From b0a658a7b7180f5f8c6bf0a41a25ad4a22015518 Mon Sep 17 00:00:00 2001
From: spirkelmann <simon.pirkelmann@gmail.com>
Date: Tue, 27 Aug 2019 11:38:04 +0200
Subject: [PATCH] made script for optimal circle compuation more general by
 allowing also other number of circles

---
 prototype/cci/cci1.pdf                   | Bin 0 -> 3183 bytes
 prototype/cci/cci1.txt                   |   1 +
 prototype/cci/cci10.pdf                  | Bin 0 -> 4933 bytes
 prototype/cci/cci10.txt                  |  10 ++
 prototype/cci/cci11.pdf                  | Bin 0 -> 5157 bytes
 prototype/cci/cci11.txt                  |  11 ++
 prototype/cci/cci12.pdf                  | Bin 0 -> 5312 bytes
 prototype/cci/cci12.txt                  |  12 ++
 prototype/cci/cci13.pdf                  | Bin 0 -> 5303 bytes
 prototype/cci/cci13.txt                  |  13 ++
 prototype/cci/cci2.pdf                   | Bin 0 -> 3365 bytes
 prototype/cci/cci2.txt                   |   2 +
 prototype/cci/cci3.pdf                   | Bin 0 -> 3657 bytes
 prototype/cci/cci3.txt                   |   3 +
 prototype/cci/cci4.pdf                   | Bin 0 -> 3716 bytes
 prototype/cci/cci4.txt                   |   4 +
 prototype/cci/cci5.pdf                   | Bin 0 -> 4025 bytes
 prototype/cci/cci5.txt                   |   5 +
 prototype/cci/cci6.pdf                   | Bin 0 -> 4067 bytes
 prototype/cci/cci6.txt                   |   6 +
 prototype/cci/cci7.pdf                   | Bin 0 -> 4250 bytes
 prototype/cci/cci7.txt                   |   7 ++
 prototype/cci/cci8.pdf                   | Bin 0 -> 4523 bytes
 prototype/cci/cci8.txt                   |   8 ++
 prototype/cci/cci9.pdf                   | Bin 0 -> 4512 bytes
 prototype/cci/cci9.txt                   |   9 ++
 prototype/cci/radii.txt                  |  15 +++
 prototype/circles.py                     | 147 +++++++++++++----------
 prototype/tmp2019_cci_08_26_11_36_00.ps  |  95 ---------------
 prototype/tmp2019_cci_08_26_11_36_00.txt |   5 -
 30 files changed, 192 insertions(+), 161 deletions(-)
 create mode 100644 prototype/cci/cci1.pdf
 create mode 100644 prototype/cci/cci1.txt
 create mode 100644 prototype/cci/cci10.pdf
 create mode 100644 prototype/cci/cci10.txt
 create mode 100644 prototype/cci/cci11.pdf
 create mode 100644 prototype/cci/cci11.txt
 create mode 100644 prototype/cci/cci12.pdf
 create mode 100644 prototype/cci/cci12.txt
 create mode 100644 prototype/cci/cci13.pdf
 create mode 100644 prototype/cci/cci13.txt
 create mode 100644 prototype/cci/cci2.pdf
 create mode 100644 prototype/cci/cci2.txt
 create mode 100644 prototype/cci/cci3.pdf
 create mode 100644 prototype/cci/cci3.txt
 create mode 100644 prototype/cci/cci4.pdf
 create mode 100644 prototype/cci/cci4.txt
 create mode 100644 prototype/cci/cci5.pdf
 create mode 100644 prototype/cci/cci5.txt
 create mode 100644 prototype/cci/cci6.pdf
 create mode 100644 prototype/cci/cci6.txt
 create mode 100644 prototype/cci/cci7.pdf
 create mode 100644 prototype/cci/cci7.txt
 create mode 100644 prototype/cci/cci8.pdf
 create mode 100644 prototype/cci/cci8.txt
 create mode 100644 prototype/cci/cci9.pdf
 create mode 100644 prototype/cci/cci9.txt
 create mode 100644 prototype/cci/radii.txt
 delete mode 100644 prototype/tmp2019_cci_08_26_11_36_00.ps
 delete mode 100644 prototype/tmp2019_cci_08_26_11_36_00.txt

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diff --git a/prototype/cci/cci1.txt b/prototype/cci/cci1.txt
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diff --git a/prototype/cci/cci11.pdf b/prototype/cci/cci11.pdf
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diff --git a/prototype/cci/cci11.txt b/prototype/cci/cci11.txt
new file mode 100644
index 0000000..02e9308
--- /dev/null
+++ b/prototype/cci/cci11.txt
@@ -0,0 +1,11 @@
+   1  -0.254854701717148909608835737700  -0.700207538209709779458522719445
+   2   0.254854701717148909608835737700  -0.700207538209709779458522719445
+   3  -0.645314757823482092972348022140  -0.372572649141425545195582131150
+   4   0.645314757823482092972348022140  -0.372572649141425545195582131150
+   5  -0.254854701717148909608835737700  -0.044937760073141310932641542855
+   6   0.254854701717148909608835737700  -0.044937760073141310932641542855
+   7  -0.733824866869546118800008853460   0.129393123143898335937886211109
+   8   0.733824866869546118800008853460   0.129393123143898335937886211109
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+  11   0.478970165152397209191173115760   0.570814415065811443520636508336
diff --git a/prototype/cci/cci12.pdf b/prototype/cci/cci12.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..7b7af7b67727cacc07174f04876f42966928cb0f
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diff --git a/prototype/cci/cci12.txt b/prototype/cci/cci12.txt
new file mode 100644
index 0000000..35d5a11
--- /dev/null
+++ b/prototype/cci/cci12.txt
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diff --git a/prototype/cci/cci13.txt b/prototype/cci/cci13.txt
new file mode 100644
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diff --git a/prototype/cci/cci2.pdf b/prototype/cci/cci2.pdf
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diff --git a/prototype/cci/cci2.txt b/prototype/cci/cci2.txt
new file mode 100644
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diff --git a/prototype/cci/cci3.pdf b/prototype/cci/cci3.pdf
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diff --git a/prototype/cci/cci3.txt b/prototype/cci/cci3.txt
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diff --git a/prototype/cci/cci4.txt b/prototype/cci/cci4.txt
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diff --git a/prototype/cci/cci5.txt b/prototype/cci/cci5.txt
new file mode 100644
index 0000000..5034ebc
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diff --git a/prototype/cci/cci6.pdf b/prototype/cci/cci6.pdf
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diff --git a/prototype/cci/cci6.txt b/prototype/cci/cci6.txt
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diff --git a/prototype/cci/cci7.pdf b/prototype/cci/cci7.pdf
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diff --git a/prototype/cci/cci7.txt b/prototype/cci/cci7.txt
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diff --git a/prototype/cci/cci8.txt b/prototype/cci/cci8.txt
new file mode 100644
index 0000000..72d4c30
--- /dev/null
+++ b/prototype/cci/cci8.txt
@@ -0,0 +1,8 @@
+   1  -0.302593388348611302909204224933  -0.628341645367213738512227388956
+   2   0.302593388348611302909204224933  -0.628341645367213738512227388956
+   3  -0.679921171839088240043878874469  -0.155187570571975671990838057814
+   4   0.679921171839088240043878874469  -0.155187570571975671990838057814
+   5   0.000000000000000000000000000000   0.000000000000000000000000000000
+   6  -0.545254445070410775447749861103   0.434825910113495061957667559237
+   7   0.545254445070410775447749861103   0.434825910113495061957667559237
+   8   0.000000000000000000000000000000   0.697406611651388697090795775067
diff --git a/prototype/cci/cci9.pdf b/prototype/cci/cci9.pdf
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diff --git a/prototype/cci/cci9.txt b/prototype/cci/cci9.txt
new file mode 100644
index 0000000..6243058
--- /dev/null
+++ b/prototype/cci/cci9.txt
@@ -0,0 +1,9 @@
+   1  -0.276768653914155215717770973808  -0.668178637919298919997757686523
+   2   0.276768653914155215717770973808  -0.668178637919298919997757686523
+   3  -0.668178637919298919997757686523  -0.276768653914155215717770973808
+   4   0.668178637919298919997757686523  -0.276768653914155215717770973808
+   5   0.000000000000000000000000000000   0.000000000000000000000000000000
+   6  -0.668178637919298919997757686523   0.276768653914155215717770973808
+   7   0.668178637919298919997757686523   0.276768653914155215717770973808
+   8  -0.276768653914155215717770973808   0.668178637919298919997757686523
+   9   0.276768653914155215717770973808   0.668178637919298919997757686523
diff --git a/prototype/cci/radii.txt b/prototype/cci/radii.txt
new file mode 100644
index 0000000..a829eec
--- /dev/null
+++ b/prototype/cci/radii.txt
@@ -0,0 +1,15 @@
+# N (number of circles) | radius of enclosed circles (enclosing circle has radius of 1)
+# source: http://www.packomania.com
+1	1.000000000000000000000000000000	
+2	0.500000000000000000000000000000	
+3	0.464101615137754587054892683012	
+4	0.414213562373095048801688724210	
+5	0.370191908158750137702237641058	
+6	0.333333333333333333333333333333	
+7	0.333333333333333333333333333333	
+8	0.302593388348611302909204224934	
+9	0.276768653914155215717770973808	
+10	0.262258924190165855095630653709	
+11	0.254854701717148909608835737700	
+12	0.248163470571686841544054487132	
+13	0.236067977499789696409173668731	
diff --git a/prototype/circles.py b/prototype/circles.py
index 1e4943e..fda173e 100644
--- a/prototype/circles.py
+++ b/prototype/circles.py
@@ -1,90 +1,115 @@
 from casadi import *
 import matplotlib.pyplot as plt
+import math
+import operator
 
