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added svg output of circles

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This commit is contained in:
Simon Pirkelmann 2019-09-03 10:38:23 +02:00
parent 7403641a87
commit f34775eb3f
1 changed files with 275 additions and 111 deletions
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386
prototype/circles.py
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@ -3,7 +3,17 @@ import matplotlib.pyplot as plt
import math import math
import operator import operator
N = 5 # number of enclosed circles
def svg_circle(id, name, c, r):
text = [' <circle\n',
' id="circle{}"\n'.format(id),
' inkscape:label="{}"\n'.format(name),
' style="fill:none;stroke:#000000;stroke-width:1.0"\n',
' r="{}mm"\n'.format(r),
' cy="{}mm"\n'.format(c[1]),
' cx="{}mm" />\n'.format(c[0])]
return text
# this function reads and processes data for optimal circle packaging obtained form packomania.com # this function reads and processes data for optimal circle packaging obtained form packomania.com
def read_circle_data(N): def read_circle_data(N):
@ -40,7 +50,6 @@ def sort_ccw(coords, center):
return coords_sort return coords_sort
# compute the two tangential points at the circle with center c and radius r intersecting the point p # compute the two tangential points at the circle with center c and radius r intersecting the point p
def compute_tangent_points(p, c, r): def compute_tangent_points(p, c, r):
b = sqrt((p[0] - c[0]) ** 2 + (p[1] - c[1]) ** 2) b = sqrt((p[0] - c[0]) ** 2 + (p[1] - c[1]) ** 2)
@ -56,146 +65,301 @@ def compute_tangent_points(p, c, r):
return (T1x, T1y), (T2x, T2y) return (T1x, T1y), (T2x, T2y)
# read radius and center coordinates for enclosed circles
rtilde, coords = read_circle_data(N)
c = (0.0, 0.0) # center of big circle class PlateLayout:
R = 1.0 # radius of big circle def __init__(self, N, plate_radius):
self.N = N # number of enclosed circles
self.plate_radius = plate_radius
plt.xlim((-1, 1)) def compute_layout(self):
plt.ylim((-1, 1)) # read radius and center coordinates for enclosed circles
plt.gca().set_aspect('equal', 'box') rtilde, coords = read_circle_data(self.N)
plt.ion() c = (0.0, 0.0) # center of big circle
plt.show() R = 1.0 # radius of big circle
for p in coords: plt.xlim((-1, 1))
plt.plot(p[0], p[1], 'o') plt.ylim((-1, 1))
circle = plt.Circle(p, rtilde, fill=False) plt.gca().set_aspect('equal', 'box')
plt.gca().add_artist(circle)
circle = plt.Circle(c, R, fill=False)
plt.gca().add_artist(circle)
plt.plot(c[0], c[1], 'o') plt.ion()
plt.show()
coords_2 = [] for p in coords:
for k in range(0, N): plt.plot(p[0], p[1], 'o')
p1 = coords[k] circle = plt.Circle(p, rtilde, fill=False)
p2 = coords[(k+1) % N] plt.gca().add_artist(circle)
circle = plt.Circle(c, R, fill=False)
plt.gca().add_artist(circle)
# midpoint between center of two circles plt.plot(c[0], c[1], 'o')
m = np.mean([p1, p2], axis=0)
# vector in direction of midpoint coords_2 = []
v = m - np.array(c) for k in range(0, self.N):
v = v/np.linalg.norm(v) p1 = coords[k]
#plt.plot(m[0], m[1], 'o') p2 = coords[(k+1) % self.N]
# midpoint between center of two circles
m = np.mean([p1, p2], axis=0)
# vector in direction of midpoint
v = m - np.array(c)
v = v/np.linalg.norm(v)
#plt.plot(m[0], m[1], 'o')
# optimization problem for computing position and radius for a maximal circle fitting in space between two big circles # optimization problem for computing position and radius for a maximal circle fitting in space between two big circles
# and being fully contained in enclosing circle # and being fully contained in enclosing circle
opti = casadi.Opti() opti = casadi.Opti()
