194 lines
5.0 KiB
Python
194 lines
5.0 KiB
Python
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import matplotlib.pyplot as plt
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import collections
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from enum import Enum, auto
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from random import randint
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Point = collections.namedtuple("Point", "x y")
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class Side(Enum):
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ON = auto()
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ABOVE = auto()
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BELOW = auto()
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def sidedness(slope, intersection, p3, eps=0.0000001):
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print(slope * p3[0] + intersection )
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""" finds where a point is in regards to a line """
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if p3[1] - eps <= slope * p3[0] + intersection <= p3[1] + eps or p3[0] - eps <= (p3[1] - intersection)/slope <= p3[0] + eps:
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return Side.ON
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elif p3[1] > slope * p3[0] + intersection:
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return Side.ABOVE
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return Side.BELOW
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def diplay_prune_points(points, p1, p2):
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xs = [p[0] for p in points]
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ys = [p[1] for p in points]
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plt.plot(xs, ys, 'ro')
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plt.plot([p1[0], p2[0]], [p1[1], p2[1]])
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plt.show()
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def solve1D(points, xm, iteration_num):
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#print("iter:", iteration_num)
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point = points[iteration_num]
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if iteration_num == 0:
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return -float('Inf'), -float('Inf')
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# lad point[1] = point[0] * a + b <=> y = x * a + b
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# isolere b og sæt ind i constraints
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a = None
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b = point[1] - point[0] # * a
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# minimere xm*a + b, hvor b har ny værdi
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# Vi regner kun med koefficienterne
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# obj_fun = (xm - point[0]) + points[1] = (xm*a - xi*a) + y
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# max eller min
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#print("XM og point[0]:", xm, point[0])
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a = xm - point[0]
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#print("a lige her:", a)
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a_constraint_list = []
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# looping over the i constraints
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for p in points[:iteration_num]:
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# we can't make a straigt vertical line
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if p[0] == point[0]:
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if p[1] > point[1]:
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p[0] = p[0] + 0.0001
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else:
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point[0] = point[0] + 0.0001
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print(p, point)
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# Spring over den i'te constraint
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if p != point:
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# y_j - yi
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c = p[1] - point[1]
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# x_j * a - xi * a
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a_diff = p[0] - point[0]
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print(c, a_diff, c/a_diff)
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# det her er forkert og skal fikses
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if a >= 0 and a_diff < 0:
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a_constraint_list.append(-float('Inf'))
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else:
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a_constraint_list.append(c/a_diff)
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# hvis a > 0 så min
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# hvis a < 0 så max.
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if a >= 0:
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v1 = max(a_constraint_list)
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v2 = point[1] - point[0] * v1
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v = (v1, v2)
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elif a < 0:
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v1 = min(a_constraint_list)
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v2 = point[1] - point[0] * v1
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v = (v1, v2)
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return v
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def findBridge(points, xm):
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if xm > 0:
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v = (-float('Inf'), -float('Inf'))
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elif xm < 0:
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4 # noget
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else:
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# TODO: xm == 0
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4
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# looping over constraints
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for point in points:
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# checking for violation
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if not point[1] <= point[0] * v[0] + v[1]:
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v = solve1D(points, xm, points.index(point))
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#print("HER OVER: ", v)
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slope = v[0]
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intercept = v[1]
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line_points = [p for p in points if sidedness(slope, intercept, p) == Side.ON]
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if len(line_points) > 3:
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print("Halli HAllo")
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print(line_points)
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return line_points[0], line_points[1]
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def find_median(points):
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if len(points) % 2 == 0:
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first_med_idx = int(len(points) / 2 - 1)
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second_med_idx = int(len(points) / 2)
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return (points[first_med_idx][0] + points[second_med_idx][0]) / 2
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else:
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idx = int((len(points)-1) / 2)
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return points[idx][0]
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def upperHull(points, all_points):
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print("Punkter:", points)
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if len(points) < 2:
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return []
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xm = find_median(points)
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# end-points of bridge
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(xi, yi), (xj, yj) = findBridge(points, xm)
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#print(xm)
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print((xi, yi), (xj, yj))
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prune_points = [p for p in points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]
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# Neden for er mest for visualisering
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prune_all_points = [p for p in all_points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]
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diplay_prune_points(prune_all_points, (xi, yi), (xj, yj))
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Pl = [p for p in prune_points if p[0] < xm]
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Pr = [p for p in prune_points if p[0] >= xm]
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#print("Pl:", Pl, "Pr", Pr)
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print("\n")
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# recurse results and return
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ret = [(xi, yi), (xj, yj)]
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ret = ret + [p for p in upperHull(Pl, prune_all_points) if p not in ret]
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ret = ret + [p for p in upperHull(Pr, prune_all_points) if p not in ret]
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return ret
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p1 = (2, 1)
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p2 = (3, 4)
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p3 = (5, 2)
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p4 = (6, 5)
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list_of_points = []
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list_of_points.append(p1)
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list_of_points.append(p2)
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list_of_points.append(p3)
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list_of_points.append(p4)
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xs = [p[0] for p in list_of_points]
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ys = [p[1] for p in list_of_points]
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plt.plot(xs, ys, 'ro')
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plt.show()
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result = list(sorted(upperHull(list_of_points, list_of_points)))
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result
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res_xs = [p[0] for p in result]
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res_ys = [p[1] for p in result]
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#print("result", result)
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plt.plot(res_xs, res_ys)
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plt.plot(xs, ys, 'ro')
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plt.show()
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