MuesliMix/prototype/circles.py

597 lines
23 KiB
Python

from casadi import *
import matplotlib.pyplot as plt
import math
import operator
from svg_utils import *
# this function reads and processes data for optimal circle packaging obtained form packomania.com
def read_circle_data(N):
coords_raw = open('cci/cci{}.txt'.format(N))
radii_raw = open('cci/radii.txt'.format(N))
coords_raw = coords_raw.readlines()
coords_raw = [c.split() for c in coords_raw if c[0] != '#']
coords = {}
for c in coords_raw:
coords[int(c[0])] = (float(c[1]), float(c[2]))
coords = sort_ccw(coords, (0,0))
radii_raw = radii_raw.readlines()
radii_raw = [r.split() for r in radii_raw if r[0] != '#']
radii = {}
for r in radii_raw:
radii[int(r[0])] = float(r[1])
return radii[N], coords
# this function sorts enclosed circle coordinates counter-clockwise w.r.t. the center point
# TODO: there is a problem when circles are present that are not touching the boundary of the enclosing circle (e.g. N = 7)
def sort_ccw(coords, center):
a = {}
for c in coords:
a[c] = math.atan2(coords[c][1] - center[1], coords[c][0] - center[0])
a_sort = sorted(a.items(), key=operator.itemgetter(1))
coords_sort = []
for a in a_sort:
coords_sort.append(coords[a[0]])
return coords_sort
# 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):
b = sqrt((p[0] - c[0]) ** 2 + (p[1] - c[1]) ** 2)
th = acos(r / b) # angle theta
d = atan2(p[1] - c[1], p[0] - c[0]) # direction angle of point p from c
d1 = d + th # direction angle of point T1 from c
d2 = d - th # direction angle of point T2 from c
T1x = c[0] + r * cos(d1)
T1y = c[1] + r * sin(d1)
T2x = c[0] + r * cos(d2)
T2y = c[1] + r * sin(d2)
return (T1x, T1y), (T2x, T2y)
class PlateLayout:
def __init__(self, N, plate_radius):
self.N = N # number of enclosed circles
self.plate_radius = plate_radius
def compute_layout(self):
# read radius and center coordinates for enclosed circles
rtilde, coords = read_circle_data(self.N)
c = (0.0, 0.0) # center of big circle
R = 1.0 # radius of big circle
plt.xlim((-1, 1))
plt.ylim((-1, 1))
plt.gca().set_aspect('equal', 'box')
plt.ion()
plt.show()
for p in coords:
plt.plot(p[0], p[1], 'o')
circle = plt.Circle(p, rtilde, fill=False)
plt.gca().add_artist(circle)
circle = plt.Circle(c, R, fill=False)
plt.gca().add_artist(circle)
plt.plot(c[0], c[1], 'o')
coords_2 = []
for k in range(0, self.N):
p1 = coords[k]
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
# and being fully contained in enclosing circle
opti = casadi.Opti()
r = opti.variable(1) # radius 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
opti.minimize(-r)
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(R == lamb + r)
opti.subject_to(r >= 0)
opti.subject_to(r <= R)
opti.solver('ipopt')
init_r = 0.1
init_lamb = R - init_r
init_p = c + v * init_lamb
opti.set_initial(r, init_r)
opti.set_initial(p, init_p)
opti.set_initial(lamb, init_lamb)
sol = opti.solve()
p = sol.value(p)
r = sol.value(r)
lamb = sol.value(lamb)
print("p = {}".format(p))
print("r = {}".format(r))
print("lambda = {}".format(lamb))
print("v = {}".format(v))
coords_2.append(p)
plt.plot(p[0], p[1], 'o')
circle = plt.Circle(p, r, fill=False)
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 = 160.0
self.target_center_hole_radius = 7.5
self.target_radius_1 = 50.5
self.target_radius_2 = 20.0
teeth = 200
D = 2 * self.target_plate_radius
self.plate_module = D/teeth
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(self.plate_module))
# parameters for dispenser gears
self.dispenser_module = 1.0
dispenser_1_target_pitch_diameter_big = 50.0
dispenser_1_target_pitch_diameter_small = 15.0
dispenser_1_teeth_big = int(dispenser_1_target_pitch_diameter_big/self.dispenser_module)
dispenser_1_teeth_small = int(dispenser_1_target_pitch_diameter_small/ self.dispenser_module)
dispenser_1_pitch_diameter_big = self.dispenser_module * dispenser_1_teeth_big
