Modeling and deformation of surfaces defined over finite elements

The dominant approach to free form surface modeling is to use a control mesh to manipulate a B-spline or other tensor product surface. This method is powerful but doesn´t provide a way to control the surface´s global properties. Moreover high level constraints such as normals or curves are difficult to enforce. In this article we propose a new deformable surface model that provides better control over obtained shapes. The finite element method is applied to C² triangular elements that minimize a surface energy function. The shape can be sculpted interactively with user defined constraints (points, normals and curves) and forces (springs, pressure or gravity for example). We present the mathematical foundation as well as several examples showing possible applications of this tool.