ABSTRACT
A partial differential equation (PDE)-based approach might be an alternative way to find a solution to the error problem. The approach to representing surfaces as solutions for PDEs was initially developed in the early 1970s (Thompson et al., 1974). It demonstrated that a wide variety of surface shapes can be made accessible by varying the boundary conditions and parameter in the PDE (Bloor and Wilson, 1989, 1990; Protopopescu et al., 1989). PDE surfaces have demonstrated many modeling advantages in many fields of design such as surface blending, free-form surface modeling, and surface functional specifications (Pasadas and Rodríguez, 2009). The PDE approach has been used in a number of research fields. For instance, sculptured surfaces, ship hulls, and propeller blades were modeled using PDE (Bloor and Wilson, 1996), and PDE application to image analysis has become a research topic of increasing interest over the past few years. A direct map between two cortical surfaces was iteratively computed by solving a PDE defined on the source cortical surface, starting from a properly designed initial map (Shi et al., 2007). Elliptic PDEs have been used to model various kinds of real physical situations such as the flow of air pollutants, temperature deflection, electrostatic potential, velocity potential, and stream function (Modani et al., 2008).