dispenser_1_outer_diameter_big = dispenser_1_pitch_diameter_big + 2 * self.dispenser_module
dispenser_1_pitch_diameter_small = self.dispenser_module * dispenser_1_teeth_small
dispenser_1_outer_diameter_small = dispenser_1_pitch_diameter_small + 2 * self.dispenser_module
dispenser_2_target_pitch_diameter_big = 20.0
dispenser_2_target_pitch_diameter_small = 15.0
dispenser_2_teeth_big = int(dispenser_2_target_pitch_diameter_big / self.dispenser_module)
dispenser_2_teeth_small = int(dispenser_2_target_pitch_diameter_small / self.dispenser_module)
dispenser_2_pitch_diameter_big = self.dispenser_module * dispenser_2_teeth_big
dispenser_2_outer_diameter_big = dispenser_2_pitch_diameter_big + 2 * self.dispenser_module
dispenser_2_pitch_diameter_small = self.dispenser_module * dispenser_2_teeth_small
dispenser_2_outer_diameter_small = dispenser_2_pitch_diameter_small + 2 * self.dispenser_module
print("parameters for dispenser gears:")
print(" big container:")
print(" module = {}".format(self.dispenser_module))
print(" pitch diameter big gear = {}".format(dispenser_1_pitch_diameter_big))
print(" number of teeth big gear = {}".format(dispenser_1_teeth_big))
print(" pitch diameter small gear = {}".format(dispenser_1_pitch_diameter_small))
print(" number of teeth small gear = {}".format(dispenser_1_teeth_small))
print(" small container:")
print(" module = {}".format(self.dispenser_module))
print(" pitch diameter big gear = {}".format(dispenser_2_pitch_diameter_big))
print(" number of teeth big gear = {}".format(dispenser_2_teeth_big))
print(" pitch diameter small gear = {}".format(dispenser_2_pitch_diameter_small))
print(" number of teeth small gear = {}".format(dispenser_2_teeth_small))
# 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_angles = {}
self.tube_2_angles = {}
self.tube_1_tangents = {}
self.tube_1_tangent_angles = {}
self.tube_1_cuts = {}
self.tube_2_tangents = {}
self.tube_2_tangent_angles = {}
self.tube_2_cuts = {}
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)
self.tube_1_angles[k] = angle
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)
p1 = dispenser_1_pitch_diameter_big
p2 = dispenser_1_pitch_diameter_small
a1 = self.dispenser_module
a2 = self.dispenser_module
offset_1 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
print("dispenser 1 offset = {}".format(offset_1))
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_rad = arctan2(t1[1], t1[0])
angle2_rad = arctan2(t2[1], t2[0])
angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)
self.tube_1_tangents[k] = (t1, t2)
self.tube_1_tangent_angles[k] = (angle1_deg, angle2_deg)
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_deg, t2[0], t2[1], angle2_deg))
plt.plot(t1[0], t1[1], 'o')
plt.plot(t2[0], t2[1], 'o')
## compute position of cut for dispenser gear
# vector pointing from center in direction of tangent point
v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])
cut_center = np.array(t1) - v * (offset_1 + dispenser_1_outer_diameter_small/2.0)
self.tube_1_cuts[k] = {}
self.tube_1_cuts[k]['center'] = cut_center
self.tube_1_cuts[k]['tangent_point'] = t1
self.tube_1_cuts[k]['angle_deg'] = angle1_deg
self.tube_1_cuts[k]['length'] = dispenser_1_outer_diameter_small
self.tube_1_cuts[k]['width'] = 5.0
plt.plot(cut_center[0], cut_center[1], 'o')
pass
print(" small circle coordinates:")
for k in range(0,self.N):
x = coords_2[k][0] * outer_radius
y = coords_2[k][1] * outer_radius
angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)
self.tube_2_coords[k] = (x, y)
self.tube_2_angles[k] = angle
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_2, fill=False)
plt.gca().add_artist(circle)
p1 = dispenser_2_pitch_diameter_big
p2 = dispenser_2_pitch_diameter_small
a1 = self.dispenser_module
a2 = self.dispenser_module
offset_2 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