r = opti.variable(1) # radius of new circle r = opti.variable(1) # radius of new circle
p = opti.variable(2) # center of new circle p = opti.variable(2) # center of new circle
lamb = opti.variable(1) # distance of center of new circle to center of enclosing circle lamb = opti.variable(1) # distance of center of new circle to center of enclosing circle
opti.minimize(-r) opti.minimize(-r)
opti.subject_to(p == c + v * lamb) opti.subject_to(p == c + v * lamb)
opti.subject_to((p[0] - p1[0])**2 + (p[1] - p1[1])**2 >= (rtilde + r)**2) opti.subject_to((p[0] - p1[0])**2 + (p[1] - p1[1])**2 >= (rtilde + r)**2)
opti.subject_to(R == lamb + r) opti.subject_to(R == lamb + r)
opti.subject_to(r >= 0) opti.subject_to(r >= 0)
opti.subject_to(r <= R) opti.subject_to(r <= R)
opti.solver('ipopt') opti.solver('ipopt')
init_r = 0.1 init_r = 0.1
init_lamb = R - init_r init_lamb = R - init_r
init_p = c + v * init_lamb init_p = c + v * init_lamb
opti.set_initial(r, init_r) opti.set_initial(r, init_r)
opti.set_initial(p, init_p) opti.set_initial(p, init_p)
opti.set_initial(lamb, init_lamb) opti.set_initial(lamb, init_lamb)
sol = opti.solve() sol = opti.solve()
p = sol.value(p) p = sol.value(p)
r = sol.value(r) r = sol.value(r)
lamb = sol.value(lamb) lamb = sol.value(lamb)
print("p = {}".format(p)) print("p = {}".format(p))
print("r = {}".format(r)) print("r = {}".format(r))
print("lambda = {}".format(lamb)) print("lambda = {}".format(lamb))
print("v = {}".format(v)) print("v = {}".format(v))
coords_2.append(p) coords_2.append(p)
plt.plot(p[0], p[1], 'o') plt.plot(p[0], p[1], 'o')
circle = plt.Circle(p, r, fill=False) circle = plt.Circle(p, r, fill=False)
plt.gca().add_artist(circle) plt.gca().add_artist(circle)
tube1 = {}
tube2 = {}
# postprocessing solution:
# - output radii for circles
# - output center coordinates, angle w.r.t. origin and distance from origin
outer_radius = self.plate_radius # desired plate radius in meters
tube1_radius = outer_radius * rtilde
tube2_radius = outer_radius * r
print("\n------------------")
print("optimal values")
print("plate radius = {:6.3} m = {:6.2f} mm".format(outer_radius / 1000, outer_radius))
print("big circles:")
print(" radius = {:6.3} m = {:6.2f} mm".format(tube1_radius / 1000, tube1_radius))
print(" diameter = {:6.3} m = {:6.2f} mm".format(2 * tube1_radius / 1000, 2 * tube1_radius))
print("small circles:")
print(" radius = {:6.3} m = {:6.2f} mm".format(tube2_radius, tube2_radius * 1000))
print(" diameter = {:6.3} m = {:6.2f} mm".format(2*tube2_radius, 2*tube2_radius * 1000))
# compute coordinates and various measurements for fixed radii of plate and tubes
self.target_plate_radius = 155.0
self.target_radius_1 = 50.0
self.target_radius_2 = 20.0
teeth = 360
D = 2 * self.target_plate_radius
m = D/teeth/math.pi
print("plate radius = {:6.2f} mm".format(self.target_plate_radius))
print("big circle radius = {:6.2f} mm".format(self.target_radius_1))
print("small circle radius = {:6.2f} mm".format(self.target_radius_2))
print("number of teeth: N = {}".format(teeth))
print("pitch diameter: D = {} mm".format(D))
print("module: M = {} mm".format(m))
# plot plate
plt.figure(2)
plt.plot(0.0, 0.0, 'o')
circle = plt.Circle((0.0, 0.0), self.target_plate_radius, fill=False)
plt.gca().add_artist(circle)
plt.xlim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
plt.ylim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
plt.gca().set_aspect('equal', 'box')
# plate coordinates
print("plate coordinates: (x,y) = ({:8.3f}, {:8.3f})".format(0.0, 0.0))
self.tube_1_coords = {}
self.tube_2_coords = {}
