Seitenverhältnis-Rechner

import math

def simplify_ratio(width: int, height: int) -> tuple[int, int]:
    """Simplify a width:height pair to its lowest integer ratio using GCD."""
    g = math.gcd(width, height)
    return width // g, height // g

def scale_to_width(orig_w: int, orig_h: int, new_w: int) -> float:
    """Calculate new height given new width, preserving aspect ratio."""
    return new_w * (orig_h / orig_w)

def scale_to_height(orig_w: int, orig_h: int, new_h: int) -> float:
    """Calculate new width given new height, preserving aspect ratio."""
    return new_h * (orig_w / orig_h)

def ratio_decimal(width: int, height: int) -> float:
    """Return aspect ratio as a decimal (e.g. 1.778 for 16:9)."""
    return width / height

# Examples
w, h = simplify_ratio(1920, 1080)
print(f"1920:1080 → {w}:{h}")          # 16:9

w, h = simplify_ratio(1280, 720)
print(f"1280:720  → {w}:{h}")          # 16:9

w, h = simplify_ratio(800, 600)
print(f"800:600   → {w}:{h}")          # 4:3

w, h = simplify_ratio(3840, 2160)
print(f"3840:2160 → {w}:{h}")          # 16:9 (4K)

# Scale operations
new_h = scale_to_width(1920, 1080, 1280)
print(f"1920×1080 → width 1280 → height {new_h:.0f}")   # 720

new_w = scale_to_height(1920, 1080, 720)
print(f"1920×1080 → height 720 → width {new_w:.0f}")    # 1280

# Batch simplification
resolutions = [(1920, 1080), (1280, 720), (3840, 2160), (2560, 1440), (800, 600)]
for rw, rh in resolutions:
    sw, sh = simplify_ratio(rw, rh)
    print(f"{rw}×{rh} = {sw}:{sh} ({ratio_decimal(rw, rh):.3f})")