Implementation of finding an index in a 1D array for a triangular grid

Question

Am using a while loop to find an index within a 1D array, is there an easier, less-time-consuming and/or mathmatical way to find the index?

Consider the next grid:

 4   o
     |\  
     | \ 
     |  \
 3   o---o
     |\  |\  
     | \ | \ 
     |  \|  \
 2   o---o---o
     |\  |\  |\  
     | \ | \ | \ 
     |  \|  \|  \
 1   o---o---o---o
     |\  |\  |\  |\  
     | \ | \ | \ | \ 
     |  \|  \|  \|  \
 0   o---o---o---o---o

     0   1   2   3   4

To find an index in the triangular grid within a 1D array I have the next function:

//int size = 5;
int getindex( int x, int y )
{

    int columnCount = size;
    while( y-- > 0 ) x += columnCount--;

    return x;

}

The array (The numbers within the parenthesis are the coordinates and to simplify your view, in reality the (x,y) is in its whole the data):

pointdata data[ 15 ] = {
    (0,0), (1,0), (2,0), (3,0), (4,0),
    (0,1), (1,1), (2,1), (3,1),
    (0,2), (1,2), (2,2),
    (0,3), (1,3),
    (0,4),
};

Answer 1

This is rather problem to sum numbers between n and m, which is pretty widely known: it is sum of numbers 1 to m minus sum of numbers 1 to n(n-1 infact, but it gets eliminated in the code) plus x, ofcourse. In your example, it is:

index = columnCount * ( columnCount + 1 ) / 2 - ( columnCount - y ) * ( columnCount - y + 1 ) / 2 ) + x;
plus, since column count is static (presumably), you can pre-cumpute the first part or even better just use total length of your array.