We present a new algorithm, using only simple geometry, to warp imagery from an arbitrarily shaped source region to an arbitrarily shaped target region. Mathematically speaking, the algorithm outputs harmonic maps (every point is at the average position of its neighbors) using new boundary conditions to curb excessive non-uniform stretching and shearing in order to appear more conformal. The algorithm has typical running times measured in seconds. We give some artistic examples to demonstrate how the results can be used in digital photography and other graphical work.