import math

def fixation_radius_normalized(theta_deg: float,
                               distance_cm: float,
                               screen_width_cm: float,
                               screen_height_cm: float,
                               resolution_x: int,
                               resolution_y: int,
                               method: str = "max"):
    """
    Berechnet den PyGaze-Fixationsradius für normierte Gaze-Daten in [0,1].
    """
    # Schritt 1: visueller Winkel → physische Distanz (cm)
    delta_cm = 2 * distance_cm * math.tan(math.radians(theta_deg) / 2)

    # Schritt 2: physische Distanz → Pixel
    delta_px_x = delta_cm * (resolution_x / screen_width_cm)
    delta_px_y = delta_cm * (resolution_y / screen_height_cm)

    # Pixelradius
    if method == "max":
        r_px = max(delta_px_x, delta_px_y)
    else:
        r_px = math.sqrt(delta_px_x**2 + delta_px_y**2)

    # Schritt 3: Pixelradius → normierter Radius
    r_norm_x = r_px / resolution_x
    r_norm_y = r_px / resolution_y

    if method == "max":
        return max(r_norm_x, r_norm_y)
    else:
        return math.sqrt(r_norm_x**2 + r_norm_y**2)






# Beispiel: 55" 4k Monitor
screen_width_cm = 3*121.8
screen_height_cm = 68.5
resolution_x = 3*3840
resolution_y = 2160
distance_to_screen_cm = 120
method = 'max'
max_angle= 1.0

maxdist_px = fixation_radius_normalized(theta_deg=max_angle,
                            distance_cm=distance_to_screen_cm,
                            screen_width_cm=screen_width_cm,
                            screen_height_cm=screen_height_cm,
                            resolution_x=resolution_x,
                            resolution_y=resolution_y,
                            method=method)

print("PyGaze max_dist (max):", maxdist_px)

method = 'euclid'
maxdist_px = fixation_radius_normalized(theta_deg=max_angle,
                            distance_cm=distance_to_screen_cm,
                            screen_width_cm=screen_width_cm,
                            screen_height_cm=screen_height_cm,
                            resolution_x=resolution_x,
                            resolution_y=resolution_y,
                            method=method)

print("PyGaze max_dist (euclid):", maxdist_px)

# Passt noch nicht zu der Breite 
#  https://osdoc.cogsci.nl/4.0/de/visualangle/
# https://reference.org/facts/Visual_angle/LUw29zy7