Twinned meshes for dynamic triangulation of implicit surfaces

Bouthors, Antoine; Nesme, Matthieu

doi:10.1145/1268517.1268521

Cited by 6 publications

(3 citation statements)

References 32 publications

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“…A different approach, making indirect use of velocities, is to seed the implicit surface with triangulated particles and use normal projection and tangential relaxation to track the particles over time while maintaining triangle quality, e.g. [BN07]. These ideas have been applied with good success in skinning, in which an implicit representation of an animated character's body drives the movement of a textured mesh, e.g.…”

Section: Related Workmentioning

confidence: 99%

Near‐Isometric Level Set Tracking

Tao

Solomon

Butscher

2016

Computer Graphics Forum

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Implicit representations of geometry have found applications in shape modeling, simulation, and other graphics pipelines. These representations, however, do not provide information about the paths of individual points as shapes move and undergo deformation. For this reason, we reconsider the problem of tracking points on level set surfaces, with the goal of designing an algorithm that — unlike previous work — can recover rotational motion and nearly isometric deformation. We track points on level sets of a time‐varying function using approximate Killing vector fields (AKVFs), the velocity fields of near‐isometric motions. To this end, we provide suitable theoretical and discrete constructions for computing AKVFs in a narrow band surrounding an animated level set surface. Furthermore, we propose time integrators well‐suited to integrating AKVFs in time to track points. We demonstrate the theoretical and practical advantages of our proposed algorithms on synthetic and practical tasks.

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Section: Related Workmentioning

confidence: 99%

Near‐Isometric Level Set Tracking

Tao

Solomon

Butscher

2016

Computer Graphics Forum

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“…The first solution was to consider mesh vertices as particles and apply a global optimization scheme in order to maintain their distribution [Witkin and Heckbert 1994]. Other relaxation schemes make use of mass-spring systems [Rodrian and Moock 1996] or of other physically inspired energies [Bouthors and Nesme 2007]. These solutions cannot easily be adapted to our problem, because the relaxation of a particle system would deform the initial skin mesh, which we would like to keep unchanged since it stores geometric details.…”

Section: Implicit Surface Trackingmentioning

confidence: 99%

“…Indeed, the energy E is by construction invariant to translation while the rotation Ri locally cancels rigid transformations. In most applications of this kind of energy, including iso-surface tracking [Bouthors and Nesme 2007], Ri is computed from the polar decomposition of the Jacobian of the unknown deformation. In addition to being an expensive process, this strategy exhibits several drawbacks.…”

Section: Tangential Relaxation Energymentioning

confidence: 99%

Robust iso-surface tracking for interactive character skinning

et al. 2014

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Figure 1: (a) The Jeff model in rest pose. Its shoulders are rotated and skinned with (b) implicit skinning (by Vaillant et al. [2013]) which locally deforms the mesh according to some preset weights and (c) our new technique which automatically produces a plausible skin elasticity (notice how the belly button stretches). On the right, the Dana's knee is bent with an extreme rotation angle. (d) Implicit Skinning fails to handle deep self-intersections while (e) our technique allows large bending angles and the self-intersection at the knee is handled correctly. AbstractWe present a novel approach to interactive character skinning, which is robust to extreme character movements, handles skin contacts and produces the effect of skin elasticity (sliding). Our approach builds on the idea of implicit skinning in which the character is approximated by a 3D scalar field and mesh-vertices are appropriately re-projected. Instead of being bound by an initial skinning solution used to initialize the shape at each time step, we use the skin mesh to directly track iso-surfaces of the field over time. Technical problems are two-fold: firstly, all contact surfaces generated between skin parts should be captured as iso-surfaces of the implicit field; secondly, the tracking method should capture elastic skin effects when the joints bend, and as the character returns to its rest shape, so the skin must follow. Our solutions include: new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem.

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On the velocity of an implicit surface

Stam

Schmidt

2011

ACM Trans. Graph.

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In this article we derive an equation for the velocity of an arbitrary time-evolving implicit surface. Strictly speaking, only the normal component of the velocity is unambiguously defined. This is because an implicit surface does not have a unique parametrization. However, by enforcing a constraint on the evolution of the normal field we obtain a unique tangential component. We apply our formulas to surface tracking and to the problem of computing velocity vectors of a motion blurred blobby surface. Other possible applications are mentioned at the end of the article.

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Twinned meshes for dynamic triangulation of implicit surfaces

Cited by 6 publications

References 32 publications

Near‐Isometric Level Set Tracking

Near‐Isometric Level Set Tracking

Robust iso-surface tracking for interactive character skinning

On the velocity of an implicit surface

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