Undulating Surface From Points

Is there a method of gaining more control over the intensity of attractor points when you create a surface from points. Right now, I'm remapping the distance from the original grid to multiple attractor points I have to create an undulating surface but I'm not really getting the results I want. I almost feel like the averages are canceling out the intensity to create a predictable surface where as I want more control over intricacies of the surface such as maybe the middle part puffs up more like a sphere where as the sides almost wrap into one another.

I can see how that can be confusing and misleading and of course I can elaborate further.

Any suggestions?

Thanks