With The Geometric Constraints Of The Space Deformation Method

In geometric modeling, the manipulation of objects may need complex operations such as compress, expand or twist a part of an object. Such operations are useful to form complex shapes or to simulate the behavior of an object. For example, during a stretch and a bump. Several deformation models propose intuitive methods to define these kinds of free form operations. In these skills, Free-form deformation and Space deformation techniques are powerful tools which could manipulate and animate objects. A lot of extensions of these techniques allow user to intuitively deform objects. But none of these propose a solution to preserve the volume of objects or to preserve the area of geometric figure throughout the deformation. In this paper, we introduce free form deformation in details and we also introduce a new method to deform an object or to deform a figure, its volume or its area being preserved. Our method is based on the space deformation model called DOGME. We use a distinctive feature of DOGME to solve the problem of volume preservation or area preservation. In the paper, we apply the method to the polyhedral figure and the result is good.