Energy Formulations of A-Splines

A-splines are implicit real algebraic curves in Bernstein-Bezier (BB) form that are smooth. We develop a spectrum of physical A-spline curve models using various energy formulations based on the theory of elasticity. Our bending and stretching energy formulations yield interactive physically based modeling with A-splines while preserving the advantages of free-form modeling of complex shapes. Algorithms which find energy-minimizing splines for these formulations are then presented.