  We introduce additively-weighted straight skeletons as a new generalization
of straight skeletons. An additively-weighted straight skeleton is the result
of a wavefront-propagation process where, unlike in previous variants of
straight skeletons, wavefront edges do not necessarily start to move at the
begin of the propagation process but at later points in time. We analyze the
properties of additively-weighted straight skeletons and show how to compute
straight skeletons with both additive and multiplicative weights.
  We then show how to use additively-weighted and multiplicatively-weighted
straight skeletons to generate roofs and terrains for polygonal shapes such as
the footprints of buildings or river networks. As a result, we get an automated
generation of roofs and terrains where the individual facets have different
inclinations and may start at different heights.
