Variations on Angle Based Flattening

achieves quasi-conformality by solving a non-linear optimization
problem. We take advantage of a characterization
of convex planar drawings of tri-connected graphs to introduce
new boundary constraints. This prevents boundary intersections
and avoids any post-processing of the parameterized mesh. We present
a simple transformation to effectively relax the non-linear constraints,
hence reducing the sparsity of the system matrix, and propose adequate
numerical methods for solving the optimization problem.