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Commit 5580c782 authored by Campbell Barton's avatar Campbell Barton
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rewrote bezier spline solver, works much better now, and with 'S' shape curves

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with 113 additions and 82 deletions
modules/curve_utils.py
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− 82
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...@@ -403,10 +403,10 @@ def points_to_bezier(points_orig, ...@@ -403,10 +403,10 @@ def points_to_bezier(points_orig,
) )
if reverse: if reverse:
p_first = self.points[-1] p_first = self.points[-2]
point_iter = reversed(self.points[:-1]) point_iter = reversed(self.points[:-1])
else: else:
p_first = self.points[0] p_first = self.points[1]
point_iter = self.points[1:] point_iter = self.points[1:]
side = (line_point_side_v2(l1, l2, p_first.co) < 0.0) side = (line_point_side_v2(l1, l2, p_first.co) < 0.0)
...@@ -433,7 +433,13 @@ def points_to_bezier(points_orig, ...@@ -433,7 +433,13 @@ def points_to_bezier(points_orig,
w1 = (p_test_1 - p_apex.co).length w1 = (p_test_1 - p_apex.co).length
w2 = (p_test_2 - p_apex_other.co).length w2 = (p_test_2 - p_apex_other.co).length
#assert(w1 + w2 != 0)
#try:
fac = w1 / (w1 + w2) 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_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 = p_apex.no.lerp(p_apex_other.no, fac)
...@@ -442,11 +448,10 @@ def points_to_bezier(points_orig, ...@@ -442,11 +448,10 @@ def points_to_bezier(points_orig,
# visualize_line(p_mid.to_3d(), corner.to_3d()) # visualize_line(p_mid.to_3d(), corner.to_3d())
# visualize_line(p_apex.co.to_3d(), p_apex_co.to_3d()) # visualize_line(p_apex.co.to_3d(), p_apex_co.to_3d())
ok = True return p_apex_co, p_apex_no, p_apex
break
return p_apex_co, p_apex_no
# intersection not found
return None, None, None
def bezier_solve(self): def bezier_solve(self):
""" Calculate bezier handles, """ Calculate bezier handles,
...@@ -464,97 +469,115 @@ def points_to_bezier(points_orig, ...@@ -464,97 +469,115 @@ def points_to_bezier(points_orig,
p2 = self.points[-1] 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) # ------
# take 2
p_vec = (p2.co - p1.co).normalized()
# vector between line and point directions
# TODO, ensure < 180d curves l1_no = (p1.no + p_vec).normalized()
l2_no = ((-p2.no) - p_vec).normalized()
p1_a, p1_b = p1.co, p1.co + p1.no l1_co = p1.co + l1_no
p2_a, p2_b = p2.co, p2.co - p2.no l2_co = p2.co + l2_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
p_apex_co, p_apex_no = self.intersect_line(p_mid, corner) # 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
v1 = (p2.co - p1.co).normalized()
v2 = p_apex_no.copy()
# find the point on the line which aligns with the apex point. if p1_apex_co is None:
# first place handles, must be distance to apex * 1.333... p1_apex_co = p1.next.co
if 1: if p2_apex_co is None:
p_mid_apex_align = intersect_point_line(p_apex_co, p2_apex_co = p2.prev.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 l1_tan = (p1.no - p1.no.project(l1_no)).normalized()
# here we extend the distance from the line to the curve apex l2_tan = -(p2.no - p2.no.project(l2_no)).normalized()
# by 33.33..% to compensate for this.
h_sca = 1 # (p_apex_co - p_mid_apex_align.xy).length / 0.75 # 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 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
# -1.0 - 1.0 fac_1 = intersect_point_line(p2_apex_co, p1.co, p1.co + l1_tan)[1] * fac_fac
bias = v1.angle(v2) / (pi / 2) fac_2 = intersect_point_line(p1_apex_co, p2.co, p2.co + l2_tan)[1] * fac_fac
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 # TODO, scale the factors some useful way
fac = intersect_point_line(p_apex_co, p_mid, corner)[1]
# assert(fac >= 0.0)
h_sca_1 = 1 h1_fac = ((p1.co - p1_apex_co).length / 0.75) - fac_1
h_sca_2 = 1 h2_fac = ((p2.co - p2_apex_co).length / 0.75) - fac_2
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 h1 = p1.co + (p1.no * h1_fac)
# vis_curve_spline(p1.co, h1, p2.co, h2) h2 = p2.co - (p2.no * h2_fac)
self.handle_left = h1 self.handle_left = h1
self.handle_right = h2 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): def bezier_error(self):
from mathutils.geometry import interpolate_bezier from mathutils.geometry import interpolate_bezier
...@@ -818,7 +841,7 @@ def points_to_bezier(points_orig, ...@@ -818,7 +841,7 @@ def points_to_bezier(points_orig,
#curve.split_func_map_point(lambda p: (p.angle_filter() >= 0) != \ #curve.split_func_map_point(lambda p: (p.angle_filter() >= 0) != \
# (p.prev.angle_filter() >= 0)) # (p.prev.angle_filter() >= 0))
curve.split_func_map_point(swap_side) # curve.split_func_map_point(swap_side)
# now split based on total spline angle. # now split based on total spline angle.
...@@ -833,10 +856,18 @@ def points_to_bezier(points_orig, ...@@ -833,10 +856,18 @@ def points_to_bezier(points_orig,
) )
# 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: curve.split_func_spline(lambda s:
len(s.points) // 2 len(s.points) // 2
if ((s.bezier_solve(), s.bezier_error())[1] > if ((s.bezier_solve(), s.bezier_error())[1] >
bezier_tolerance) and (len(s.points) > 2) bezier_tolerance) and (len(s.points))
else -1, else -1,
recursive=True, recursive=True,
) )
...@@ -853,7 +884,7 @@ def points_to_bezier(points_orig, ...@@ -853,7 +884,7 @@ def points_to_bezier(points_orig,
if __name__ == "__main__": if __name__ == "__main__":
print("A") print("A")
bpy.ops.wm.open_mainfile(filepath="/root/curve_test.blend") bpy.ops.wm.open_mainfile(filepath="/root/curve_test1.blend")
ob = bpy.data.objects["Curve"] ob = bpy.data.objects["Curve"]
points = [p.co.xy for s in ob.data.splines for p in s.points] points = [p.co.xy for s in ob.data.splines for p in s.points]
......
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