  The log-aesthetic curves include the logarithmic (equiangular) spiral,
clothoid, and involute curves. Although most of them are expressed only by an
integral form of the tangent vector, it is possible to interactively generate
and deform them and they are expected to be utilized for practical use of
industrial and graphical design. The discrete log-aesthetic filter based on the
formulation of the log-aesthetic curve has successfully been introduced not to
impose strong constraints on the designer's activity, to let him/her design
freely and to embed the properties of the log-aesthetic curves for complicated
ones with both increasing and decreasing curvature. In this paper, in order to
define the log-aesthetic surface and develop surface filters based on its
formulation, at first we reformulate the log-aesthetic curve with variational
principle. Then we propose several new functionals to be minimized for
free-form surfaces and define the log-aesthetic surface. Furthermore we propose
new discrete surface filters based on the log-aesthetic surface formulation