print("dispenser 2 offset = {}".format(offset_2))
print(" small circle tangent points: ")
for k in range(0, self.N):
x = coords_2[k][0] * outer_radius
y = coords_2[k][1] * outer_radius
t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_2)
angle1_rad = arctan2(t1[1], t1[0])
angle2_rad = arctan2(t2[1], t2[0])
angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)
self.tube_2_tangents[k] = (t1, t2)
self.tube_2_tangent_angles[k] = (angle1_deg, angle2_deg)
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_deg, t2[0], t2[1], angle2_deg))
plt.plot(t1[0], t1[1], 'o')
plt.plot(t2[0], t2[1], 'o')
## compute position of cut for dispenser gear
# vector pointing from center in direction of tangent point
v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])
cut_center = np.array(t1) + v * (offset_2 + dispenser_2_outer_diameter_small/2.0)
self.tube_2_cuts[k] = {}
self.tube_2_cuts[k]['center'] = cut_center
self.tube_2_cuts[k]['tangent_point'] = t1
self.tube_2_cuts[k]['angle_deg'] = angle1_deg
self.tube_2_cuts[k]['length'] = dispenser_2_outer_diameter_small
self.tube_2_cuts[k]['width'] = 5.0
plt.plot(cut_center[0], cut_center[1], 'o')
pass
pass
"""
input: file = svg with plate gear centered at (0,0)
"""
def generate_svg(self, file):
f = open(file)
f_lines = f.readlines()
f.close()
circle_found = False
for k in range(len(f_lines)):
current_line = f_lines[k]
if 'transform' in current_line:
# rotate gear such that teeth match the cut lines
index = current_line.find('"\n')
f_lines[k] = current_line[0:index] + " rotate(0.9)" + current_line[-2:]
if 'd="m ' in current_line:
# remove center whole drawn by gear-dev
gear_data = current_line
index = gear_data.find('z') # end of path containing gear outline coordinates
f_lines[k] = gear_data[0:index+1] + gear_data[-2:]
if '<circle' in current_line:
circle_found = True
if circle_found and 'r=' in current_line:
# adjust center hole radius
f_lines[k] = ' r="{}mm"\n'.format(self.target_center_hole_radius)
# delete last line with </svg> command
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_all = False
if output_all:
f_lines = self.output_whole(f_lines)
else:
f_lines = self.output_segment(f_lines, 2)
f_lines.append('</svg>\n')
# write new svg image
fw = open('output.svg', 'w')
fw.writelines(f_lines)
fw.close()
pass
def output_segment(self, f_lines, k):
# k = which segment?
k_next = (k + 1) % self.N
# center hole
a = self.tube_1_angles[k]
a = a / 360.0 * 2.0 * np.pi
vunit = np.array([np.cos(a), np.sin(a)])
p1 = vunit * self.target_center_hole_radius
a2 = self.tube_1_angles[k_next]
a2 = a2 / 360.0 * 2.0 * np.pi
vunit2 = np.array([np.cos(a2), np.sin(a2)])
p2 = vunit2 * self.target_center_hole_radius
f_lines += svg_arc(p1, p2, self.target_center_hole_radius, 0, 1)
# big circles arcs
f_lines += svg_half_circle(k, 'big circle', self.tube_1_coords[k], self.target_radius_1, self.tube_1_angles[k])
f_lines += svg_half_circle(k_next, 'big circle', self.tube_1_coords[k_next], self.target_radius_1,
self.tube_1_angles[k_next], orientation_flag=0)
# small circle
f_lines += svg_circle(k, 'small circle', self.tube_2_coords[k], self.target_radius_2)
# gear pos for big circle
f_lines += svg_gear_marking(self.tube_1_tangents[k_next], self.tube_1_coords[k_next])
# cutout rectangle for big circles
f_lines += svg_rectangle(k_next, 'cut', self.tube_1_cuts[k_next])
# gear pos for small circle
f_lines += svg_gear_marking(self.tube_2_tangents[k], self.tube_2_coords[k])
# cutout rectangle for small circles
f_lines += svg_rectangle(k, 'cut', self.tube_2_cuts[k])
# first segment border
f_lines += svg_segment_border_inner(self.tube_1_angles[k], self.target_center_hole_radius,
self.tube_1_coords[k], self.target_radius_1)
f_lines += svg_segment_border_outer(self.tube_1_angles[k], self.target_plate_radius, self.plate_module,
