旋转立方体并追踪它的边

Question

我一直在尝试解决旋转体素（3d 立方体）并在旋转后跟踪边的问题。

以这张图片为例。

旋转后，我需要知道后面的边在哪里。例如，如果我将此立方体沿其 Z 轴旋转 90 度，则 Y 和 X 将交换。

这适用于用 Unity 编写的 3d 体素游戏的服务器端 mod。所以 Unity methods/utils 也可用。但这又是服务器端和 mod，所以我无法访问网格或对象本身，我只能告诉它旋转 x、y 或 z，并且需要根据最终旋转执行逻辑。如果有人能指出我的大致方向或告诉我可以实现此目的的方法，我将不胜感激。谢谢！

编辑：旋转存储在 x、y、z 旋转中

Answer 1

也许有点 "stupid" 解决方案，但我会简单地将相应的边名称存储在一个数组中，并针对特定轴的每 90° 步长执行相应的值偏移。

所以让我们说例如在默认状态下你有

0 : X_l
1 : Z_u
2 : Y_l
3 : Z_l
4 : Y_u
5 : X_u

那么实际你需要知道的是每个轴和每个方向（+或-）一个90°步长的变化矩阵：

X轴

                     positive step              negative step

original index    0 | 1 | 2 | 3 | 4 | 5      0 | 1 | 2 | 3 | 4 | 5
new index         0 | 2 | 3 | 4 | 1 | 5      0 | 4 | 1 | 2 | 1 | 0

Y轴

                     positive step              negative step

original index    0 | 1 | 2 | 3 | 4 | 5      0 | 1 | 2 | 3 | 4 | 5
new index         3 | 0 | 2 | 5 | 4 | 1      1 | 5 | 2 | 0 | 4 | 3

Z轴

                     positive step              negative step

original index    0 | 1 | 2 | 3 | 4 | 5      0 | 1 | 2 | 3 | 4 | 5
new index         4 | 1 | 0 | 3 | 5 | 2      2 | 1 | 5 | 3 | 0 | 4

我在 class Cube 中实现了这个

// The possible names of your cube sides
public enum CubeSideName
{
    X_l,
    X_u,
    Y_l,
    Y_u,
    Z_l,
    Z_u
}

// This stores the relationship between one certain
// position (Front,Back,Top,Bottom,Right,Left)
// and a cube side (x_l, x_u, y_l, y_u, z_l, z_u)
[Serializable]
public struct CubeSidePair
{
    // For the example I used GameObjects with according names
    // instead of GameObjects you could also simply have a string ID or another enum 
    // for the name of the according position
    public GameObject GameObject;
    public CubeSideName Name;
}

[Serializable]
public class Cube
{
    // This stores which position (Front,Back,Top,Bottom,Right,Left)
    // is currently taken by which cube side (x_l, x_u, y_l, y_u, z_l, z_u)
    public CubeSidePair[] CubeSidesPair = new CubeSidePair[6];

    public Vector3Int Rotation
    {
        get { return _rotation; }
        set
        {
            UpdateRotation(value);
        }
    }

    // This is actually just for making it visual
    private readonly Dictionary<CubeSideName, Color> colors = new Dictionary<CubeSideName, Color>(6)
    {
        {CubeSideName.X_u, Color.blue },
        {CubeSideName.X_l, Color.cyan },

        {CubeSideName.Y_u, Color.red },
        {CubeSideName.Y_l, Color.magenta },

        {CubeSideName.Z_u,Color.green },
        {CubeSideName.Z_l,Color.yellow }
    };

    [Header("Debug only")]
    [SerializeField] private Vector3Int _rotation;

    public void Reset()
    {
        _rotation = Vector3Int.zero;

        CubeSidesPair[0].Name = CubeSideName.X_l;
        CubeSidesPair[1].Name = CubeSideName.Z_u;
        CubeSidesPair[2].Name = CubeSideName.Y_l;
        CubeSidesPair[3].Name = CubeSideName.Z_l;
        CubeSidesPair[4].Name = CubeSideName.Y_u;
        CubeSidesPair[5].Name = CubeSideName.X_u;

        UpdateColors();
    }

    // Here all the magic happens
    private void UpdateRotation(Vector3Int newRotaion)
    {
        // get difference to current rotation
        var newRotationInput = newRotaion - _rotation;

