  This paper gives a detailed pedagogic presentation of the central concepts
underlying a new algorithm for the numerical solution of Einstein's equations
for gravitation. This approach incorporates the best features of the two
leading approaches to computational gravitation, carving up spacetime via
Cauchy hypersurfaces within a central worldtube, and using characteristic
hypersurfaces in its exterior to connect this region with null infinity and
study gravitational radiation. It has worked well in simplified test problems,
and is currently being used to build computer codes to simulate black hole
collisions in 3-D.
