Energy formulations of A-splines Original Research Article

A-splines are implicit real algebraic curves in Bernstein-Bézier (BB) form that are smooth. We develop A-spline curve models using various energy formulations, incorporating bending and stretching energy, based on the theory of elasticity. The attempt to find true energy minimizing curves usually leads to complicated integrals which can only be solved numerically, we introduce a simplified energy formulation which is much faster to compute yet still provides reasonably accurate results. Several examples for C1-continuous quadratic A-splines using the true and simplified energy models are then presented.