  We present convergent gravitational waveforms extracted from
three-dimensional, numerical simulations in the wave zone and with causally
disconnected boundaries. These waveforms last for multiple periods and are very
accurate, showing a peak error to peak amplitude ratio of 2% or better. Our
approach includes defining the Weyl scalar Psi_4 in terms of a three-plus-one
decomposition of the Einstein equations; applying, for the first time, a novel
algorithm due to Misner for computing spherical harmonic components of our wave
data; and using fixed mesh refinement to focus resolution on non-linear sources
while simultaneously resolving the wave zone and maintaining a causally
disconnected computational boundary. We apply our techniques to a (linear)
Teukolsky wave, and then to an equal mass, head-on collision of two black
holes. We argue both for the quality of our results and for the value of these
problems as standard test cases for wave extraction techniques.
