Fusion of 3D Shapes

Many modeling techniques for geometric objects have been developed; they allow the user to create, deform, animate objects and produce complex ones from simple primitives. This paper presents a new technique which composes two 2D or 3D interpenetrating shapes by creating another one including them and having a smooth aspect. By moving into each other, composed objects fuse smoothly and naturally. To determine the fusion, the technique is based upon a constraint : the resulting shape has the same volume (or area in 2D) as the sum of the components. This technique is available for shapes having a polygonal (in 2D) or a polyhedral (in 3D) description. Inside a modeler, it can be utilized to design modeling and animation tools. We present three of them: a creation tool, an animated deformation tool and a morphing tool which is an adaptation of our technique to this problem. One of the advantages of these tools is that the user may easily guess what will be the result.