轴方向反转下的不变坐标与变坐标

Question

对于涉及对象在笛卡尔坐标系中的坐标（例如一维笛卡尔坐标系中的有界区间的坐标）的算法，用坐标表示它们有什么优点或缺点独立 * 来自轴方向（例如 x_min 和 x_max），相对在坐标中依赖 ** 轴方向（例如 x_left和x_right，或者x_left 和width)？

例如，对于一个测试两个有界区间是否重叠的算法，你会写

def test_overlap(x_min_1, x_max_1, x_min_2, x_max_2):
    """Test if two bounded intervals overlap.
    Coordinates are independent from axis orientation.
    """
    assert x_min_1 <= x_max_1
    assert x_min_2 <= x_max_2
    return x_min_1 <= x_max_2 and x_min_2 <= x_max_1

或两者之一

def test_overlap(x_left_1, x_right_1, x_left_2, x_right_2):
    """Test if two bounded intervals overlap.
    Coordinates are dependent on axis orientation.
    """
    assert (x_left_1 <= x_right_1 and x_left_2 <= x_right_2
            or x_left_1 >= x_right_1 and x_left_2 >= x_right_2)

    if x_left_1 <= x_right_1:  # x-axis oriented to the right
        return x_left_1 <= x_right_2 and x_left_2 <= x_right_1
    else:                      # x-axis oriented to the left
        return x_left_1 >= x_right_2 and x_left_2 >= x_right_1

或

# Here the orientation of the x-axis cannot be deduced from the arguments,
# so you need to pass it explicitly to the algorithm.
def test_overlap(x_left_1, width_1, x_left_2, width_2, x_orientation):
    """Test if two bounded intervals overlap.
    Coordinates are dependent on axis orientation.
    """
    assert width_1 >= 0
    assert width_2 >= 0
    assert x_orientation in ["right", "left"]

    if x_orientation == "right":  # x-axis oriented to the right
        x_right_1 = x_left_1 + width_1
        x_right_2 = x_left_2 + width_2
        return x_left_1 <= x_right_2 and x_left_2 <= x_right_1
    else:                         # x-axis oriented to the left
        x_right_1 = x_left_1 - width_1
        x_right_2 = x_left_2 - width_2
        return x_left_1 >= x_right_2 and x_left_2 >= x_right_1

---

^{* 坐标指定一个特定的点并随坐标系而变化。当我说“坐标独立于轴方向”时，它意味着所考虑的点会发生变化，以使坐标在轴方向反转下保持不变。}

^{** 当我说“坐标取决于轴方向”时，这意味着 坐标 会发生变化，以使所考虑的点在轴方向反转下保持不变。这是标准用法。}

Answer 1

我不知道这是否是“更好”，但我的方式做了一个项目，它的表现还算不错，是定义class类似如下： P>

class Interval(object):
    """ Representation of a closed interval.

    "a" & "b" can be any numeric type, or any other type than can be
    compared. If the type can also be incremented by 1, then it
    will be possible to iterate between the two values in
    ascending order.
    """
    def __init__(self, a, b):
        self.lowerbound, self.upperbound = (a, b) if a < b else (b, a)

    def __contains__(self, val):
        return self.lowerbound <= val <= self.upperbound

    # Implemented as a generator (so no 'next' method is needed)
    def __iter__(self):
        nextvalue = self.lowerbound  # Initialize iteration state.
        while nextvalue <= self.upperbound:
            yield nextvalue
            nextvalue += 1

在__contains__()方法控制表达式等if x in interval:如何检查x靠在@ 987654326值@“的上部以及下部边界。 （在我自己的应用程序中，我使用Date S作为间隔的边界。） P>

这样做，这样使您能够控制一切到底是怎样的作品近，再加上你也可以将专用的方法，它如果需要的话。例如：一个test_overlap()方法可以做你决定它是什么你想要的任何方式。事实上，这样的方法可以被写入到返回结果作为Interval P>