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Is there a method or modifier that would allow me to dynamically create an effect on a mesh similar to the proportional edit, that would accept a magnitude, position and directional vector by using empty arrow object? I want to have multiple arrows on and around the object and animate them, then bake that into key-framed animation.

dynamic proportional edit

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    $\begingroup$ You can use a hook modifier. $\endgroup$ – lemon Aug 24 '16 at 14:57
  • $\begingroup$ lemon, that's incredibly close to how I'm hoping to manipulate the mesh except that after watching a tutorial about the hook modifier: youtube.com/watch?v=Z7WXOM3iQYM it appears that you have to attach it to a vertex, not necessarily the entire mesh. I'd like the empty or arrow object to be able to manipulate vertices in close proximity instead of pre-selected ones, so that it can move along the mesh, instead of pulling just one point out. $\endgroup$ – falldeaf Aug 24 '16 at 15:09
  • $\begingroup$ surely the second option in the answer is closer to what you want. $\endgroup$ – lemon Aug 24 '16 at 15:16
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Two possibilities (at least) : hook modifier and vertex weight proximity + shrinkwrap. And an edit using dynamic paint (following the comments).

  • Hook modifier :

enter image description here

The setting is the following :

The hook modifier is defined for the plane, and an empty is use as a hook. You can tune the falloff and the proximity. You must define a vertex group (assign the wanted vertices to it).

enter image description here

  • Vertex weight proximity and shrink wrap :

This can be a more dynamic solution.

First add a vertex weight proximity modifier. That will assign to the vertex group a value depending on the distance to the empty. Then add a skrinkwrap (targeting to another plane) and using this vertex group.

You need to define another plane to skrinkwrap to (this plane is placed near to the surface... not visible here as it is in wire display mode).

enter image description here

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  • A third solution using dynamic paint :

The object is in wireframe here to allow to see the moving object (here spheres replace that was empties previously).

enter image description here

The principle is the same, as before but the weights of the vertex group are given using dynamic paint.

Configuration for the spheres used as brushes : here 'proximity' is used (other options available) and you have also some option for the falloff.

enter image description here

Configuration for the grid : we are painting on 'weights' on the vertex group.

enter image description here

And as before the grid has a shrinkwrap using the same vertex group :

enter image description here

Updated blend file :

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  • $\begingroup$ Amazing answer, exactly what I need and practically a tutorial! Thank you very much for taking the time! $\endgroup$ – falldeaf Aug 24 '16 at 15:31
  • $\begingroup$ I was able to replicate your results here, but it looks like this approach is only working for a single point? Is there a way to get this to work for an arbitrary number of points? $\endgroup$ – falldeaf Aug 24 '16 at 16:45
  • $\begingroup$ @falldeaf, I see... so... just let me the time to right a complement... $\endgroup$ – lemon Aug 24 '16 at 17:05
  • $\begingroup$ @falldeaf, done, using dynamic paint, at the end of the answer. $\endgroup$ – lemon Aug 24 '16 at 17:22
  • $\begingroup$ I wish I could do more to say thanks. I sincerely appreciate your help and the time you've put in. $\endgroup$ – falldeaf Aug 24 '16 at 17:35
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You can use a warp modifier to create this type of effect.
As with any modifier you can add as many as you need, one for each bump.

As the manual says "The Warp Modifier is a bit tricky at first," indeed there was a time I did not know what it did.

In your case, add the warp modifier to your plane. Add any object (empties are commonly used) under the plane, and another above the plane. Like in this picture.
warp modifier object setup

The empty below the plane is set as the From object, and empty above the plane is set as the To object in the warp modifier.
warp modifier settings

The benefit to using the modifier is that everything is easily scriptable, or animatable.

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