        // Go in 90° steps around the according axis
        // untilt he rotation is done
        while (newRotationInput != Vector3Int.zero)
        {
            // For each rotation step just take the index matrices from before
            // and use them to perform an array shift
            if (newRotationInput.x < 0)
            {
                // do negative X rotation
                var temp = CubeSidesPair[1].Name;
                CubeSidesPair[1].Name = CubeSidesPair[2].Name;
                CubeSidesPair[2].Name = CubeSidesPair[3].Name;
                CubeSidesPair[3].Name = CubeSidesPair[4].Name;
                CubeSidesPair[4].Name = temp;

                newRotationInput.x += 90;
            }
            else if (newRotationInput.x > 0)
            {
                // do positive X rotation
                var temp = CubeSidesPair[4].Name;
                CubeSidesPair[4].Name = CubeSidesPair[3].Name;
                CubeSidesPair[3].Name = CubeSidesPair[2].Name;
                CubeSidesPair[2].Name = CubeSidesPair[1].Name;
                CubeSidesPair[1].Name = temp;

                newRotationInput.x -= 90;
            }
            else if (newRotationInput.y < 0)
            {
                // do negative Y rotation
                var temp = CubeSidesPair[1].Name;
                CubeSidesPair[1].Name = CubeSidesPair[0].Name;
                CubeSidesPair[0].Name = CubeSidesPair[3].Name;
                CubeSidesPair[3].Name = CubeSidesPair[5].Name;
                CubeSidesPair[5].Name = temp;

                newRotationInput.y += 90;
            }
            else if (newRotationInput.y > 0)
            {
                // do positive Y rotation
                var temp = CubeSidesPair[3].Name;
                CubeSidesPair[3].Name = CubeSidesPair[0].Name;
                CubeSidesPair[0].Name = CubeSidesPair[1].Name;
                CubeSidesPair[1].Name = CubeSidesPair[5].Name;
                CubeSidesPair[5].Name = temp;

                newRotationInput.y -= 90;
            }
            else if (newRotationInput.z < 0)
            {
                // do negative Z rotation
                var temp = CubeSidesPair[2].Name;
                CubeSidesPair[2].Name = CubeSidesPair[0].Name;
                CubeSidesPair[0].Name = CubeSidesPair[4].Name;
                CubeSidesPair[4].Name = CubeSidesPair[5].Name;
                CubeSidesPair[5].Name = temp;

                newRotationInput.z += 90;
            }
            else if (newRotationInput.z > 0)
            {
                // do positive Z rotation
                var temp = CubeSidesPair[4].Name;
                CubeSidesPair[4].Name = CubeSidesPair[0].Name;
                CubeSidesPair[0].Name = CubeSidesPair[2].Name;
                CubeSidesPair[2].Name = CubeSidesPair[5].Name;
                CubeSidesPair[5].Name = temp;

                newRotationInput.z -= 90;
            }
        }

        _rotation = newRotaion;

        UpdateColors();
    }

    // Just for the visual
    private void UpdateColors()
    {
        foreach (var cubeSide in CubeSidesPair)
        {
            var renderer = cubeSide.GameObject.GetComponent<Renderer>();

            renderer.material.color = colors[cubeSide.Name];
        }
    }
}

这是我在演示中使用它的方式（见底部）：

public class CubeController : MonoBehaviour
{
    public Cube Cube;

    private void Awake()
    {
        // Initial setup
        Cube.Reset();
    }

    private void Update()
    {
        var multiplier = 90;

        if (Input.GetKey(KeyCode.LeftShift))
        {
            multiplier = -90;
        }

        if (Input.GetKeyDown(KeyCode.X))
        {
            Cube.Rotation += Vector3Int.right * multiplier;
        }
        else if (Input.GetKeyDown(KeyCode.Y))
        {
            Cube.Rotation += Vector3Int.up * multiplier;
        }
        else if (Input.GetKeyDown(KeyCode.Z))
        {
            Cube.Rotation += new Vector3Int(0, 0, 1) * multiplier;
        }
    }
}

我希望我能把这个想法形象化一点；）

我当然只是逐步旋转，但如果进入像

这样的固定旋转，它应该以相同的方式工作

Cube.Rotation = new Vector3(-90, 180, 270);

但是，您可能想要更改旋转的顺序。

旋转立方体并追踪它的边

Rotate Cube and track its sides

c#

voxel

unity3d