self.tube_1_tangents = {}
self.tube_1_tangent_angles = {}
self.tube_2_tangents = {}
self.tube_2_tangent_angles = {}
print(" big circle coordinates:")
for k in range(0,self.N):
x = coords[k][0] * outer_radius
y = coords[k][1] * outer_radius
angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
self.tube_1_coords[k] = (x,y)
print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg".format(k, x, y, angle))
circle = plt.Circle((x,y), self.target_radius_1, fill=False)
plt.gca().add_artist(circle)
print(" big circle tangent points: ")
for k in range(0, self.N):
x = coords[k][0] * outer_radius
y = coords[k][1] * outer_radius
t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_1)
angle1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi)
angle2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi)
self.tube_1_tangents[k] = (t1, t2)
self.tube_1_tangent_angles[k] = (angle1, angle2)
print(
" k = {}, t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg\n t2 = ({:8.3f}, {:8.3f}), angle "
"= {:8.3f} deg".format(k, t1[0], t1[1], angle1, t2[0], t2[1], angle2))
plt.plot(t1[0], t1[1], 'o')
plt.plot(t2[0], t2[1], 'o')
# postprocessing solution: print(" small circle coordinates:")
# - output radii for circles for k in range(0,self.N):
# - output center coordinates, angle w.r.t. origin and distance from origin x = coords_2[k][0] * outer_radius
outer_radius = 0.15 # desired plate radius in meters y = coords_2[k][1] * outer_radius
tube1_radius = outer_radius * rtilde
tube2_radius = outer_radius * r
print("\n------------------") angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
print("plate radius = {:6.3} m = {:6.2f} mm".format(outer_radius, outer_radius * 1000))
print("big circles:")
print(" radius = {:6.3} m = {:6.2f} mm".format(tube1_radius, tube1_radius * 1000))
print(" diameter = {:6.3} m = {:6.2f} mm".format(2*tube1_radius, 2*tube1_radius * 1000))
print(" coordinates:")
for k in range(0,N):
x = coords[k][0] * 1000
y = coords[k][1] * 1000
t1, t2 = compute_tangent_points((0,0),(x,y), rtilde * 1000) self.tube_2_coords[k] = (x, y)
plt.plot(t1[0] / 1000, t1[1] / 1000, 'o')
plt.plot(t2[0] / 1000, t2[1] / 1000, 'o')
angle = arctan2(y,x) * 360.0 / (2.0 * math.pi) print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg".format(k, x, y, angle))
dist = (x**2 + y**2)**0.5
angle_t1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi) circle = plt.Circle((x, y), self.target_radius_2, fill=False)
dist_t1 = (t1[0] ** 2 + t1[1] ** 2) ** 0.5 plt.gca().add_artist(circle)
angle_t2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi) print(" small circle tangent points: ")
dist_t2 = (t2[0] ** 2 + t2[1] ** 2) ** 0.5 for k in range(0, self.N):
print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(k, x, y, angle, dist)) x = coords_2[k][0] * outer_radius
print(" t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t1[0], t1[1], angle_t1, y = coords_2[k][1] * outer_radius
dist_t1))
print(" t2 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t2[0], t2[1], angle_t2,
dist_t2))
print("\n")
print("small circles:") t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_2)
print(" radius = {:6.3} m = {:6.2f} mm".format(tube2_radius, tube2_radius * 1000)) angle1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi)
print(" diameter = {:6.3} m = {:6.2f} mm".format(2*tube2_radius, 2*tube2_radius * 1000)) angle2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi)
print(" coordinates:") self.tube_2_tangents[k] = (t1, t2)
for k in range(0,N): self.tube_2_tangent_angles[k] = (angle1, angle2)
x = coords_2[k][0] * 1000
y = coords_2[k][1] * 1000
