just iterate through those arrays to find min and max for x and y?

unless:

1. you mean bounding box of a curve or ellipse or other shape that may extend beyond those points (you said "shape"not "polygon," so it's not clear what you meant)
2. You meant the on-screen bounds of a shape that may hev been transformed via scale and rotate.

knowing what to measure makes measuring easier

kb, http://www.riftgame.com/

i tried checking using min and max, but iterating through several times with only 1024 points per shape freezes processingjs! (i am putting the bounding box check within shape generation, i.e., while loop if beyond bounds, generate shape again.) 

Iterate once, and keep the information along with the arrays.

it depends how many shapes you're creating the bounding box for, and whether they're polygons or polybeziers. If you have even a reasonably low number of shapes you will probably get the best performance from a scanline/sweepline algorith to determine the bounds for your shapes, then track your shapes as they move so that you can update the bounds without having to run a new scanline. While an expensive initial operation, the fact that you only have to do it once makes it highly suitable for animated sketches.

maybe a convex hull (http://www.leebyron.com/else/mesh/) gets you the speed-bump you need.