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ItemSimulation of Bubbles in Foam With The Volume Control Method(Georgia Institute of Technology, 2007) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Jiao, Xiangmin ; Rossignac, JarekLiquid 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.
ItemAdvections with Significantly Reduced Dissipation and Diffusion(Georgia Institute of Technology, 2006) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, JarekBack and Forth Error Compensation and Correction (BFECC) can be applied to reduce dissipation and diffusion in advection steps, such as velocity, smoke density, and image advections. It 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 and reduces volume loss significantly. We demonstrate its benefits on the simulation of smoke, bubbles, and interaction between water, a solid, and air.
ItemSimulation of Bubbles and Liquid Films(Georgia Institute of Technology, 2006) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, JarekLiquid and gas interactions often contain bubbles surrounded by thin liquid films. Simulation of these liquid films is challenging since they quickly become thinner than the grid resolution, which leads to premature bursting or merging of the bubbles. We prevent this thinning process by applying a disjoining force to the film, obtaining bubbles that last much longer without bursting or merging. The surface tension on the liquid film is the next diffuculty. Since the level set is not differentiable at the center of the thin liquid film, the curvature computed from the level set gradient is noisy, and the thin liquid film ruptures quickly. To prevent this, we compute the surface tension from the local isosurface, obtaining long-lasting liquid films. However, since bubbles stay longer without bursting or merging, the volume loss of each bubble is noticeable. To solve this problem, we modify the pressure projection to produce a velocity field whose divergence is controlled by the proportional and integral feedback. This allows us to preserve the volume or, if desired, to inflate or deflate the bubbles. In addition to premature bursting and volume change, another difficulty is the complicated liquid surface, which increases memory and computational costs. To reduce storage requirement, we collocate the velocity and pressure to simplify the octree mesh. To reduce the computational complexity of the pressure projection, we use a multigrid method.
ItemFlowFixer: Using BFECC for Fluid Simulation(Georgia Institute of Technology, 2005) Kim, Byungmoon ; Liu, Yingjie ; Llamas, Ignacio ; Rossignac, JarekBack and Forth Error Compensation and Correction (BFECC) was recently developed for interface computation by using the level set method. We show that it can be applied to reduce dissipation and diffusion encountered in various advection steps in fluid simulation such as velocity, smoke density and image advections. BFECC can be implemented easily on top of the first order upwinding or semi-Lagrangian integration of advection equations, while providing second order accuracy both in space and time. When applied to level set evolution, BFECC reduces volume loss significantly. We combine these techniques with variable density projection and show that they yield a realistic animations of two-phase flows. We demonstrate the benefits of this approach on the image advection and on the simulation of smoke, of bubbles in water, and of a highly dynamic interaction between water, a solid, and air.
ItemBender: A Virtual Ribbon for Deforming 3D Shapes in Biomedical and Styling Applications(Georgia Institute of Technology, 2004) Llamas, Ignacio ; Powell, Alexander ; Rossignac, Jarek ; Shaw, Christopher D.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.
ItemDeforming 3D Shapes by Bending and Twisting a Virtual Ribbon with Both Hands(Georgia Institute of Technology, 2004) Llamas, Ignacio ; Powell, Alexander ; Rossignac, Jarek ; Shaw, Christopher D.Bender is an interactive tool for bending and warping triangulated surfaces. The designer uses a virtual ribbon to grab a portion of the shape and to deform it through direct manipulation. The ribbon is defined by its centerline-a wire made of two smoothly joined circular arcs-and by its twist-the continuous field of normal directions along the wire. The wire and the twist are controlled by a Polhemus tracker in each hand. The deformation model is based on a new formulation of a 3D space warp that uses screw-motions to map coordinate systems aligned with the initial ribbon to corresponding coordinate systems aligned with the final ribbon. Circular biarcs are easy to control and permit the correct handling of situations where a vertex is influenced by different sections of the wire. Screw-motions define smoother and more intuitive warps than other formulations. The combination significantly extends the editing capabilities of previously proposed shape deformation tools and produces smooth and predictable results for configurations where the radius of the tubular region of influence around the ribbon does not exceed the radii of the arcs.
ItemTwister: A Space-Warp Operator for the Two-Handed Editing of 3D Shapes(Georgia Institute of Technology, 2003) Llamas, Ignacio ; Kim, Byungmoon ; Gargus, Joshua ; Rossignac, Jarek ; Shaw, Christopher D.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.
ItemFinger Sculpting with Digital Clay: 3D Shape Input and Output through a Computer-Controlled Real Surface(Georgia Institute of Technology, 2003) Book, Wayne J. ; Glezer, Ari ; Ebert-Uphoff, Imme ; Shaw, Christopher D. ; Rossignac, Jarek ; Allen, Mark G. ; Rosen, David W. ; Askins, Stephen Alexander ; Bai, Jing ; Bosscher, Paul Michael ; Gargus, Joshua ; Kim, Byungmoon ; Llamas, Ignacio ; Nguyen, Austina Nga ; Yuan, Guang ; Zhu, HaihongThe 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.