Bender: a virtual ribbon for deforming 3D shapes in biomedical and styling applications

In contrast to machined mechanical parts, the 3D shapes encountered in biomedical or styling applications contain many tubular parts, protrusions, engravings, embossings, folds, and smooth bends. It is difficult to design and edit such features using the parameterized operations or even free-form deformations available in CAD or animation systems. The Bender tool proposed here complements previous solutions by allowing a designer holding a 6 DoF 3D tracker in each hand to control the position and orientation of the ends of a stretchable virtual ribbon, which is used to grab the shape in its vicinity and to deform it in realtime, as the designer continues to move, bend, and twist the ribbon. To ensure realtime performance and intuitive control of the ribbon, we model its centerline as a circular biarc and perform adaptive refinement of the triangle-mesh approximation of the surface. To produce a natural and predictable warp, we use the initial and final shapes of the ribbon to define a one-parameter family of screw-motions. The deformation of a surface point is computed by finding its locally closest projection, or projections, on the biarc and by applying the corresponding screws, weighted by a function that decays with the distance to the projection. The combination of these solutions leads to an easy-to-use and effective tool for the direct manipulation of organic or stylized shapes.