Liquid and gas interactions often produce bubbles that stay for a long time without bursting on the surface, making a dry foam structure. Such long lasting bubbles simulated by the level set method can suffer from a small but steady volume error that accumulates to a visible amount of volume change. We propose to address this problem by using the volume control method. We track the volume change of each connected region, and apply a carefully computed divergence that compensates undesired volume changes. To compute the divergence, we construct a mathematical model of the volume change, choose control strategies that regulate the modeled volume error, and establish methods to compute the control gains that provide robust and fast reduction of the volume error, and (if desired) the control of how the volume changes over time.

Back and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation using a level set method. We show that BFECC can be applied to reduce dissipation and diffusion encountered in a variety of advection steps, such as velocity, smoke density, and image advections on uniform and adaptive grids and on a triangulated surface. BFECC can be implemented trivially as a small modification of the first-order upwind or semi-Lagrangian integration of advection equations. It provides second-order accuracy in both space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We demonstrate the benefits of this approach on image advection and on the simulation of smoke, bubbles in water, and the highly dynamic interaction between water, a solid, and air. We also apply BFECC to dye advection to visualize vector fields.

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.

The NSF Digital Clay project is focused on the design, prototyping, integration, and validation of a computer-controlled physical device capable of taking any of a wide range of possible shapes in response to changes in a digital 3D model or to changes in the pressure exercised upon it by human hands. Although it clearly is a natural and unavoidable evolution of 3D graphical user interfaces, its unprecedented capabilities constitute a major leap in technologies and paradigms for 3D display, for 3D input, and for collaborative 3D design. In this paper, we provide an overview of the Digital Clay project and discuss the challenges, design choices, and initial solutions for a new finger sculpting interface designed for the Digital Clay and prototyped using conventional 3D I/O hardware.

A free-form deformation that warps a surface or solid may be specified in terms of one or several point-displacement constraints that must be interpolated by the deformation. The Twister approach introduced here, adds the capability to impose an orientation change, adding three rotational constraints, at each displaced point. Furthermore, 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 constraints. It is continuously applied to the shape, providing realtime graphic feedback. The two-hand interface and the resulting deformation are intuitive and hence offer an effective direct manipulation tool for creating or modifying 3D shapes.