lerp(p_apex.prev.co, fac)
p_apex_no = p_apex.no.lerp(p_apex.prev.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())
ok = True
break
del p_apex, w1, w2, fac, p_test_1, p_test_2
assert(ok == True)
v1 = (p2.co - p1.co).normalized()
v2 = p_apex_no.copy()
# find the point on the line which aligns with the apex point.
# first place handles, must be distance to apex * 1.333...
if 1:
p_mid_apex_align = intersect_point_line(p_apex_co,
p1.co,
p2.co)[0]
else:
p_mid_apex_align = p_mid
# visualize_line(p_mid_apex_align.to_3d(), p_apex_co.to_3d())
# The point is always 75% of the handle distance
# here we extend the distance from the line to the curve apex
# by 33.33..% to compensate for this.
h_sca = 1 # (p_apex_co - p_mid_apex_align.xy).length / 0.75
from math import pi
# -1.0 - 1.0
bias = v1.angle(v2) / (pi / 2)
print(bias)
if abs(bias) < 0.001:
h_sca_1 = h_sca
h_sca_2 = h_sca
elif line_point_side_v2(Vector((0.0, 0.0)), v2, v1) < 0:
h_sca_1 = h_sca / (1.0 + bias)
h_sca_2 = h_sca * (1.0 + bias)
else:
h_sca_1 = h_sca * (1.0 + bias)
h_sca_2 = h_sca / (1.0 + bias)
# find the factor
fac = intersect_point_line(p_apex_co, p_mid, corner)[1]
# assert(fac >= 0.0)
h_sca_1 = 1
h_sca_2 = 1
h1 = p1.co.lerp(corner, (fac / 0.75) * h_sca_1)
h2 = p2.co.lerp(corner, (fac / 0.75) * h_sca_2)
# rare cases this can mess up, because of almost straight lines
# good for debugging single splines
# vis_curve_spline(p1.co, h1, p2.co, h2)
self.handle_left = h1
self.handle_right = h2
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,
)
curve.split_func_spline(lambda s:
len(s.points) // 2
if ((s.bezier_solve(), s.bezier_error())[1] >
bezier_tolerance) and (len(s.points) > 2)
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_test.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!")
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment