made script for optimal circle compuation more general by allowing also other number of circles
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prototype/cci/cci1.pdf
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1 0.000000000000000000000000000000 0.000000000000000000000000000000
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8 0.000000000000000000000000000000 0.289211491381498022358656198900
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9 -0.415055617900124834285924684739 0.609910427019080420778753583334
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10 0.415055617900124834285924684739 0.609910427019080420778753583334
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1 -0.254854701717148909608835737700 -0.700207538209709779458522719445
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4 0.645314757823482092972348022140 -0.372572649141425545195582131150
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6 0.254854701717148909608835737700 -0.044937760073141310932641542855
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8 0.733824866869546118800008853460 0.129393123143898335937886211109
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9 0.000000000000000000000000000000 0.396483531848771796650108754372
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10 -0.478970165152397209191173115760 0.570814415065811443520636508336
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11 0.478970165152397209191173115760 0.570814415065811443520636508336
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prototype/cci/cci12.pdf
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1 0.000000000000000000000000000000 -0.751836529428313158455945512868
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3 0.468509916422022800799147453449 -0.588010735613764119868275923156
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4 -0.248163470571686841544054487132 -0.143277246537595169579619996000
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5 0.248163470571686841544054487132 -0.143277246537595169579619996000
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6 -0.743487192950506270382840218584 -0.111736121739513839036609043190
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7 0.743487192950506270382840218584 -0.111736121739513839036609043190
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8 0.000000000000000000000000000000 0.286554493075190339159239992000
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10 0.651109533978045892394293176753 0.375918264714156579227972756434
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11 -0.274977276528483469583692765135 0.699746857353277958904884966346
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12 0.274977276528483469583692765135 0.699746857353277958904884966346
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prototype/cci/cci13.pdf
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1 0.000000000000000000000000000000 -0.763932022500210303590826331269
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2 -0.449027976579585372441945151797 -0.618033988749894848204586834366
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3 0.449027976579585372441945151797 -0.618033988749894848204586834366
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4 0.000000000000000000000000000000 -0.291796067500630910772478993806
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5 -0.726542528005360885895466757481 -0.236067977499789696409173668731
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6 0.726542528005360885895466757481 -0.236067977499789696409173668731
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8 0.277514551425775513453521605683 0.090169943749474241022934171828
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10 0.726542528005360885895466757481 0.236067977499789696409173668731
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11 0.000000000000000000000000000000 0.472135954999579392818347337463
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12 -0.449027976579585372441945151797 0.618033988749894848204586834366
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13 0.449027976579585372441945151797 0.618033988749894848204586834366
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1 -0.500000000000000000000000000000 0.000000000000000000000000000000
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2 0.500000000000000000000000000000 0.000000000000000000000000000000
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prototype/cci/cci3.pdf
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1 -0.464101615137754587054892683011 -0.267949192431122706472553658494
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2 0.464101615137754587054892683011 -0.267949192431122706472553658494
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3 0.000000000000000000000000000000 0.535898384862245412945107316988
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prototype/cci/cci4.pdf
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1 -0.414213562373095048801688724210 -0.414213562373095048801688724210
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2 0.414213562373095048801688724210 -0.414213562373095048801688724210
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3 -0.414213562373095048801688724210 0.414213562373095048801688724210
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4 0.414213562373095048801688724210 0.414213562373095048801688724210
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1 -0.370191908158750137702237641058 -0.509525449494428810513706911251
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2 0.370191908158750137702237641058 -0.509525449494428810513706911251
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3 -0.598983089761037227177173011864 0.194621403573803879364825731779
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4 0.598983089761037227177173011864 0.194621403573803879364825731779
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5 0.000000000000000000000000000000 0.629808091841249862297762358942
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1 -0.333333333333333333333333333333 -0.577350269189625764509148780502
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2 0.333333333333333333333333333333 -0.577350269189625764509148780502
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3 -0.666666666666666666666666666667 0.000000000000000000000000000000
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4 0.666666666666666666666666666667 0.000000000000000000000000000000
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5 -0.333333333333333333333333333333 0.577350269189625764509148780502
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6 0.333333333333333333333333333333 0.577350269189625764509148780502
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1 -0.333333333333333333333333333333 -0.577350269189625764509148780502
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2 0.333333333333333333333333333333 -0.577350269189625764509148780502
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3 -0.666666666666666666666666666667 0.000000000000000000000000000000
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4 0.000000000000000000000000000000 0.000000000000000000000000000000
