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Rossignac,
Jarek
Rossignac,
Jarek
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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.

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 longlasting 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.

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 firstorder upwind or semiLagrangian integration of advection equations. It provides secondorder 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.

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 semiLagrangian 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 twophase 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.

ItemLocalized biLaplacian Solver on a Triangle Mesh and Its Applications(Georgia Institute of Technology, 2004) Kim, Byungmoon ; Rossignac, JarekPartial differential equations(PDE) defined over a surface are used in various graphics applications, such as mesh fairing, smoothing, surface editing, and simulation. Often these applications involve PDEs with Laplacian or biLaplacian terms. We propose a new approach to a finite element method for solving these PDEs that works directly on the triangle mesh connectivity graph that has more connectivity information than the sparse matrix. Thanks to these extra information in the triangle mesh, the solver can be restricted to operate on a subdomain, which is a portion of the surface defined by user or automatically selfadjusting. Our formulation permits us to solve high order terms such as biLaplacian by using a simple linear triangle element. We demonstrate the benefits of our approach on two applications: scattered data interpolation over a triangle mesh(painting), and haptic interaction with a deformable surface.

ItemCollision Prediction for Polyhedra under Screw Motions(Georgia Institute of Technology, 2003) Kim, Byungmoon ; Rossignac, JarekThe prediction of collisions amongst N rigid objects may be reduced to a series of computations of the time to first contact for all pairs of objects. Simple enclosing bounds and hierarchical partitions of the spacetime domain are often used to avoid testing objectpairs that clearly will not collide. When the remaining pairs involve only polyhedra under straightline translation, the exact computation of the collision time and of the contacts requires only solving for intersections between linear geometries. When a pair is subject to a more general relative motion, such a direct collision prediction calculation may be intractable. The popular brute force collision detection strategy of executing the motion for a series of small time steps and of checking for static interferences after each step is often computationally prohibitive. We propose instead a less expensive collision prediction strategy, where we approximate the relative motion between pairs of objects by a sequence of screw motion segments, each defined by the relative position and orientation of the two objects at the beginning and at the end of the segment. We reduce the computation of the exact collision time and of the corresponding face/vertex and edge/edge collision points to the numeric extraction of the roots of simple univariate analytic functions. Furthermore, we propose a series of simple rejection tests, which exploit the particularity of the screw motion to immediately decide that some objects do not collide or to speedup the prediction of collisions by about 30%, avoiding on average 3/4 of the rootfinding queries even when the object actually collide.

ItemFinger Sculpting with Digital Clay: 3D Shape Input and Output through a ComputerControlled Real Surface(Georgia Institute of Technology, 2003) Book, Wayne J. ; Glezer, Ari ; EbertUphoff, 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 computercontrolled 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.

ItemTwister: A SpaceWarp Operator for the TwoHanded Editing of 3D Shapes(Georgia Institute of Technology, 2003) Llamas, Ignacio ; Kim, Byungmoon ; Gargus, Joshua ; Rossignac, Jarek ; Shaw, Christopher D.A freeform deformation that warps a surface or solid may be specified in terms of one or several pointdisplacement 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 twohand 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(Georgia Institute of Technology, 2002) Gargus, Joshua ; Kim, Byungmoon ; Rossignac, Jarek ; Shaw, Christopher D."Digital Clay" is a term that signifies a computercontrolled physical surface, capable of taking any of a wide variety of possible shapes in response to changes in a digital 3D model or changes in the pressure exerted upon it by bare hands. The physical properties of such a device impose design and userinterface constraints not encountered in traditional, trackerbased software for the manipulation of virtual models. This paper describes the interaction techniques we have developed to work with this future medium. In particular, we present our solution for tracking the user's fingers using a local deformation of the surface, which we call a "blister", that senses the tangential and normal displacements of the finger. We also present a solution for creating variableheight bosses and creases with the simple sweep of a finger. Since the Digital Clay hardware is not yet operational, we have implemented a haptic simulation framework based on a PHANTOM device.