def get_outer_angle(p1, p2, center, radius):
xp1, yp1 = p1
xp2, yp2 = p2
xc, yc = center
a = math.atan2(yp1 - yc, xp1 - xc)
b = math.atan2(yp2 - yc, xp2 - xc)
beta = abs((a - b) % (2 * math.pi))
mid = (xp1 + xp2) / 2, (yp1 + yp2) / 2
proj_1 = functions.euclid_dist(center, mid)
alpha_a = functions.euclid_dist(mid, p2)
proj_2 = alpha_a * math.tan(beta / 2)
p3 = project_to_circle(mid, center, proj_1 + proj_2)
return beta / 2, p3
def get_curve_length(c):
l = 0
for i in range(len(c.evalpts) - 1):
l += functions.euclid_dist(c.evalpts[i], c.evalpts[i + 1])
return l
def get_cm_from_interpolation_length(pts, interpolation_factor, center_circle,
radius): # 0 is circ
center = center_circle
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
circle_length = 2 * math.pi * radius
tangents = []
curve_lengths = []
for i in range(len(pts)):
p1 = pts[(i - 1) % len(pts)]
p2 = pts[(i + 1) % len(pts)]
pr = (p2[0] - p1[0], p2[1] - p1[1])
alpha = math.atan2(pr[1], pr[0]) % math.pi
tangents.append(alpha)
dists = []
for i in range(len(pts)):
dist = functions.euclid_dist(pts[i], pts[(i + 1) % len(pts)])
d = dist * 0.25
dists.append(d)
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
length = get_curve_length(c)
curve_lengths.append(length)
cm.add(c)
curve_lengths.reverse()
xc, yc = center_circle
pts_r = list(pts)
pts_r.reverse()
distance_factor = circle_length / sum(curve_lengths)
pts_interpolated = []
starting_point = functions.project_to_circle(pts[0], center_circle, radius)
pts_interpolated.append(starting_point)
starting_angle = math.atan2(starting_point[1] - yc, starting_point[0] - xc)
alpha = curve_lengths[0] * distance_factor / radius
xp = xc + radius * math.cos(alpha)
yp = yc + radius * math.sin(alpha)
angle_sum = starting_angle
for i in range(len(pts) - 1):
alpha = curve_lengths[i] * distance_factor / radius
angle_sum += alpha
xp = xc + radius * math.cos(angle_sum)
yp = yc + radius * math.sin(angle_sum)
pts_interpolated.append((xp, yp))
pts_interpolated.reverse()
pts_interpolated.insert(0, pts_interpolated.pop())
tangents_interpolated = []
for i in range(len(pts_interpolated)):
x, y = pts_interpolated[i]
alpha = math.atan2(y - center_circle[1], x - center_circle[0])
alpha -= 0.5 * math.pi
alpha = alpha % math.pi
tangents_interpolated.append(alpha)
dists_interpolated = []
for i in range(len(pts_interpolated)):
x1, y1 = pts_interpolated[i]
x4, y4 = pts_interpolated[(i + 1) % len(pts_interpolated)]
xc, yc = center_circle
axx = x1 - xc
ay = y1 - yc
bx = x4 - xc
by = y4 - yc
q1 = axx * axx + ay * ay
q2 = q1 + axx * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (axx * by - ay * bx)
d = math.sqrt((k2 * ay)**2 + (k2 * axx)**2)
dists_interpolated.append(d)
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
pts = [[
interpolation_factor * pp[0] + (1 - interpolation_factor) * pc[0],
interpolation_factor * pp[1] + (1 - interpolation_factor) * pc[1]
] for (pp, pc) in zip(pts, pts_interpolated)]
new_tangents = []
for tp, tc in zip(tangents, tangents_interpolated):
if abs(tp - tc) > math.pi / 2:
if tp < math.pi / 2:
t = interpolation_factor * (tp + math.pi) + (
1 - interpolation_factor) * tc
elif tc < math.pi / 2:
t = interpolation_factor * tp + (1 - interpolation_factor) * (
tc + math.pi)
else:
t = interpolation_factor * tp + (1 - interpolation_factor) * tc
new_tangents.append(t)
tangents = new_tangents
dists = [
interpolation_factor * dp + (1 - interpolation_factor) * dc
for (dp, dc) in zip(dists, dists_interpolated)
]
angle_mapping = {}
ctrlpts = []
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if i == 0:
print(tangents[i])
if p1[1] < p2[1] and tangents[i] < math.pi:
p1, p2 = p2, p1
elif p1[1] > p2[1] and tangents[i] > math.pi:
p1, p2 = p2, p1
else:
if math.atan2(p1[1] - center[1], p1[0] - center[0]) < math.atan2(
p2[1] - center[1], p2[0] - center[0]):
p1, p2 = p2, p1
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
xp, yp = pts[i]
if (xp, yp) in angle_mapping:
p = angle_mapping[(xp, yp)]
if p[0] > xp and p2[0] > xp or p[0] < xp and p2[0] < xp:
p1, p2 = p2, p1
angle_mapping[(xp, yp)] = p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
xp, yp = pts[(i + 1) % len(pts)]
angle_mapping[(xp, yp)] = p3