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5 0.666666666666666666666666666667 0.000000000000000000000000000000
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6 -0.333333333333333333333333333333 0.577350269189625764509148780502
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7 0.333333333333333333333333333333 0.577350269189625764509148780502
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1 -0.302593388348611302909204224933 -0.628341645367213738512227388956
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2 0.302593388348611302909204224933 -0.628341645367213738512227388956
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3 -0.679921171839088240043878874469 -0.155187570571975671990838057814
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4 0.679921171839088240043878874469 -0.155187570571975671990838057814
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5 0.000000000000000000000000000000 0.000000000000000000000000000000
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6 -0.545254445070410775447749861103 0.434825910113495061957667559237
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7 0.545254445070410775447749861103 0.434825910113495061957667559237
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8 0.000000000000000000000000000000 0.697406611651388697090795775067
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1 -0.276768653914155215717770973808 -0.668178637919298919997757686523
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2 0.276768653914155215717770973808 -0.668178637919298919997757686523
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3 -0.668178637919298919997757686523 -0.276768653914155215717770973808
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4 0.668178637919298919997757686523 -0.276768653914155215717770973808
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5 0.000000000000000000000000000000 0.000000000000000000000000000000
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6 -0.668178637919298919997757686523 0.276768653914155215717770973808
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7 0.668178637919298919997757686523 0.276768653914155215717770973808
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8 -0.276768653914155215717770973808 0.668178637919298919997757686523
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9 0.276768653914155215717770973808 0.668178637919298919997757686523
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prototype/cci/radii.txt
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# N (number of circles) | radius of enclosed circles (enclosing circle has radius of 1)
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# source: http://www.packomania.com
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1 1.000000000000000000000000000000
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2 0.500000000000000000000000000000
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3 0.464101615137754587054892683012
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4 0.414213562373095048801688724210
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5 0.370191908158750137702237641058
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6 0.333333333333333333333333333333
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7 0.333333333333333333333333333333
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8 0.302593388348611302909204224934
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9 0.276768653914155215717770973808
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10 0.262258924190165855095630653709
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11 0.254854701717148909608835737700
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12 0.248163470571686841544054487132
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13 0.236067977499789696409173668731
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@ -1,20 +1,70 @@
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from casadi import *
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import matplotlib.pyplot as plt
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import math
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import operator
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file = open('tmp2019_cci_08_26_11_36_00.txt')
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N = 7 # 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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coords_raw = open('cci/cci{}.txt'.format(N))
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radii_raw = open('cci/radii.txt'.format(N))
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coords_raw = coords_raw.readlines()
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coords_raw = [c.split() for c in coords_raw if c[0] != '#']
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coords = {}
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for c in coords_raw:
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coords[int(c[0])] = (float(c[1]), float(c[2]))
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coords = sort_ccw(coords, (0,0))
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radii_raw = radii_raw.readlines()
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radii_raw = [r.split() for r in radii_raw if r[0] != '#']
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radii = {}
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for r in radii_raw:
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radii[int(r[0])] = float(r[1])
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return radii[N], coords
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# this function sorts enclosed circle coordinates counter-clockwise w.r.t. the center point
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# TODO: there is a problem when circles are present that are not touching the boundary of the enclosing circle (e.g. N = 7)
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def sort_ccw(coords, center):
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a = {}
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for c in coords:
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a[c] = math.atan2(coords[c][1] - center[1], coords[c][0] - center[0])
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a_sort = sorted(a.items(), key=operator.itemgetter(1))
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coords_sort = []
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for a in a_sort:
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coords_sort.append(coords[a[0]])
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return coords_sort
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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 = 15.0 # radius of big circle
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R = 1.0 # radius of big circle
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# center for smaller circles
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p1 = (-5.55287862, -7.64288174)
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p2 = (5.55287862, -7.64288174)
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p3 = (-8.98474635, 2.91932105)
