如何利用Parallel.For迭代索引计算任意尺寸3D数组的三维坐标？

我有一个X、Y、Z长度任意的3D数组，想用Parallel.For循环遍历。听说嵌套Parallel.For会浪费任务，所以改用长度为ArrayLengthX * ArrayLengthY * ArrayLengthZ的单循环。请问能不能通过当前迭代次数结合数组的X、Y、Z长度，用数学方法得到对应的三维坐标？如果可以，具体怎么实现？

示例代码如下：

DimensionSettings dimensionSettings = dimension.Settings;
Vector3Int DimSize = dimensionSettings.GetDimensionSize();

TaskProgressMutex.WaitOne();
CurrentProgress = 0;
TotalProgress = DimSize.x * DimSize.y * DimSize.z;
TaskProgressMutex.ReleaseMutex();

int ChunkAmount = DimSize.x * DimSize.y * DimSize.z;
GD.Print("Chunks to generate : " + ChunkAmount);

ParallelLoopResult result = Parallel.For(0, ChunkAmount, (int i) =>
{
    GD.Print(i);
    int xcoords = ???;

    int ycoords = ???;

    int zcoords = ???;


    Vector3Int ChunkCoords = new Vector3Int(xcoords, ycoords, zcoords);
    GD.Print("Current Chunk : " + xcoords + " " + ycoords + " " + zcoords);

    GenerateChunk(ChunkCoords, seed);

    TaskProgressMutex.WaitOne();
    CurrentProgress += 1;
    //GD.Print("Chunk " + xcoords + " " + ycoords + " " + zcoords + " finished generating. Current Progress : " + CurrentProgress);
    TaskProgressMutex.ReleaseMutex();
});

实现方法 #

完全可以通过数学运算将一维迭代索引i转换为三维坐标，核心利用整除和取余运算拆分维度（以下逻辑基于行优先遍历顺序：先遍历X轴所有元素，再推进Y轴，最后推进Z轴）：

• X坐标计算：xcoords = i % DimSize.x
  每次X轴遍历完一轮后，余数会重置为0，刚好对应X轴的起始位置，以此循环。
• Y坐标计算：ycoords = (i / DimSize.x) % DimSize.y
  先除以X轴长度，得到已完成的X轴循环次数，再对Y轴长度取余，即可得到当前Y轴的位置。
• Z坐标计算：zcoords = i / (DimSize.x * DimSize.y)
  除以X、Y轴长度的乘积，得到已完成的XY平面循环次数，也就是当前Z轴的位置。

修改后的完整代码 #

DimensionSettings dimensionSettings = dimension.Settings;
Vector3Int DimSize = dimensionSettings.GetDimensionSize();

TaskProgressMutex.WaitOne();
CurrentProgress = 0;
TotalProgress = DimSize.x * DimSize.y * DimSize.z;
TaskProgressMutex.ReleaseMutex();

int ChunkAmount = DimSize.x * DimSize.y * DimSize.z;
GD.Print("Chunks to generate : " + ChunkAmount);

// 提前计算XY乘积，避免重复计算提升效率
int xyProduct = DimSize.x * DimSize.y;

ParallelLoopResult result = Parallel.For(0, ChunkAmount, (int i) =>
{
    GD.Print(i);
    int xcoords = i % DimSize.x;
    int ycoords = (i / DimSize.x) % DimSize.y;
    int zcoords = i / xyProduct;

    Vector3Int ChunkCoords = new Vector3Int(xcoords, ycoords, zcoords);
    GD.Print("Current Chunk : " + xcoords + " " + ycoords + " " + zcoords);

    GenerateChunk(ChunkCoords, seed);

    TaskProgressMutex.WaitOne();
    CurrentProgress += 1;
    TaskProgressMutex.ReleaseMutex();
});

内容的提问来源于stack exchange，提问作者PaperMartin