reasonable theory?

Before coding this in C, I wanted to test the idea out in R.

But I'm unsure if the theory is well-founded.

I have a (user-supplied) black-box function which takes R^n ->  R^3
and a defined domain for each of the input reals.

I want to send some samples through the box to determine an
approximation of the convex hull of the function's range.
(I'll use the library from http://www.qhull.org to compute
the convex hull from the function's outputs.)

My plan is to use the permutation of the min and max values
for the n inputs along with k-1 samples w/in [min,max], but
I want the adjust the k samples a bit to avoid sampling bias.

To make it simpler, let's set the domain to [0,1].

Then, K = { 1/k, 2/k, ... (k-1)/k }

One reasonably easy possibility is to add to each Kn
a linear RV in, say, [-1/k?,1/k?].

Would a normal RV be better?  Some other bell-shaped RV?

Does adding a bit (but not too much) of randomness to the
input values have reason at all?

-JimC