Create app.py

app.py

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+import numpy as np
+from numpy.random import normal
+import matplotlib.pyplot as plt
+
+# ---------------------------
+# Physical constants
+# ---------------------------
+g = 9.81
+rho = 1.2
+Cd = 0.47
+r = 0.02
+A = np.pi * r**2
+m = 0.0027
+
+k_drag = 0.5 * rho * Cd * A / m
+k_mag = 4e-4    # Magnus coefficient (tuned)
+
+# Table + net
+table_length = 2.74
+x_net = table_length / 2
+h_net = 0.1525
+y_thresh = h_net + r   # clearance threshold
+
+
+# ---------------------------
+# 2D flight ODE
+# ---------------------------
+def f(state, omega):
+    x, y, vx, vy = state
+    v = np.sqrt(vx**2 + vy**2)
+
+    ax_drag = -k_drag * v * vx
+    ay_drag = -k_drag * v * vy
+
+    ax_mag =   k_mag * omega * vy
+    ay_mag =  -k_mag * omega * vx
+
+    return np.array([
+        vx,
+        vy,
+        ax_drag + ax_mag,
+        -g + ay_drag + ay_mag
+    ])
+
+
+# ---------------------------
+# Single trajectory (NO BOUNCE)
+# ---------------------------
+def simulate_trajectory(S, theta_deg, omega, dt=0.001, t_max=2.0):
+    theta = np.deg2rad(theta_deg)
+
+    # initial conditions
+    vx = S * np.cos(theta)
+    vy = S * np.sin(theta)
+    x, y = 0.0, 0.3     # contact height ~30 cm
+
+    prev_x, prev_y = x, y
+    cleared_net = False
+    hit_net = False
+
+    for _ in np.arange(0, t_max, dt):
+
+        # ------------- NET CHECK -------------
+        if (prev_x - x_net) * (x - x_net) <= 0 and (x != prev_x):
+            tau = (x_net - prev_x) / (x - prev_x)
+            y_cross = prev_y + tau * (y - prev_y)
+
+            if y_cross <= y_thresh:
+                return x_net, "net"      # hit net
+            else:
+                cleared_net = True
+
+        # ------------- GROUND (TABLE) IMPACT -------------
+        if y <= 0:
+            # Ball lands
+            if x < x_net:
+                return x, "undershoot"      # lands on own side
+            elif x <= table_length:
+                return x, "valid"           # lands on opponent side
+            else:
+                return x, "overshoot"       # lands beyond table
+
+        # ------------- INTEGRATE (RK4) -------------
+        state = np.array([x, y, vx, vy])
+        k1 = f(state, omega)
+        k2 = f(state + 0.5*dt*k1, omega)
+        k3 = f(state + 0.5*dt*k2, omega)
+        k4 = f(state + dt*k3, omega)
+        state += (dt/6)*(k1 + 2*k2 + 2*k3 + k4)
+
+        prev_x, prev_y = x, y
+        x, y, vx, vy = state
+
+        # If ball goes far past table without landing → overshoot
+        if x > table_length + 0.5:
+            return x, "overshoot"
+
+    return x, "unknown"
+
+
+# ---------------------------
+# Monte Carlo
+# ---------------------------
+def monte_carlo(n=2000):
+    landings = []
+    outcomes = {"valid": 0, "net": 0, "undershoot": 0, "overshoot": 0}
+
+    for _ in range(n):
+        # Random shot parameters
+        S = normal(8.0, 0.4)
+        ang = normal(12.0, 2.0)
+        spin = normal(150, 20)
+
+        x_land, outcome = simulate_trajectory(S, ang, spin)
+
+        landings.append(x_land)
+        outcomes[outcome] += 1
+
+    return np.array(landings), outcomes
+
+
+# ---------------------------
+# Run + Plot
+# ---------------------------
+landings, outcomes = monte_carlo(2000)
+
+print(outcomes)
+print("Valid shot probability:", outcomes["valid"] / 2000)
+
+plt.hist(landings, bins=80, density=True)
+plt.axvline(x_net, color='r', linestyle='--', label='Net')
+plt.axvline(table_length, color='k', linestyle='--', label='End of table")
+plt.title("Landing distribution (PDF approx)")
+plt.xlabel("Landing x-position (m)")
+plt.ylabel("Probability density")
+plt.legend()
+plt.show()