  Inspired by the increasingly popular research on extending partial graph
drawings, we propose a new perspective on the traditional and arguably most
important geometric graph parameter, the crossing number. Specifically, we
define the partially predrawn crossing number to be the smallest number of
crossings in any drawing of a graph, part of which is prescribed on the input
(not counting the prescribed crossings). Our main result - an FPT-algorithm to
compute the partially predrawn crossing number - combines advanced ideas from
research on the classical crossing number and so called partial planarity in a
very natural but intricate way. Not only do our techniques generalise the known
FPT-algorithm by Grohe for computing the standard crossing number, they also
allow us to substantially improve a number of recent parameterised results for
various drawing extension problems.
