Bounding box surface/volume question


#1

Question for you out there that are better in math than I am (that means almost everyone…) :confused:

If I have a minimum volume bounding box for a given arbitrary object, is it also the minimum surface area box?

Thanks! --Mitch


#2

Well, the volume of a box with length = L, width = W and height = H is:

V = L x W x H and the surface area is S = 2 x ((L x W) + (W x H) + (L x H))

so for any given size box of dimensions a x b x c, if any dimension is increased both the volume and surface area will increase linearly. This means that if a x b x c is the minimum volume box then it must be the minimum surface area box also.

Sound reasonable?


#3

Yes, and it’s what I am finding empirically, but I just wanted to be sure there wasn’t some sort of hidden trick there…

Thx, --Mitch