Space Deformation Based On Free-Form Surfaces

Space deformation has been widely applied to geometric modeling and computer animation. Many space deformation methods have been proposed since 1980's. How to achieve efficient and intuitive deformation control is the important topic in space deformation research.A new space deformation based on free-form surfaces is presented in this paper. The object deformation is controlled by a control mesh of arbitrary topology. First the control mesh is refined twice by using subdivision rules such as Doo-Sabin subdivision, Catmull-Clark subdivision. Then the refined control mesh is transformed into control polygons of Bézier surfaces or B-spline surfaces. At a point of the free-form surface, the tangents and its normal span an intermediate deformation space. The object is embedded into the deformation space by the nearest point rule. When the shape of the control mesh is changed, the object embedded in the intermediate deformation space will be deformed accordingly. Because the free-form surfaces are at least tangent continuous globally, i.e. G~1 continuous, the deformation space spanned is also smooth. Thus the deformed object is smoother than that deformed by a subdivision surface. Since the subdivision surface has local property, if a few vertexes of the control mesh are modified, only part of the subdivision surface is influenced and changed accordingly. As a result, only part of the free-form surfaces need to be updated according to the smooth surface generation algorithms. Only the points of the object attached to the updated surfaces need to be recalculated. Thus local deformation is achieved which is very efficient.A space deformation system is realized based on the proposed method. In our system, the deformations based on subdivision surface and free-form surfaces are comparied. Secondly, deformations based on Doo-Sabin subdivision surface and Catmull-Clark subdivision surface are also compared. The implementation results show that the proposed method inherit the flexibility and simplicity of the space deformation method based on subdivision surface. Furthermore the deformationresults are G1 smooth instead of G° smooth.