六边形棋盘格（Hexagonal Grids）的坐标

news2025/4/20 22:50:09

1. 二位坐标转六边形棋盘的方式

1-1这是“波动式”的

这种就是把【方格子坐标】“左右各错开半个格子”做到的

具体来说有如下几种情况

具体到庙算平台上，是很巧妙的用一个4位整数，前两位为x、后两位为y来进行表示

附上计算距离的代码

def get_hex_distance(x1, y1, x2, y2):
    """
    计算六边形网格中两个点之间的曼哈顿距离。
    假设使用奇数行偏移坐标系（odd-r offset）。
    """
    dx = x2 - x1
    dy = y2 - y1
    return max(abs(dx), abs(dy), abs(dx + dy))

有多种计算方式的话可以用以下代码测试【可以对照着上面的图一个个格子数需要走几步】


def get_hex_distance(x1, y1, x2, y2):
    """
    计算六边形网格中两个点之间的曼哈顿距离。
    假设使用奇数行偏移坐标系（odd-r offset）。
    """
    dx = x2 - x1
    dy = y2 - y1
    return max(abs(dx), abs(dy), abs(dx + dy))


def get_grid_distance(row1, col1, row2, col2): # TODO: not sure
    """
    计算两个坐标间距离
    :param pos1:
    :param pos2:
    :return:
    """
    '''转换为立方坐标'''
    q1 = col1 - (row1 - (row1 & 1)) // 2
    r1 = row1
    s1 = 0 - q1 - r1
    q2 = col2 - (row2 - (row2 & 1)) // 2
    r2 = row2
    s2 = 0 - q2 - r2
    '''输出距离为曼哈顿距离的1/2'''
    return (abs(q1 - q2) + abs(r1 - r2) + abs(s1 - s2)) // 2



def test_hex_distance():
    """
    测试 get_hex_distance 和 get_grid_distance 函数的正确性。
    """
    # 测试用例：六边形网格中的点及其预期距离
    test_cases = [
        # 格式: (x1, y1, x2, y2, expected_distance)
        ((0, 0, 0, 0), 0),  # 同一个点
        ((0, 0, 1, 0), 1),  # 相邻点
        ((0, 0, 1, 1), 2),  # 
        ((0, 0, 2, 0), 2),  # 两步距离
        ((0, 0, 2, 2), 4),  # 
        ((0, 0, 3, 0), 3),  # 三步距离
        ((0, 0, 3, 3), 6),  # 
        ((1, 1, 4, 4), 6),  # 
    ]

    print("Testing get_hex_distance:")
    for (x1, y1, x2, y2), expected in test_cases:
        try:
            result = get_hex_distance(x1, y1, x2, y2)
            print(f"get_hex_distance({x1}, {y1}, {x2}, {y2}) = {result}, expected = {expected}")
            if result != expected:
                raise ValueError(f"Test failed for get_hex_distance({x1}, {y1}, {x2}, {y2})")
        except Exception as e:
            print(f"Test failed: {result} {(x1, y1, x2, y2, expected, 'get_hex_distance')}")

    print("\nTesting get_grid_distance:")
    for (row1, col1, row2, col2), expected in test_cases:
        try:
            result = get_grid_distance(row1, col1, row2, col2)
            print(f"get_grid_distance({row1}, {col1}, {row2}, {col2}) = {result}, expected = {expected}")
            if result != expected:
                raise ValueError(f"Test failed for get_grid_distance({row1}, {col1}, {row2}, {col2})")
        except Exception as e:
            print(f"Test failed: {result} {(row1, col1, row2, col2, expected, 'get_grid_distance')}")

if __name__ == "__main__":
    test_hex_distance()