The function that maps two coordinates into a node index is similar to Cantor pairing function (in the linked page, indices start from 0). See section "Inverting the Cantor pairing function".
If I have a triangle like this:
1 2 4 7 11 16
3 5 8 12 17
6 9 13
... which goes on to contain numbers (although I don't think the size is relavent).
Notice the way it's ordered. The numbers can be considered as the ordinal index of a node of the triangle. The numbers are ordered going diagonally from top right to bottom left, and creating a new diagonal line which is longer as you go right.
The problem is, given a node with ordinal index , how can I find what the and coordinate is of ? Is there a formula?
get_x_index(13) = 2
get_y_index(13) = 2
get_x_index(17) = 4
get_y_index(17) = 1
Does anyone know how to do this?
ok thanks, that worked, but now given the triangle has n numbers where n is the amount of numbers in the triangle, how can I find the width and height of the triangle?
In the example in the beginning post, the width would be 6 and the height would be 5.