Free Form Deformation with Scattered

Free form deformation has applications in computer animation, in data acquisition , and in computer aided geometric design. One approach is to deform the space in order to induce a deformation of an embedded object. A new method of this class is proposed which is based on scattered data interpolation. The usefulness of two selected classes of scattered data interpolation methods in this context is analyzed, with emphasis on the two-dimensional case. It turns out that suitable scattered data methods do exist, and that the new approach should compete well with more complex, computationally expensive physically based models. Suppose we are given an image of two-dimensional geometric objects. The task is to distort the image irregularly. In the physical world, this goal can be reached by drawing the image on an elastic skin. The elastic skin is deformed by moving some of its points into a new position. This causes a deformation of the image too. In a computer, the elastic skin, the image drawn on it, and the input of the points to be moved can be easily modeled by an interactive program. The user interface of such a program is shown in g. 1. Besides some menus it consists of two neighboring rectangular regions. The left region shows the image before transformation, in the example a digitized cross section of a blossom. If a second image is known which is to be used as a target for the deformation, it can be displayed in the right region. The example in g. 1a shows another cross section of the blossom at a later stage of evolution. By consecutively choosing a point in the left and a point in the right region, pairs of an original point and its image under the deformation to be carried out are deened. This displacement of control points is displayed by dashed lines. The calculation of the deformation is initiated