Interpolation algorithms in computer graphics
Some ideas:


rotate the image in 2D
compute the Radon transform.  This is used in tomography applications.
Other 2D effects, like swirling or adding ripples
Map the 2D image onto the surface a 3D shape, such as a sphere
Simulate the effect of a lens, or refraction by some other transparent 3D object in front of your bitmap
Simulate gravitational lensing by a black hole


2D image rotation is what comes to mind first as the simplest application of 2D interpolation after rescaling.  The obvious approach is to simply apply the well-known coordinate transformation; an alternative trick is to decompose the rotation into a sequence of three sheers so that only 1D interpolation is needed.

The 3D examples are more involved, since they will probably require implementation of raytracing.