Deformation

Abstract

In the continuous model of a solid object, which is ideally considered composed of such material points that each one of them is surrounded by a dense neighbourhood fully occupied by other points, the deformation is a variation carried out by a transformation, which does not preserve isometry. Deformations differ from displacements caused by rigid motions. For a closed boundary curve in the three-dimensional space, Plateau wondered what surfaces would minimize the potential surface energy. Deformation was held to underlie the evolution of biological forms, described by the “Cartesian transformations”, or the interpolation function of landmarks covariation over a thin-plate spline, the perception of depth, plastic arts, and art expression.