t1, t2 = compute_tangent_points((0, 0), (x, y), r * 1000) print(" k = {}, t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg\n t2 = ({:8.3f}, {:8.3f}), angle "
plt.plot(t1[0] / 1000, t1[1] / 1000, 'o') "= {:8.3f} deg".format(k, t1[0], t1[1], angle1, t2[0], t2[1], angle2))
plt.plot(t2[0] / 1000, t2[1] / 1000, 'o')
angle = arctan2(y, x) * 360.0 / (2.0 * math.pi) plt.plot(t1[0], t1[1], 'o')
dist = (x ** 2 + y ** 2) ** 0.5 plt.plot(t2[0], t2[1], 'o')
angle_t1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi) # for k in range(0, self.N):
dist_t1 = (t1[0] ** 2 + t1[1] ** 2) ** 0.5 #
# t1, t2 = compute_tangent_points((0,0),(x,y), target_radius_1)
# self.tube_1_tangents[k] = (t1, t2)
#
# plt.plot(t1[0] / 1000, t1[1] / 1000, 'o')
# plt.plot(t2[0] / 1000, t2[1] / 1000, 'o')
#
# angle = arctan2(y,x) * 360.0 / (2.0 * math.pi)
# dist = (x**2 + y**2)**0.5
#
# angle_t1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi)
# dist_t1 = (t1[0] ** 2 + t1[1] ** 2) ** 0.5
#
# angle_t2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi)
# dist_t2 = (t2[0] ** 2 + t2[1] ** 2) ** 0.5
# print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(k, x, y, angle, dist))
# print(" t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t1[0], t1[1], angle_t1,
# dist_t1))
# print(" t2 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t2[0], t2[1], angle_t2,
# dist_t2))
# print("\n")
# tube1['coords'] = tube_1_coords
# tube1['tangents'] = tube_1_tangents
#
# tube_2_coords = {}
# tube_2_tangents = {}
# print(" coordinates:")
# for k in range(0,self.N):
# x = coords_2[k][0] * 1000
# y = coords_2[k][1] * 1000
#
# tube_2_coords[k] = (x, y)
#
# t1, t2 = compute_tangent_points((0, 0), (x, y), r * 100)
# tube_2_tangents[k] = (t1, t2)
# plt.plot(t1[0] / 1000, t1[1] / 1000, 'o')
# plt.plot(t2[0] / 1000, t2[1] / 1000, 'o')
#
# angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
# dist = (x ** 2 + y ** 2) ** 0.5
#
# angle_t1 = arctan2(t1[1], t1[0]) * 360.0 / (2.0 * math.pi)
# dist_t1 = (t1[0] ** 2 + t1[1] ** 2) ** 0.5
#
# angle_t2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi)
# dist_t2 = (t2[0] ** 2 + t2[1] ** 2) ** 0.5
# print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(k, x, y, angle, dist))
# print(" t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t1[0], t1[1], angle_t1,
# dist_t1))
# print(" t2 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t2[0], t2[1], angle_t2,
# dist_t2))
# tube2['coords'] = tube_2_coords
# tube2['tangents'] = tube_2_tangents
#
# return tube1, tube2
angle_t2 = arctan2(t2[1], t2[0]) * 360.0 / (2.0 * math.pi) """
dist_t2 = (t2[0] ** 2 + t2[1] ** 2) ** 0.5 input: file = svg with plate gear centered at (0,0)
print(" k = {}, (x,y) = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(k, x, y, angle, dist)) """
print(" t1 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t1[0], t1[1], angle_t1, def generate_svg(self, file):
dist_t1))
print(" t2 = ({:8.3f}, {:8.3f}), angle = {:8.3f} deg, dist = {:8.3f} mm".format(t2[0], t2[1], angle_t2,
dist_t2))
f = open(file)
f_lines = f.readlines()
f.close()
pass f_lines.remove(f_lines[-1])
# output plate as svg
text = svg_circle(0, 'plate', (0,0), self.target_plate_radius)
f_lines = f_lines + text
# output big circles as svg
for k, c in self.tube_1_coords.items():
text = svg_circle(k, 'big circle', c, self.target_radius_1)
f_lines = f_lines + text
pass
# output small circles as svg
for k, c in self.tube_2_coords.items():
text = svg_circle(k, 'small circle', c, self.target_radius_2)
f_lines = f_lines + text
pass
f_lines.append('</svg>\n')
fw = open('output.svg', 'w')
fw.writelines(f_lines)
fw.close()
pass