added angle and distance computation + computation of tangent points

prototype/circles.py

@@ -3,7 +3,7 @@ import matplotlib.pyplot as plt
 import math
 import operator
 
-N = 7 # number of enclosed circles
+N = 5 # number of enclosed circles
 
 # this function reads and processes data for optimal circle packaging obtained form packomania.com
 def read_circle_data(N):
@@ -40,6 +40,22 @@ def sort_ccw(coords, center):
 
     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)
+
 # read radius and center coordinates for enclosed circles
 rtilde, coords = read_circle_data(N)
 
@@ -62,6 +78,7 @@ plt.gca().add_artist(circle)
 
 plt.plot(c[0], c[1], 'o')
 
+coords_2 = []
 for k in range(0, N):
     p1 = coords[k]
     p2 = coords[(k+1) % N]
@@ -72,13 +89,16 @@ for k in range(0, N):
     # vector in direction of midpoint
     v = m - np.array(c)
     v = v/np.linalg.norm(v)
-    plt.plot(m[0], m[1], 'o')
+    #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)
+    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)
@@ -108,8 +128,74 @@ for k in range(0, N):
     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)
 
+
+# postprocessing solution:
+# - output radii for circles
+# - output center coordinates, angle w.r.t. origin and distance from origin
+outer_radius = 0.15 # desired plate radius in meters
+tube1_radius = outer_radius * rtilde
+tube2_radius = outer_radius * r
+
+print("\n------------------")
+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)
+    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")
+
+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))
+print("  coordinates:")
+for k in range(0,N):
+    x = coords_2[k][0] * 1000
+    y = coords_2[k][1] * 1000
+
+    t1, t2 = compute_tangent_points((0, 0), (x, y), r * 1000)
+    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))
+
+
 pass