8 个立方体的最小/最大角，围绕原点形成一个立方体

Question

这是一个更通用的数学/代码问题，在我的例子中，我需要它用于 Godot/GDScript。我有一个虚拟立方体定义为具有厚度偏移的原点，我循环遍历每个轴上的最小值和最大值以执行每个单位的操作。普通立方体因此表示为：

const org = Vector3(32, 48, 64)
const thick = 16
const mins = Vector3(org.x - thick, org.y - thick, org.z - thick)
const maxs = Vector3(org.x + thick, org.y + thick, org.z + thick)

for x in range(mins.x, maxs.x, thick):
    for y in range(mins.y, maxs.y, thick):
        for z in range(mins.z, maxs.z, thick):
            var vec = Vector3(x, y, z)

结果是我想将这个立方体细分为 8 个相互完美接触的立方体。我需要有一个 mins_0 / maxs_0, mins_1 / maxs_1, ... , mins_7 / maxs_7 每个代表的一部分立方体。

我被困在数学上：我不知道如何转置原点和厚度偏移，显然要保持顺序以便任何循环都从正确的位置开始（mins.# < maxs.# 总是）。我只知道其中两个很明显的组合：

mins_0 = Vector3(org.x - thick, org.y - thick, org.z - thick)
maxs_0 = Vector3(org.x, org.y, org.z)
mins_4 = Vector3(org.x, org.y, org.z)
maxs_4 = Vector3(org.x + thick, org.y + thick, org.z + thick)

如何按正确顺序填充其他 6 个空格以覆盖剩余区域？

Answer 1

如果使用矢量运算，这会很多简单，但我们可以使用原始坐标来完成：

mins_0 = Vector3(org.x - thick, org.y - thick, org.z - thick)
maxs_0 = Vector3(org.x,         org.y,         org.z)

mins_1 = Vector3(org.x - thick, org.y - thick, org.z)
maxs_1 = Vector3(org.x,         org.y,         org.z + thick)

mins_2 = Vector3(org.x - thick, org.y,         org.z - thick)
maxs_2 = Vector3(org.x,         org.y + thick, org.z)

mins_3 = Vector3(org.x - thick, org.y,         org.z)
maxs_3 = Vector3(org.x,         org.y + thick, org.z + thick)

mins_4 = Vector3(org.x,         org.y - thick, org.z - thick)
maxs_4 = Vector3(org.x + thick, org.y,         org.z)

mins_5 = Vector3(org.x,         org.y - thick, org.z)
maxs_5 = Vector3(org.x + thick, org.y,         org.z + thick)

mins_6 = Vector3(org.x,         org.y,         org.z - thick)
maxs_6 = Vector3(org.x + thick, org.y + thick, org.z)

mins_7 = Vector3(org.x,         org.y,         org.z)
maxs_7 = Vector3(org.x + thick, org.y + thick, org.z + thick)

8 个立方体的最小/最大角，围绕原点形成一个立方体

min / max corners for 8 cubes forming a single cube around an origin

math

vector

gdscript