self.tube_1_coords[k], self.target_radius_1)
# second segment border
f_lines += svg_segment_border_inner(self.tube_1_angles[k_next], self.target_center_hole_radius,
self.tube_1_coords[k_next], self.target_radius_1)
f_lines += svg_segment_border_outer(self.tube_1_angles[k_next], self.target_plate_radius, self.plate_module,
self.tube_1_coords[k_next], self.target_radius_1)
# find outmost points for segment cut lines
# in addition we rotate the points by 0.9 degrees because we also rotated the gear path
# by this amount above
r_pitch_minus_module = self.target_plate_radius - self.plate_module
a1 = (self.tube_1_angles[k] - 0.9) / 360.0 * 2.0 * np.pi
vunit1 = np.array([np.cos(a1), np.sin(a1)])
outer_point_1 = vunit1 * r_pitch_minus_module
a2 = (self.tube_1_angles[k_next] - 0.9) / 360.0 * 2.0 * np.pi
vunit2 = np.array([np.cos(a2), np.sin(a2)])
outer_point_2 = vunit2 * r_pitch_minus_module
# truncate gear path
for j in range(len(f_lines)):
current_line = f_lines[j]
if 'd="m ' in current_line:
# remove center whole drawn by gear-dev
gear_data = current_line
index_start = gear_data.find('m') # end of path containing gear outline coordinates
index_end = gear_data.find('z')
coordinates_data_raw = gear_data[index_start+1:index_end].split()
c_running = np.array([float(v) for v in coordinates_data_raw[0].split(',')])
coordinates = [c_running]
for c in coordinates_data_raw[1:]:
dv = np.array([float(v) for v in c.split(',')])
c_running = c_running + dv
coordinates.append(c_running)
pass
# find nodes on gear path with minimal distance to segment cuts
dist_1 = [np.linalg.norm(c - outer_point_1 * svg_scale) for c in coordinates]
dist_2 = [np.linalg.norm(c - outer_point_2 * svg_scale) for c in coordinates]
min_dist_index_1 = np.argmin(dist_1)
min_dist_index_2 = np.argmin(dist_2)
if min_dist_index_2 > min_dist_index_1:
coordinates = coordinates[min_dist_index_1:min_dist_index_2+1]
else:
coordinates = coordinates[min_dist_index_1:] + coordinates[0:min_dist_index_2]
coordinates_data_raw_new = "".join(['{},{} '.format(c[0], c[1]) for c in coordinates])
# keep only those nodes from the gear path that are between the segment cuts
gear_data_new = gear_data[0:index_start] + "M " + coordinates_data_raw_new + gear_data[index_end+1:]
f_lines[j] = gear_data_new
return f_lines
def output_whole(self, f_lines):
# 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
# gear markings for big cirlces and small circles
for k, c in self.tube_1_tangents.items():
circle_midpoint = self.tube_1_coords[k]
v = np.array(c[0]) - np.array(circle_midpoint)
v = v/np.linalg.norm(v)
marking_length = 5.0
p1 = c[0]
p2 = c[0] + v * marking_length
text = svg_line(p1, p2)
f_lines = f_lines + text
for k, c in self.tube_2_tangents.items():
circle_midpoint = self.tube_2_coords[k]
v = np.array(c[0]) - np.array(circle_midpoint)
v = v/np.linalg.norm(v)
marking_length = 5.0
p1 = c[0]
p2 = c[0] + v * marking_length
text = svg_line(p1, p2)
f_lines = f_lines + text
pass
# output cuts for big circles
for k, c in self.tube_1_cuts.items():
text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
f_lines = f_lines + text
pass
# output cuts for small circles
for k, c in self.tube_2_cuts.items():
text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
f_lines = f_lines + text
pass
# lines for manufacturing out of multiple pieces
for k, a in self.tube_1_angles.items():
a = a/360.0 * 2.0 * np.pi
r1 = np.linalg.norm(np.array(self.tube_1_coords[k])) - self.target_radius_1
vunit = np.array([np.cos(a), np.sin(a)])
p1 = vunit * self.target_center_hole_radius
p2 = vunit * r1
text = svg_line(p1, p2, 0.1)
f_lines = f_lines + text
r2 = np.linalg.norm(np.array(self.tube_1_coords[k])) + self.target_radius_1
p3 = vunit * r2
r3 = self.target_plate_radius - self.plate_module
p4 = vunit * r3
text = svg_line(p3, p4, 0.1)
f_lines = f_lines + text
pass
return f_lines