added angle and distance computation + computation of tangent points
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@ -3,7 +3,7 @@ import matplotlib.pyplot as plt
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import math
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import operator
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N = 7 # number of enclosed circles
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N = 5 # number of enclosed circles
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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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@ -40,6 +40,22 @@ 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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th = acos(r / b) # angle theta
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d = atan2(p[1] - c[1], p[0] - c[0]) # direction angle of point p from c
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d1 = d + th # direction angle of point T1 from c
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d2 = d - th # direction angle of point T2 from c
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T1x = c[0] + r * cos(d1)
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T1y = c[1] + r * sin(d1)
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T2x = c[0] + r * cos(d2)
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T2y = c[1] + r * sin(d2)
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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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@ -62,6 +78,7 @@ plt.gca().add_artist(circle)
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plt.plot(c[0], c[1], 'o')
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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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@ -72,13 +89,16 @@ for k in range(0, N):
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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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#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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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)
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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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@ -108,8 +128,74 @@ for k in range(0, N):
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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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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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# 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("\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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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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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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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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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 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), 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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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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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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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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pass
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