import statistics from math import inf, isnan, sqrt from typing import Set, List, Tuple import util from scipy.optimize import linprog import scipy import random from util import Side, Point, gen_point, display, display_line_only, gen_circular_point, gen_weird_point, gen_triangular_point def sidedness(slope: float, intersection: float, p3: Point, flipper: callable, eps=0.0000001) -> Side: # finds where a point is in regards to a line if flipper(p3.y) - eps <= flipper(slope * p3.x + intersection) <= flipper(p3.y) + eps: return Side.ON elif p3.y > slope * p3.x + intersection: return Side.ABOVE return Side.BELOW def solve_1dlp(c: float, constraints: List[Tuple[float, float]]): """ :param c: c1 :param constraints: [(ai, bi), ...] :return: x1 """ min_ = -10000 max_ = 10000 for constraint in constraints: (a, b) = constraint if a == 0: assert(b >= 0) if a > 0: max_ = min(b/a, max_) elif a < 0: min_ = max(b/a, min_) if c > 0: return min_ else: return max_ assert solve_1dlp(1, [(-1, -2)]) == 2 assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3 assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3 assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2 assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2 def new_solve_1dlp(c, constraints, idx): c1, c2 = c ((a1, a2), b) = constraints[-1] q, p = b / a2, a1 /a2 interval = [-9999999, 9999999] for new_idx, ((lel_a1, lel_a2), lel_b) in enumerate(constraints): bj, aj = (lel_b - lel_a2 * q), (lel_a1 - lel_a2 * p) if aj < 0 and bj / aj > interval[0]: interval[0] = bj / aj elif aj > 0 and bj / aj < interval[1]: interval[1] = bj/aj c = -(c1 - c2 * p) if c < 0: return interval[0], q - (p * interval[0]) elif c >= 0: return interval[1], q - (p * interval[1]) def new_solve_2dlp(c, constraints): c1, c2 = c x1 = -10000 if c1 > 0 else 10000 x2 = -10000 if c2 > 0 else 10000 for idx, ((a1, a2), b) in enumerate(constraints): if not (a1*x1 + a2*x2 <= b): x1,x2 = new_solve_1dlp(c, constraints[:idx+1], idx) return x1,x2 def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, float], float]]): """ :param c: (c1, c2) :param constraints: [(ai1, ai2, bi), ...] :return: x1, x2 """ c1, c2 = c x1 = -10000 if c1 > 0 else 10000 x2 = -10000 if c2 > 0 else 10000 #random.shuffle(constraints) for idx, ((a1, a2), b) in enumerate(constraints[1:]): #print("x1 and x2", x1, x2) #print("{} + {} <= {}".format(a1*x1, a2*x2, b)) #print("pls",a1*x1 + a2*x2) #print("yes"*10) if isnan(a1*x1+a2*x2) else print("no"*10) if not (a1*x1 + a2*x2 <= b): constraint_for_1d = [] new_obj = c[0] - ((c[1]*a1)/a2) for constraint in constraints[:idx]: (a_i1, a_i2), b_i = constraint a_prime = a_i1 - ((a_i2*a1)/a2) b_prime = b_i - ((a_i2*b)/a2) constraint_for_1d.append((a_prime, b_prime)) #print("obj", new_obj) #print("const", constraint_for_1d) #print("lol",[cons[0] for cons in constraint_for_1d]) #res = linprog([new_obj], [[cons[0]] for cons in constraint_for_1d], [[cons[1]] for cons in constraint_for_1d], bounds=[(None, None)]) x1 = solve_1dlp(new_obj, constraint_for_1d) #x1 = res.x #print(res) x2 = ((b/a2) - (a1/a2)*x1) return x1, x2 def find_median(points): num_candidates = min(5, len(points)) candidates = random.sample(points, num_candidates) candidates.sort(key=lambda p: p.x) median_i = num_candidates // 2 median = ((candidates[median_i - 1].x + candidates[median_i].x)/2, (candidates[median_i - 1].y + candidates[median_i].y)/2) return median[0] def mbc_ch(points: Set[Point], flipper: callable) -> Set[Point]: if len(points) < 2: return points # Find the point with median x-coordinate, and partition the points on this point med_x = find_median(points) #med_x = statistics.median(p.x for p in points) #print(med_x) # Find left and right points in regards to median pl = {p for p in points if p.x < med_x} pr = {p for p in points if p.x >= med_x} #print("pl\n",pl) #print("pr\n",pr) c = [flipper(med_x), flipper(1)] A = [[flipper(-p.x), flipper(-1)] for p in points] b = [flipper(-p.y) for p in points] # Find the bridge over the vertical line in pm #slope, intercept = solve_2dlp((flipper(med_x), flipper(1)), # [((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points]) # confirmed correct slope, intercept = new_solve_2dlp((flipper(med_x), flipper(1)), [((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points]) #print("slope, intercept:",slope, intercept) res = linprog(c, A, b, bounds=[[None, None], [None, None]], options={"tol": 0.01}) #print("res0, res1:",res.x[0], res.x[1]) #slope, intercept = res.x[0], res.x[1] #display_line_only(points, slope, intercept, []) # Find the two points which are on the line, should work #on = {p for p in points if sidedness(slope, intercept, p, flipper) == Side.ON} #print("On Points:",on) #left_point = min(on) #right_point = max(on) #dist_to_line = lambda p: abs(intercept + slope * p.x - p.y)/sqrt(1 + slope**2) #left_point = min(pl, key = dist_to_line) #right_point = min(pr, key=dist_to_line) #display_line_only(points, slope, intercept, [left_point, right_point]) left_point = next(p for p in pl if sidedness(slope, intercept, p, flipper) == Side.ON) right_point = next(p for p in pr if sidedness(slope, intercept, p, flipper) == Side.ON) def find_med_point(points, med_x): for p in points: if med_x+0.001 >= p.x >= med_x-0.001: return {p} return {} #print("med point:",find_med_point(points, med_x)) #display_line_only(points, slope, intercept, {left_point, right_point}) # Prune the points between the two line points pl = {p for p in pl if p.x <= left_point.x} pr = {p for p in pr if p.x >= right_point.x} return set.union(mbc_ch(pl, flipper), {left_point, right_point}, mbc_ch(pr, flipper)) def mbc(points: Set[Point]) -> Set[Point]: return set.union(mbc_ch(points, lambda x: x), mbc_ch(points, lambda x: -x)) if __name__ == '__main__': random.seed(1337_420) points = {gen_point(0, 20) for _ in range(20)} #points = {gen_circular_point(1, 100, 50) for _ in range(200)} #points = {gen_triangular_point(Point(1,1), Point(51,1), Point(26, 30)) for _ in range(200)} #points = {Point(x=-33.11091053638924, y=38.88967778961347), Point(x=61.20269947424177, y=-78.96305419217254), Point(x=99.44053842147957, y=-89.11579172297581), Point(x=-92.40380889537532, y=84.33904351991652), Point(x=-90.63139185545595, y=-91.13793846505985)} #points = {Point(x=5.2, y=9.7), Point(x=5.3, y=4.9), Point(x=3.3, y=3.6), Point(x=9.2, y=4.8), Point(x=9.7, y=5.7), Point(x=5.6, y=8.7)} upper_hull_points = mbc_ch(points, lambda x: x) lower_hull_points = mbc_ch(points, lambda x: -x) display(points, upper_hull_points.union(lower_hull_points))