  We present an efficient, parallel, constrained optimization technique for
approximating CAD curves with super-convergent rates.
  The optimization function is a disparity measure in terms of a piece-wise
polynomial approximation and a curve re-parametrization.
  The constrained problem solves the disparity functional fixing the mesh
element interfaces.
  We have numerical evidence that the constrained disparity preserves the
original super-convergence: ${2p}$ order for planar curves and $\lfloor\frac
32(p-1)\rfloor + 2$ for 3D curves, $p$ being the mesh polynomial degree.
  Our optimization scheme consists of a globalized Newton method with a
nonmonotone line search, and a log barrier function preventing element
inversion in the curve re-parameterization. Moreover, we introduce a
\emph{Julia} interface to the EGADS geometry kernel and a parallel optimization
algorithm. We test the potential of our curve mesh generation tool on a
computer cluster using several aircraft CAD models. We conclude that the solver
is well-suited for parallel computing, producing super-convergent
approximations to CAD curves.
