sailboat_navigation_algorithm_v1

    import math
    import matplotlib.pyplot as plt

    class Boat:
        def __init__(self, boat_x=0.0, boat_y=0.0, heading_angle=0.0, goal_x=100.0, goal_y=100.0):
            self.boat_x = boat_x
            self.boat_y = boat_y
            self.heading_angle = heading_angle
            self.goal_x = goal_x
            self.goal_y = goal_y

            self.speed = 0.0
            self.wind_speed = 0.0
            self.wind_angle = 0.0

            self.trail = [(boat_x, boat_y)]

            self.no_go_limit = math.pi / 4
            self.tack_angle = math.radians(50)
            self.tack_side = 1

        def set_wind(self, wind_speed, wind_x, wind_y):
            self.wind_speed = wind_speed
            self.wind_x = wind_x
            self.wind_y = wind_y
            self.wind_angle = math.atan2(wind_y, wind_x)

        def angle_to_goal(self):
            return math.atan2(self.goal_y - self.boat_y, self.goal_x - self.boat_x)

        def move_fwd(self):
            goal_angle = self.angle_to_goal()
            rel_goal_wind = (goal_angle - self.wind_angle + math.pi) % (2 * math.pi) - math.pi

            # no-go zone
            if -self.no_go_limit < rel_goal_wind < self.no_go_limit:
                print("Alert! No-go-zone reached. Changing tack!")
                self.heading_angle = self.wind_angle + self.tack_side * self.tack_angle
                self.rudder_angle = -0.8 * self.tack_side
            else:
                self.heading_angle = goal_angle
                self.rudder_angle = 0.0

            # polar efficiency (very simplified)
            rel_heading_wind = (self.heading_angle - self.wind_angle + math.pi) % (2 * math.pi) - math.pi
            polar_efficiency = max(0, 1 + math.sin(rel_heading_wind))
            self.speed = self.wind_speed * 0.1 * polar_efficiency

            # update position
            self.boat_x += self.speed * math.cos(self.heading_angle)
            self.boat_y += self.speed * math.sin(self.heading_angle)
            self.trail.append((self.boat_x, self.boat_y))

            # Switch tacks midway (simple logic)
            if (self.tack_side == 1 and self.boat_x > self.goal_x / 2) or \
            (self.tack_side == -1 and self.boat_x < -self.goal_x / 2):
                self.tack_side *= -1

        def distance_to_goal(self):
            return math.sqrt((self.goal_x - self.boat_x) ** 2 + (self.goal_y - self.boat_y) ** 2)


    def sail():
        boat = Boat(boat_x=0, boat_y=0, heading_angle=0, goal_x=100, goal_y=100)
        boat.set_wind(30, 0, -1)

        for step in range(500):
            boat.move_fwd()
            if boat.distance_to_goal() < 5:
                print("Goal reached successfully!")
                break