Twister: A Space-warp Operator for the Two-handed Editing of 3D Shapes

A free-form deformation that warps a surface or solid may be spec- ied in terms of one or several point-displacement constraints that must be interpolated by the deformation. The Twister approach in- troduced here, adds the capability to impose an orientation change, adding three rotational constraints, at each displaced point. Further- more, it solves for a space warp that simultaneously interpolates two sets of such displacement and orientation constraints. With a 6 DoF magnetic tracker in each hand, the user may grab two points on or near the surface of an object and simultaneously drag them to new locations while rotating the trackers to tilt, bend, or twist the shape near the displaced points. Using a new formalism based on a weighted average of screw displacements, Twister computes in realtime a smooth deformation, whose effect decays with distance from the grabbed points, simultaneously interpolating the 12 con- straints. It is continuously applied to the shape, providing realtime graphic feedback. The two-hand interface and the resulting defor- mation are intuitive and hence offer an effective direct manipulation tool for creating or modifying 3D shapes.