3D Array as 1D array?

[FatalSleep]

How would I go about creating a 3D array using the "new" operator? I noticed that I could do:

int* array = new int[ width * height * depth ];

Which is the format I'd like to stick with since using [width,height,depth] does not work with or without the new operator.

However, I am not sure how to access array elements with this format. I found here http://gmc.yoyogames.com/index.php?showtopic=414085 that I could use:

array[ x * Height * Depth + y * Depth + z ] = value;

However, I am not sure how right/accurate this method is. Is this correct? Also, how do I go about grouping that indexing algorithm with parenthesis?

[ats15]

This is a very efficient way to store arrays, and it is right.
If you use a 3D array A[x][y][z] should be replaced by A[ x * height * depth + y * depth + z ]
If you have the 1D array A[index] and you want to see what that corresponds to in 3D,

width_index=index/(height*depth);  //Note the integer division . This is x
height_index=(index-width_index*height*depth)/depth; //This is y
depth_index=index-width_index*height*depth- height_index*depth;//This is z 

[FatalSleep]

Thank you for the bonus info there. Now taking the aforementioned indexing algorithm into play:

x * Height * Depth + y * Depth + z;

How is that split up using parenthesis? I like to group everything in parenthesis to keep a good understanding of how it works.

[Lachlan Easton]

BEDMAS.
In this case you only have multiplications and additions. Do the multiplications first moving left to right
((x * Height) * Depth) + (y * Depth) + z
then additions (left to right as well)
((((x * Height) * Depth) + (y * Depth)) + z)
frankly I think that makes it much harder to read :P

[FatalSleep]

It looks like it's harder to read, because it is... however, it makes a better "at a glance" impression, making the overall readability far higher despite the overuse of parenthesis.

[FatalSleep]

However, based on this little calculation I did: (3 x 3 x 3)

Depth: 0 (cells 0 to 8)
0,0,0
1,1,1
2,2,2

Depth: 1 (cells 9 to 17)
0,0,0
1,1,1
2,2,2

Depth: 2 (cells 18 to 26)
0,0,0
1,1,1
2,2,2

By plugging in cell: [ 1 , 2 , 0 ] I should get the 7th cell.
However based on:

((((x * Height) * Depth) + (y * Depth)) + z)

I get the 15th cell. So what is the issue here?

Instead wouldn't this make more sense?

( ( ( Width * Height ) * Zpos ) + ( Width * Ypos ) ) + Xpos;

[htirwin]

I would wrap this in a class if I were to do this. Calculate the index in a getter. Allocate in the constructor and delete in the destructor.

int at( int x, int y, int z ) {
    return data[ z*width*height + y*width + x ];
}

[cire]

Instead wouldn't this make more sense?

It makes the same amount of sense.

As long as you treat the dimensions consistently, it doesn't really matter which one is named x, y or z. Encapsulating access to the data structure as htirwin suggests is one way to ensure the dimensions are treated consistently.

[10X9216C]

If you use a 3D array A[x][y][z] should be replaced by A[ x * height * depth + y * depth + z ]

This is false, C++'s implementation of 3D array is exactly the same as taking a 1D array and handling the index yourself. Though you do have mroe control, such as which way to store it (row vs col major). C++'s implementation just uses row major if i recall correctly. You might be confused with std::vector<> and how people tend to use that to create a N dimension array std::vector<std::vector<std::vector<int>>>. In this case a lot of memory is wasted storing the data of the vectors, which usually just corresponds some data such as pointers and such.

You can just use boost's implementation, multi_array.

[htirwin]

This is false, C++'s implementation of 3D array is exactly the same as taking a 1D array and handling the index yourself.

This isn't true if it's dynamically allocated.

[10X9216C]

This isn't true if it's dynamically allocated.

Yes it is... http://ideone.com/559Cyj
What difference do you think it makes having it on the stack or having it allocated else where in memory, it makes no difference how C++ handles arrays.

[htirwin]

I meant this,

int ***a;
a = new int**[DEPTH];
for ( int i = 0; i < 10; ++i ) {
    a[i] = new int*[HEIGHT];
    for ( int j = 0; j < 10; ++j ) 
        a[i][j] = new int[WIDTH];	
}

[10X9216C]

http://ideone.com/f8Q7VN

What you've created isn't a 3D array.

Ah i get what you mean now. Still better to create a class to handle that, boost::multi_array should handle that. Your wording man, so much communication.