isometric deformation of a plane can you please address my query.

I want to smoothly deform a plane such that the distance between the 2 points on the plane are preserved(Isometric deformation). 

For example 

1) In the 1stfigure, you can see in the flat mesh grid(undeformed) the distance between the vertices are constant (.222 blender units).
2) In the 2ndrd figure, i apply the wave modifier to deform the mesh. As you can see, the distance between the 2 vertices is not the same anymore.

I want to achieve the smooth, isometric deformation. Where the distance between the vertices remain constant after deformation.

How can i achieve this isometric deformation in blender?(using any of the available modifiers such as wave, wrap, deform, cloth etc etc).

Thanks
Demon
Final:

As far as I know your best shot would be with Curve modifier. It will not be perfectly even though but I don't think it's possible to preserve 1:1 edge length with any modifier.



Steps:




Add Curve > Bezier Curve.
Rotate it 90 degrees on X axis.
Select Plane and add Curve Modifier.
Choose BezierCurve.
Move a Plane on X axis.