  The vast majority of mesh-based modelling applications iteratively transform
the mesh vertices under prescribed geometric conditions. This occurs in
particular in methods cycling through the constraint set such as Position-Based
Dynamics (PBD). A common case is the approximate local area preservation of
triangular 2D meshes under external editing constraints. At the constraint
level, this yields the nonconvex optimal triangle projection under prescribed
area problem, for which there does not currently exist a direct solution
method. In current PBD implementations, the area preservation constraint is
linearised. The solution comes out through the iterations, without a guarantee
of optimality, and the process may fail for degenerate inputs where the
vertices are colinear or colocated. We propose a closed-form solution method
and its numerically robust algebraic implementation. Our method handles
degenerate inputs through a two-case analysis of the problem's generic
ambiguities. We show in a series of experiments in area-based 2D mesh editing
that using optimal projection in place of area constraint linearisation in PBD
speeds up and stabilises convergence.
