座標與邊界框

import math


def count_image_tokens(width: int, height: int) -> int:
    """Visual tokens consumed by an image: one token per 28x28 pixel patch."""
    return math.ceil(width / 28) * math.ceil(height / 28)


def resized_size(
    width: int,
    height: int,
    max_edge: int = 1568,
    max_tokens: int = 1568,
) -> tuple[int, int]:
    """The size Claude resizes an image to before padding.

    Defaults are for the standard resolution tier. For high-resolution-tier
    models, use max_edge=2576 and max_tokens=4784. Returns (width, height).
    Images that already fit within the limits are returned unchanged.
    """

    def fits(w: int, h: int) -> bool:
        return (
            math.ceil(w / 28) * 28 <= max_edge
            and math.ceil(h / 28) * 28 <= max_edge
            and count_image_tokens(w, h) <= max_tokens
        )

    if fits(width, height):
        return (width, height)
    if height > width:
        resized_h, resized_w = resized_size(height, width, max_edge, max_tokens)
        return (resized_w, resized_h)

    # 沿長邊進行二分搜尋，找出保持長寬比且能容納的
    # 最大尺寸。
    aspect_ratio = width / height
    lo, hi = 1, width  # lo always fits; hi never fits
    while lo + 1 < hi:
        mid = (lo + hi) // 2
        if fits(mid, max(round(mid / aspect_ratio), 1)):
            lo = mid
        else:
            hi = mid
    return (lo, max(round(lo / aspect_ratio), 1))


# 「Claude 如何調整大小與填補影像」中的 A4 範例：
print(resized_size(1075, 1520))  # (924, 1307)

# 若要套用調整大小，請使用您的影像函式庫，例如 Pillow：
# image.resize(resized_size(*image.size))

# 此輔助函式呼叫本頁調整大小範例中的 resized_size。
def to_relative_coordinates(
    x: float,
    y: float,
    original_width: int,
    original_height: int,
    max_edge: int = 1568,
    max_tokens: int = 1568,
) -> tuple[float, float]:
    """Map a pixel coordinate returned by Claude to relative coordinates in [0, 1].

    Pass the dimensions of the image you uploaded. For high-resolution-tier
    models, use max_edge=2576 and max_tokens=4784.
    """
    resized_w, resized_h = resized_size(
        original_width, original_height, max_edge, max_tokens
    )
    return (x / resized_w, y / resized_h)


# Claude 在調整大小後的 A4 頁面上回傳位於 (462, 653.5) 的表格角落，
# 對應回 1075x1520 原圖的方式如下：
rel_x, rel_y = to_relative_coordinates(462, 653.5, 1075, 1520)
print((rel_x * 1075, rel_y * 1520))  # (537.5, 760.0)