  A picture of confinement in QCD based on a condensate of thick vortices with
fluxes in the center of the gauge group (center vortices) is studied. Previous
concrete model realizations of this picture utilized a hypercubic space-time
scaffolding, which, together with many advantages, also has some disadvantages,
e.g., in the treatment of vortex topological charge. In the present work, we
explore a center vortex model which does not rely on such a scaffolding.
Vortices are represented by closed random lines in continuous 2+1-dimensional
space-time. These random lines are modeled as being piece-wise linear, and an
ensemble is generated by Monte Carlo methods. The physical space in which the
vortex lines are defined is a torus with periodic boundary conditions. Besides
moving, growing and shrinking of the vortex configurations, also reconnections
are allowed. Our ensemble therefore contains not a fixed, but a variable number
of closed vortex lines. This is expected to be important for realizing the
deconfining phase transition. We study both vortex percolation and the
potential V (R) between quark and anti-quark as a function of distance R at
different vortex densities, vortex segment lengths, reconnection conditions and
at different temperatures. We find three deconfinement phase transitions, as a
function of density, as a function of vortex segment length, and as a function
of temperature.
