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