-file = open('tmp2019_cci_08_26_11_36_00.txt')
+N = 7 # number of enclosed circles
+
+# 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
+
+# read radius and center coordinates for enclosed circles
+rtilde, coords = read_circle_data(N)
 
 c = (0.0, 0.0)  # center of big circle
-R = 15.0        # radius of big circle
+R = 1.0        # radius of big circle
 
-# center for smaller circles
-p1 = (-5.55287862,  -7.64288174)
-p2 = (5.55287862,  -7.64288174)
-p3 = (-8.98474635,   2.91932105)
-p4 = (8.98474635,   2.91932105)
-p5 = (0.00000000,   9.44712138)
-rtilde = 5.5 # radius of smaller circles
-
-points = [p1, p2, p3, p4, p5]
-
-# 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.xlim((-16, 16))
-plt.ylim((-16, 16))
+plt.xlim((-1, 1))
+plt.ylim((-1, 1))
 plt.gca().set_aspect('equal', 'box')
 
+plt.ion()
+plt.show()
 
-for p in points:
+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.show()
 
 plt.plot(c[0], c[1], 'o')
-plt.plot(m[0], m[1], 'o')
 
-opti = casadi.Opti()
+for k in range(0, N):
+    p1 = coords[k]
+    p2 = coords[(k+1) % N]
 
-r = opti.variable(1)    # radius of new circle
-p = opti.variable(2)    # center of new circle
-#v1 = opti.variable(2)   # direction vector from
-#v2 = opti.variable(2)
-lamb = opti.variable(1)
+    # midpoint between center of two circles
+    m = np.mean([p1, p2], axis=0)
 
-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(p == (rtilde + r) * v1 + p1)
-#opti.subject_to(p == (rtilde + r) * v2 + p2)
-#opti.subject_to((v1[0]**2+v1[1]**2)**0.5 == 1)
-#opti.subject_to((v2[0]**2+v2[1]**2)**0.5 == 1)
-opti.subject_to(R == lamb + r)
-opti.subject_to(r >= 0)
-opti.subject_to(r <= R)
-#opti.subject_to(lamb >= 0.6 * R)
+    # vector in direction of midpoint
+    v = m - np.array(c)
+    v = v/np.linalg.norm(v)
+    plt.plot(m[0], m[1], 'o')
 
-opti.solver('ipopt')
+    opti = casadi.Opti()
 
-init_r = 0.1
-init_lamb = R - init_r
-init_p = c + v * init_lamb
+    r = opti.variable(1)    # radius of new circle
+    p = opti.variable(2)    # center of new circle
+    lamb = opti.variable(1)
 
+    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.set_initial(r, init_r)
-opti.set_initial(p, init_p)
-opti.set_initial(lamb, init_lamb)
-#opti.set_initial(v1, )
+    opti.solver('ipopt')
 
-sol = opti.solve()
+    init_r = 0.1
+    init_lamb = R - init_r
+    init_p = c + v * init_lamb
 
-p = sol.value(p)
-r = sol.value(r)
-lamb = sol.value(lamb)
+    opti.set_initial(r, init_r)
+    opti.set_initial(p, init_p)
+    opti.set_initial(lamb, init_lamb)
 
-print("p = {}".format(p))
-print("r = {}".format(r))
-print("lambda = {}".format(lamb))
-print("v = {}".format(v))
+    sol = opti.solve()
 
-plt.plot(p[0], p[1], 'o')
-circle = plt.Circle(p, r, fill=False)
-plt.gca().add_artist(circle)
-plt.show()
+    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))
+
+    plt.plot(p[0], p[1], 'o')
+    circle = plt.Circle(p, r, fill=False)
+    plt.gca().add_artist(circle)
 
 pass
\ No newline at end of file
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deleted file mode 100644
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