Update app.py

app.py

@@ -93,9 +93,18 @@ def estimate_trajectory_3d(ball_positions, detection_frames, frames):
     impact_point = (x_coords[impact_idx], y_coords[impact_idx], 0)
     impact_frame = detection_frames[impact_idx]
 
-    fx = interp1d(times[:impact_idx + 1], x_coords[:impact_idx + 1], kind='linear', fill_value="extrapolate")
-    fy = interp1d(times[:impact_idx + 1], y_coords[:impact_idx + 1], kind='quadratic', fill_value="extrapolate")
-    fz = interp1d(times[:impact_idx + 1], z_coords[:impact_idx + 1], kind='linear', fill_value="extrapolate")
+    # Use cubic interpolation to avoid derivative mismatch
+    try:
+        fx = interp1d(times[:impact_idx + 1], x_coords[:impact_idx + 1], kind='cubic', fill_value="extrapolate")
+        fy = interp1d(times[:impact_idx + 1], y_coords[:impact_idx + 1], kind='cubic', fill_value="extrapolate")
+        fz = interp1d(times[:impact_idx + 1], z_coords[:impact_idx + 1], kind='cubic', fill_value="extrapolate")
+    except ValueError as e:
+        # Fallback to linear if cubic fails (e.g., too few points)
+        fx = interp1d(times[:impact_idx + 1], x_coords[:impact_idx + 1], kind='linear', fill_value="extrapolate")
+        fy = interp1d(times[:impact_idx + 1], y_coords[:impact_idx + 1], kind='linear', fill_value="extrapolate")
+        fz = interp1d(times[:impact_idx + 1], z_coords[:impact_idx + 1], kind='linear', fill_value="extrapolate")
+        print(f"Warning: Cubic interpolation failed, falling back to linear. Error: {str(e)}")
+
     t_full = np.linspace(times[0], times[impact_idx] + 0.5, 50)
     full_trajectory = list(zip(fx(t_full), fy(t_full), fz(t_full)))