arrays - How do I compute the linear index of a 3D coordinate and vice versa? -

if have point (x, y z), how find linear index, point? numbering scheme (0,0,0) 0, (1, 0, 0) 1, . . ., (0, 1, 0) max-x-dimension, .... also, if have linear coordinate, i, how find (x, y, z)? can't seem find on google, results filled other irrelevant stuff. thank you!

there few ways map 3d coordinate single number. here's 1 way.

some function f(x,y,z) gives linear index of coordinate(x,y,z). has constants a,b,c,d want derive can write useful conversion function.

f(x,y,z) = a*x + b*y + c*z + d 

you've specified (0,0,0) maps 0. so:

f(0,0,0) = a*0 + b*0 + c*0 + d = 0 d = 0 f(x,y,z) = a*x + b*y + c*z 

that's d solved. you've specified (1,0,0) maps 1. so:

f(1,0,0) = a*1 + b*0 + c*0 = 1 = 1 f(x,y,z) = x + b*y + c*z 

that's solved. let's arbitrarily decide next highest number after (max_x, 0, 0) (0,1,0).

f(max_x, 0, 0) = max_x f(0, 1, 0) = 0 + b*1 + c*0 = max_x + 1 b = max_x + 1 f(x,y,z) = x + (max_x + 1)*y + c*z 

that's b solved. let's arbitrarily decide next highest number after (max_x, max_y, 0) (0,0,1).

f(max_x, max_y, 0) = max_x + max_y * (max_x + 1) f(0,0,1) = 0 + (max_x + 1) * 0  + c*1 = max_x + max_y * (max_x + 1) + 1 c = max_x + max_y * (max_x + 1) + 1 c = (max_x + 1) + max_y * (max_x + 1) c = (max_x + 1) * (max_y + 1) 

now know a, b, c, , d, can write function follows:

function linearindexfromcoordinate(x,y,z, max_x, max_y){     = 1     b = max_x + 1     c = (max_x + 1) * (max_y + 1)     d = 0     return a*x + b*y + c*z + d } 

you can coordinate linear index similar logic. have marvelous demonstration of this, page small contain. i'll skip math lecture , give final method.

function coordinatefromlinearindex(idx, max_x, max_y){     x =  idx % (max_x+1)     idx /= (max_x+1)     y = idx % (max_y+1)     idx /= (max_y+1)     z = idx     return (x,y,z) }