Advections with Significantly Reduced Dissipation and Diffusion

Kim, B.; Liu, Y.; Llamas, Ignacio; Rossignac, Jarek

doi:10.1109/tvcg.2007.3

Cited by 86 publications

(55 citation statements)

References 36 publications

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“…The methods of a two-dimensional semidry painting and ink diffusion based on the force feedback are also presented in our previous papers [17,18]. In the painting process of virtual 3D, the preset value and corresponding parameters of rice paper fiber model are determined according to the 3D product exterior property, and then the half-dry stroke and the ink diffusion on 3D product exterior (useful out of shape) are simulated by the mapping of 2D half-dry stroke and ink diffusion, respectively, which support designers to catch design inspiration.…”

Section: The Formation Of 3d Brush Strokementioning

confidence: 99%

Haptic Decorating on the Surface of Virtual Clay Model

Huang¹,

Zeng-xuan²,

Guo³

et al. 2018

Mathematical Problems in Engineering

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A novel haptic decorating method on the surface of virtual clay model is proposed. The relationship between brush deformation and endured force is researched for the first time by applying the spring-mass model to construct the 3D brush model. Then, the collision detection between virtual hairy brush and virtual clay model is researched based on collision algorithm of weighted average distance. When the hairy brush initially collides with 3D exterior, the tactility is simulated and the interactive virtual painting on the 3D exterior is carried out practically. The 3D brush stroke is formed by superimposing 3D brush footprints along the painting direction and controlling the stress of the brush. The ink quantity in the brush footprint is determined according to the proposed positive correlation between the exerted pressure on brush and outflow ink quantity of the brush. A painting storage method is also presented for storing and displaying 3D stroke painting results. The proposed method has been successfully applied in the 3D virtual painting system based on real-time force feedback technology. With this system, the 3D brush strokes with 3D half-dry and ink diffusion results can be painted with a Phantom Desktop haptic device, which effectively enhance reality to users.

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Section: The Formation Of 3d Brush Strokementioning

confidence: 99%

Haptic Decorating on the Surface of Virtual Clay Model

Huang¹,

Zeng-xuan²,

Guo³

et al. 2018

Mathematical Problems in Engineering

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“…Unlike the momentum update, where the pressure itself acts as a momentum flux and the result of the projection does conserve momentum, for kinetic energy we not only don't have good values for the flux p u in Equation (18), but the resulting post-velocity projection does not have the same kinetic energy as the pre-projected velocity. Indeed, the change in kinetic energy due to the projection is…”

Section: Projectionmentioning

confidence: 98%

“…The simplicity of these schemes makes them quite useful for adaptive grids and other data structures, see for example [7,31,30,47,16]. Recently, authors have considered using semi-Lagrangian methods as building blocks in other schemes, for example [17,18,6] showed that the second order accurate BFECC method of [5] can be made unconditionally stable using the first order accurate semiLagrangian method as a building block. In addition, [44] showed that the original scheme of MacCormack [36] can be made unconditionally stable in a similar way.…”

Section: Introductionmentioning

confidence: 99%

An unconditionally stable fully conservative semi-Lagrangian method

Lentine

Gretarsson

Fedkiw

2011

Journal of Computational Physics

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Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.

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“…This can be achieved by nonlinear numerical discretizations, e.g., using flux limiters [18], essentially nonoscillatory schemes [16], or schemes aiming at a diffusion reduction [30,17], but may not always be necessary as shown in Sec. 7.…”

Section: Numerical Considerationsmentioning

confidence: 99%

An optimal control approach for deformable registration

Hart¹,

Zach²,

Niethammer³

2009

2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops

119

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This paper addresses large-displacement-diffeomorphic mapping registration from an optimal control perspective. This viewpoint leads to two complementary formulations. One approach requires the explicit computation of coordinate maps, whereas the other is formulated strictly in the image domain (thus making it also applicable to manifolds which require multiple coordinate charts). We discuss their intrinsic relation as well as the advantages and disadvantages of the two approaches. Further, we propose a novel formulation for unbiased image registration, which naturally extends to the case of time-series of images. We discuss numerical implementation details and carefully evaluate the properties of the alternative algorithms.

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Advections with Significantly Reduced Dissipation and Diffusion

Cited by 86 publications

References 36 publications

Haptic Decorating on the Surface of Virtual Clay Model

Haptic Decorating on the Surface of Virtual Clay Model

An unconditionally stable fully conservative semi-Lagrangian method

An optimal control approach for deformable registration

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