Bernd Hamann

The source function in this case was a photograph of Professor Hamann (taken from his homepage), resampled to a resolution of 172x216 pixels.
The left column shows the linear spline itself, the right column shows the spline's connectivity as a triangle mesh.

Linear spline with 400 vertices
Linear spline with 800 vertices
Linear spline with 1600 vertices
Linear spline with 3200 vertices