hyperboule.py

#!/usr/bin/env python3


import os
import typing as t
from dataclasses import dataclass
from pathlib import Path

import gpxpy.gpx
import matplotlib.pyplot as plt
import numpy as np
from geopy.distance import geodesic, great_circle
from scipy import optimize


@dataclass
class Position:
    rank: int
    """Rank."""
    boat: int
    """Boat ID."""
    pos: t.Tuple[float, float]
    """(latitude,longitude)."""
    dtf: float
    """Distance To Finish."""


# situation à 2024-11-19 18:00:00Z
boats = [
    (1, 100, (11.38819, -29.69734), 21898.62),
    (2, 112, (12.29817, -28.87315), 21942.12),
    (3, 59, (11.90237, -32.12561), 21962.91),
    (4, 79, (12.33021, -30.47561), 21963.93),
    (5, 29, (13.31248, -23.19468), 21981.4),
    (6, 85, (12.46197, -31.18362), 21981.4),
    (7, 24, (12.83107, -30.36251), 21991.72),
    (8, 17, (13.03418, -29.82524), 21996.75),
    (9, 109, (13.12718, -29.47032), 21997.88),
    (10, 3, (13.04665, -30.4648), 22005.68),
    (11, 15, (13.24158, -29.79702), 22008.57),
    (12, 8, (13.36931, -30.3552), 22023.13),
    (13, 2030, (13.55294, -31.22079), 22045.5),
    (14, 13, (15.01302, -29.69932), 22111.45),
    (15, 9, (14.75602, -31.11975), 22114.32),
    (16, 777, (14.6393, -31.84201), 22117.56),
    (17, 1297, (15.30331, -31.1623), 22146.86),
    (18, 64, (15.5461, -20.21022), 22150.58),
    (19, 83, (15.86659, -28.71502), 22150.83),
    (20, 10, (15.2953, -31.69812), 22153.72),
    (21, 5, (16.07474, -28.7498), 22163.48),
    (22, 30, (16.10143, -29.05133), 22168.25),
    (23, 14, (16.23872, -28.53493), 22170.96),
    (24, 27, (15.83012, -30.84266), 22173.47),
    (25, 18, (16.03118, -30.41587), 22179.88),
    (26, 172, (16.01677, -31.02538), 22186.76),
    (27, 1000, (16.36148, -30.19907), 22196.62),
    (28, 34, (17.06822, -27.10704), 22207.26),
    (29, 1461, (17.02256, -27.80812), 22210.35),
    (30, 1, (16.83, -29.30191), 22213.93),
    (31, 22, (16.82604, -30.60685), 22228.85),
    (32, 56, (17.32101, -28.82298), 22237.85),
    (33, 1101, (17.11098, -30.76336), 22247.49),
    (34, 7, (18.10653, -27.17554), 22269.61),
    (35, 71, (17.9222, -30.9677), 22297.58),
    (36, 49, (20.08421, -26.79358), 22385.4),
    (37, 26, (20.27418, -30.45783), 22429.58),
    (38, 5005, (21.44229, -27.90038), 22473.51),
    (39, 23, (26.48877, -15.8225), 22851.54),
    (40, 53, (39.20913, -13.00027), 23619.75),
]

boats = [Position(*p) for p in boats]
leader = boats[0]

# dtl = dtf - min(dtf)
# min(dtf) <=> leader


def dist_to_leader(boat, marque):
    # return (great_circle(marque, boat.pos).meters - great_circle(marque, leader.pos).meters) / 1852
    return (geodesic(marque, boat.pos).meters - geodesic(marque, leader.pos).meters) / 1852


def dichotomie(lat, lon_a, lon_b, d_cible, boat):

    while (lon_b - lon_a) > 0.1:
        lon = (lon_a + lon_b) / 2
        d = dist_to_leader(boat, (lat, lon))
        if d <= d_cible:
            lon_b = lon
        else:
            lon_a = lon

    lon = round((lon_a + lon_b) / 2, 6)
    return (lat, lon)


marque = (-34.994004, 19.335938)  # Le Cap
marque = (-4.313546, -25.587158)
for boat in boats[1:]:
    dtl_calc = dist_to_leader(boat, marque)
    dtl = boat.dtf - leader.dtf
    e = round(abs(dtl_calc - dtl) / dtl * 100, 1)
    print(f"{boat.boat:4} {dtl_calc:8.3f}  {dtl:8.3f}  {e:g}")
exit()


for i in range(35, 40):

    boat = boats[i]

    gpx = gpxpy.gpx.GPX()
    gpx_track = gpxpy.gpx.GPXTrack(name="test")
    gpx.tracks.append(gpx_track)
    gpx_segment = gpxpy.gpx.GPXTrackSegment()
    gpx_track.segments.append(gpx_segment)

    lon_w = -45
    lon_e = 22

    lon = (lon_w + lon_e) / 2

    for lat in range(-32, 8, 4):

        ######

        def f(lon):
            return dist_to_leader(boat, (lat, lon))

        dtl = boat.dtf - leader.dtf

        x = np.linspace(lon_w, lon_e, 100)
        y = [f(lon) for lon in x]
        plt.plot(x, y, color="red")
        plt.axhline(y=dtl, color="blue", linestyle="-")
        plt.show()

        roots = optimize.fsolve(lambda x: f(x) - dtl, lon)
        lon = roots[0]
        ######

        print(f"{lat},{lon}")

        gpx_segment.points.append(gpxpy.gpx.GPXTrackPoint(lat, lon))

    Path(f"hyperboule{i}.gpx").write_text(gpx.to_xml())
    os.system(f"open -a GPXSee dicho{i}.gpx")