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p4 = (8.98474635, 2.91932105)
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p5 = (0.00000000, 9.44712138)
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rtilde = 5.5 # radius of smaller circles
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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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points = [p1, p2, p3, p4, p5]
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plt.ion()
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plt.show()
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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.plot(c[0], c[1], 'o')
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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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# midpoint between center of two circles
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m = np.mean([p1, p2], axis=0)
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@ -22,42 +72,20 @@ 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.xlim((-16, 16))
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plt.ylim((-16, 16))
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plt.gca().set_aspect('equal', 'box')
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for p in points:
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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.show()
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plt.plot(c[0], c[1], 'o')
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plt.plot(m[0], m[1], 'o')
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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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#v1 = opti.variable(2) # direction vector from
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#v2 = opti.variable(2)
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lamb = opti.variable(1)
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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(p == (rtilde + r) * v1 + p1)
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#opti.subject_to(p == (rtilde + r) * v2 + p2)
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#opti.subject_to((v1[0]**2+v1[1]**2)**0.5 == 1)
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#opti.subject_to((v2[0]**2+v2[1]**2)**0.5 == 1)
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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.subject_to(lamb >= 0.6 * R)
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opti.solver('ipopt')
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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(v1, )
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sol = opti.solve()
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@ -85,6 +111,5 @@ print("v = {}".format(v))
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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.show()
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pass
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@ -1,95 +0,0 @@
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%!PS-Adobe-3.0 EPSF-3.0
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%%Title: /srv/http/htdocs/packing/tmp/tmp2019_cci_08_26_11_36_00.ps
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%%Creator: nicefig-2.0
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%%Pages: 1
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%%BoundingBox: 40 250 580 790
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%%DocumentProcessColors: Cyan Magenta Yellow Black
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%%CreationDate: 26-Aug-2019 11:36:00
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%%DocumentFonts: Courier
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%%+ Courier-Bold
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%%+ Helvetica
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%%+ Helvetica-Oblique
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%%+ Symbol
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%%EndComments
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%%EndProlog
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20 dict begin
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gsave
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/g { setgray } bind def
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/rgb { setrgbcolor } bind def
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/np { newpath } bind def
|
||||
/m { moveto } bind def
|
||||
/rm { rmoveto } bind def
|
||||
/l { lineto } bind def
|
||||
/rl { rlineto } bind def
|
||||
/c { curveto } bind def
|
||||
/s { stroke } bind def
|
||||
/f { closepath fill } bind def
|
||||
/la { setlinejoin setlinecap 1.0417 mul setlinewidth } bind def
|
||||
/lc { setlinecap } bind def
|
||||
/lj { setlinejoin } bind def
|
||||
/ld { setdash } bind def
|
||||
/lw { setlinewidth } bind def
|
||||
/font { findfont exch scalefont setfont } bind def
|
||||
/rgh { dup stringwidth pop neg 0 rm } bind def
|
||||
/ctr { dup stringwidth pop 2 div neg 0 rm } bind def
|
||||
|
||||
1 lj 1 lc 0.200 lw
|
||||
|
||||
%
|
||||
0.400 lw
|
||||
%
|
||||
% box
|
||||
%
|
||||
310.000 520.000 250.000 0 360 arc s
|
||||
%
|
||||
% circles
|
||||
%
|
||||
1.000 0.843 0.000 rgb
|
||||
309.119 392.619 m 217.452 392.619 91.667 0 360 arc f
|
||||
0.000 0.000 0.000 rgb
|
||||
1.000 0.843 0.000 rgb
|
||||
494.215 392.619 m 402.548 392.619 91.667 0 360 arc f
|
||||
0.000 0.000 0.000 rgb
|
||||
1.000 0.843 0.000 rgb
|
||||
251.921 568.655 m 160.254 568.655 91.667 0 360 arc f
|
||||
0.000 0.000 0.000 rgb
|
||||
1.000 0.843 0.000 rgb
|
||||
551.412 568.655 m 459.746 568.655 91.667 0 360 arc f
|
||||
0.000 0.000 0.000 rgb
|
||||
1.000 0.843 0.000 rgb
|
||||
401.667 677.452 m 310.000 677.452 91.667 0 360 arc f
|
||||
0.000 0.000 0.000 rgb
|
||||
0.000 0.000 0.000 rgb
|
||||
217.452 392.619 91.667 0 360 arc s
|
||||
0.000 0.000 0.000 rgb
|
||||
402.548 392.619 91.667 0 360 arc s
|
||||
0.000 0.000 0.000 rgb
|
||||
160.254 568.655 91.667 0 360 arc s
|
||||
0.000 0.000 0.000 rgb
|
||||
459.746 568.655 91.667 0 360 arc s
|
||||
0.000 0.000 0.000 rgb
|
||||
310.000 677.452 91.667 0 360 arc s
|
||||
%
|
||||
% centers
|
||||
%
|
||||
218.580 392.619 m 217.452 392.619 1.128 0 360 arc f
|
||||
403.676 392.619 m 402.548 392.619 1.128 0 360 arc f
|
||||
161.383 568.655 m 160.254 568.655 1.128 0 360 arc f
|
||||
460.874 568.655 m 459.746 568.655 1.128 0 360 arc f
|
||||
311.128 677.452 m 310.000 677.452 1.128 0 360 arc f
|
||||
%
|
||||
12.00 /Courier font
|
||||
70.000 251.000 m (www.packomania.com) show
|
||||
12.00 /Symbol font
|
||||
430.000 250.000 m (Ó) show
|
||||
12.00 /Courier font
|
||||
442.000 251.000 m (E.S) show
|
||||
9.00 /Courier font
|
||||
464.000 251.000 m (PECHT) show
|
||||
500.000 251.000 m (26-AUG-2019) show
|
||||
|
||||
showpage
|
||||
grestore end
|
||||
%%Trailer
|
||||
%%EOF
|
||||
|
|
@ -1,5 +0,0 @@
|
|||
1 -5.55287862 -7.64288174
|
||||
2 5.55287862 -7.64288174
|
||||
3 -8.98474635 2.91932105
|
||||
4 8.98474635 2.91932105
|
||||
5 0.00000000 9.44712138
|
||||
Loading…
Reference in New Issue
Block a user