Free-Form Deformation of Solid Models in CSR

Abstract

Existing free-form deformation (FFD) techniques deform an object by deforming the space enclosing the object. Points on the object are thus deformed relative to the undeformed space (or world space). The deformed object is visualized by sampling points on the object surfaces, or by approximating the object with a polyhedral model. This provides good visual effect for the deformed objects. However, the deformed solid is represented in terms of the lattice of the FFD and the undeformed solid. There is no precise explicit representation of the deformed object so that existing solid modeling techniques, such as Boolean operations, on the deformed object may not be applied. This paper is concerned with the techniques of applying free-form deformation on solid models represented by the Constructive Shell Representation (CSR). By applying free-form deformation on the surface points of the trunctets of a CSR object so that the vertices and the quadric patch polynomial of the trunctets are changed, the shape of the object can be modified. This technique can be used to deform globally smooth solid models or general solid models with sharp edges. The deformation can be applied either globally or locally. Techniques for the deformation are discussed in detail. Experiments are conducted and the results are also presented.