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
cm.add(c)
return cm
def get_cm_from_interpolation_radial(pts, interpolation_factor): # 0 is circ
center_circle = (200, 540)
center_polygon = (223, 555)
center = center_circle[0] * (
1 - interpolation_factor
) + center_polygon[0] * interpolation_factor, center_circle[1] * (
1 - interpolation_factor) + center_polygon[1] * interpolation_factor
radius = 70
tangents = []
for i in range(len(pts)):
p1 = pts[(i - 1) % len(pts)]
p2 = pts[(i + 1) % len(pts)]
pr = (p2[0] - p1[0], p2[1] - p1[1])
alpha = math.atan2(pr[1], pr[0])
tangents.append(alpha)
dists = []
for i in range(len(pts)):
dist = functions.euclid_dist(pts[i], pts[(i + 1) % len(pts)])
d = dist * 0.3
dists.append(d)
pts_interpolated = [
functions.project_to_circle(p, center_circle, radius) for p in pts
]
tangents_interpolated = []
for i in range(len(pts)):
x, y = pts[i]
alpha = math.atan2(y - center_circle[1], x - center_circle[0])
alpha -= 0.5 * math.pi
alpha = alpha % math.pi
tangents_interpolated.append(alpha)
dists_interpolated = []
for i in range(len(pts_interpolated)):
x1, y1 = pts_interpolated[i]
x4, y4 = pts_interpolated[(i + 1) % len(pts_interpolated)]
xc, yc = center_circle
axx = x1 - xc
ay = y1 - yc
bx = x4 - xc
by = y4 - yc
q1 = axx * axx + ay * ay
q2 = q1 + axx * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (axx * by - ay * bx)
d = math.sqrt((k2 * ay)**2 + (k2 * axx)**2)
dists_interpolated.append(d)
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
pts = [[
interpolation_factor * pp[0] + (1 - interpolation_factor) * pc[0],
interpolation_factor * pp[1] + (1 - interpolation_factor) * pc[1]
] for (pp, pc) in zip(pts, pts_interpolated)]
new_tangents = []
for tp, tc in zip(tangents, tangents_interpolated):
if abs(tp - tc) > math.pi / 2:
if tp < math.pi / 2:
t = interpolation_factor * (tp + math.pi) + (
1 - interpolation_factor) * tc
elif tc < math.pi / 2:
t = interpolation_factor * tp + (1 - interpolation_factor) * (
tc + math.pi)
else:
t = interpolation_factor * tp + (1 - interpolation_factor) * tc
new_tangents.append(t)
tangents = new_tangents
dists = [
interpolation_factor * dp + (1 - interpolation_factor) * dc
for (dp, dc) in zip(dists, dists_interpolated)
]
ctrlpts = []
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if math.atan2(p1[1] - center[1], p1[0] - center[0]) < math.atan2(
p2[1] - center[1], p2[0] - center[0]):
p1, p2 = p2, p1
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
cm.add(c)
return cm
import numpy as np
from scipy import interpolate
from matplotlib import pyplot as plt
import functions
import math
CIRCLE = False
#pts = [[485, 475], [387, 577]]
pts = [[485, 475], [430, 366], [325, 231], [274, 438], [193, 436], [150, 525],
[204, 604], [284, 612], [387, 577]]
#pts = [[100, 0], [0, -100], [-100, 0], [0, 100]]
center = (317, 465)
radius = max([functions.euclid_dist(p, center) for p in pts])
if CIRCLE:
pts = [functions.project_to_circle(p, center, radius) for p in pts]
circle_pts = [[center[0] + radius, center[1]],
[center[0] - radius, center[1]],
[center[0], center[1] + radius],
[center[0], center[1] - radius]]
circle_pts_2 = [[center[0] + radius, center[1] + radius],
[center[0] - radius, center[1] - radius],
[center[0] - radius, center[1] + radius],
[center[0] + radius, center[1] - radius]]
circle_pts_2 = [
functions.project_to_circle(p, center, radius) for p in circle_pts_2
]
pts.extend(circle_pts)
pts.extend(circle_pts_2)
curves_0 = []
curve.degree = 3 # order = degree + 1
curve.ctrlpts = pts_c
curve.knotvector = utilities.generate_knot_vector(curve.degree,
len(curve.ctrlpts),
clamped=False)
curve_list = operations.decompose_curve(curve)
knot_vectors = []
radius = 0
for c in curve_list:
knot_vectors.append(c.knotvector)
curves_0.append(c)
radius = max(radius,
max([functions.euclid_dist(center, p) for p in c.ctrlpts]))
base_pts = [(p[0], p[1]) for c in curve_list for p in c.ctrlpts]
x, y, r = make_circle(base_pts) # O(n)
center = (x, y)
radius = r
pts_pr = []
for c in curves_0:
pts_pr.append(project_to_circle(c.ctrlpts[0], center, radius))
#print(project_to_circle(c.ctrlpts[0], center, radius))
#print(len(pts_pr))
pts_pr[0] = pts_pr[-1]
circle_ctrl = []