问将一个大长方体切割成任意尺寸在一定范围内的小长方体。

EN

rng = np.random.default_rng(0)
def split_dimension(length, low, high):
    '''
    Attempt to partition a segment of the given length in segments
    of length between low and high
    '''
    acc = 0
    while length - acc > high:
        assert length - acc >= low, \
          'Failed to get a solution, maybe it was bad luck, maybe there is no solution'
        # of course this choice could be made in a more clever way
        v = rng.uniform(low, high)
        yield acc, v
        acc += v
    yield acc, length - acc

def split_hypercuboid(dimension, dim_ranges):
    '''
    Attempt to split a given cuboid in sub cuboids with dimensions
    
    '''
    low, high = dim_ranges[-1]
    length = dimension[-1] 
    if len(dimension) == 1:
        for c,v in split_dimension(length, low, high):
            yield (c,), (v,)
    else:
        for c,v in split_dimension(length, low, high):
            for corner, size in split_hypercuboid(dimension[:-1], dim_ranges[:-1]):
                yield corner + (c,), size + (v,)
def solve(L, W, H):
    ''' Apply it to the original question '''
    return list(split_hypercuboid((L, W, H), ((0.2*L, 0.5*L), (0.2*W, 0.5*W), (0.0, 0.3*H))))

plt.figure(figsize=(5,5))
for (z, x, y), (l, w, h) in solve(100, 100, 100):
    if z == 0:
        plt.plot([x, x, x+w, x+w, x], [y, y+h, y+h, y, y], '-k')