Deformations of Dubrovin’s Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters where g is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of solutions to the Painlevé-VI equation with coefficients (1/8,−1/8, 1/8, 3/8) . A...

In the absence of contact, several solutions have been proposed for skin deformations. In his hand animation system MOP, Catmull proposed a hand envelop made up of polygons in 1972 (5), spheres and B-splines were proposed by Badler and Morris in 1981 for hand deformations (6), Bézier surfaces were used by Komatsu for arm deformations (7), Magnenat-Thalmann et al. (8) used operators which are ad...

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on σ-derivations. We show that σ-twisted Jacobi type identity holds for generators of such deformations. For the σ-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie ...

Deformations of the structure constants for a class of associative noncommutative algebras generated by Deformation Driving Algebras (DDA’s) are defined and studied. These deformations are governed by the Central System (CS). Such a CS is studied for the case of DDA being the algebra of shifts. Concrete examples of deformations for the three-dimensional algebra governed by discrete and mixed co...

The neoclassical model of Sm-C (and Sm-C*) elastomers developed by Warner and Adams predicts a class of "soft" (zero energy) deformations. We find and describe the full set of stripe domains-laminate structures in which the laminates alternate between two different deformations-that can form between pairs of these soft deformations. All the stripe domains fall into two classes, one in which the...

It is established that there exists an intimate connection between isometric deformations of polyhedral surfaces and discrete integrable systems. In particular, Sauer’s kinematic approach is adopted to show that second-order infinitesimal isometric deformations of discrete surfaces composed of planar quadrilaterals (discrete conjugate nets) are determined by the solutions of an integrable discr...

Contact with objects and the environment will cause complex deformations in soft hands. While the space of possible deformations of soft hands is very large due to their flexible materials, deformations that actually occur during contact interactions are much more limited. We use this knowledge to add sensors that measure task-relevant deformations. This demo presents the Sensorized RBO Hand 2,...

This paper describes a new technique to incorporate accurate mechanical deformations of soft tissue into interactive training simulators designed to teach medical procedures. The technique is based on pre-computing a representative set of deformations accurately, then encoding these using principal component analysis such that they can be reconstructed quickly using a small number of shape para...

Simulated deformations and images can act as the gold standard for evaluating various template-based image segmentation and registration algorithms. Traditional deformable simulation methods, such as the use of analytic deformation fields or the displacement of landmarks followed by some form of interpolation, are often unable to construct rich (complex) and/or realistic deformations of anatomi...

Statistical shape models (SSM) capture the variation of shape across a population, in order to allow further analysis. Previous work demonstrates that deformation fields contain global transformation components, even if global preregistration is performed. It is crucial to construction of SSMs to remove these global transformation components from the local deformations thus obtaining minimal de...