We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off–diagonal metrics, nonholonomic (non–integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel–Killing and Killing–Yano te...

In these notes we’ll give an introduction to deformation theory and apply it to the special case of abelian schemes. We’ll start by defining the deformation functor and show how the cohomology groups of the sheaf of derivations of a scheme can be used to both determine if deformations exist and if so, what the set of deformations looks like. After that, we’ll introduce the 800 pound gorilla of ...

In this paper, a new free-form shape deformation approach is proposed. We combine a skeleton-based mesh deformation technique with discrete differential coordinates in order to create natural-looking global shape deformations. Given a triangle mesh, we first extract a skeletal mesh, a two-sided Voronoi-based approximation of the medial axis. Next the skeletal mesh is modified by free-form defor...

Freeform curves, surface and solids are generally represented in B-spline basis. Various geometric quantities, such as control points, knots and weights have to be specified. Controlling the shape of an object under complex deformations by manipulating the control points directly is often difficult. The movement of control points gives an indication of the resulting deformation, but being extra...

In this paper, we propose a new and accurate 3D reconstruction technique for the scoliotic spine from a pair planar and conventional radiographic images (postero-anterior and lateral). The proposed model uses a priori hierarchical global knowledge, both on the geometric structure of the whole spine and of each vertebra. More precisely, it relies on the specification of two 3D templates. The fir...

Freeform curves, surface and solids are generally represented in B-spline basis. Various geometric quantities, such as control points, knots and weights have to be specified. Controlling the shape of an object under complex deformations by manipulating the control points directly is often difficult. The movement of control points gives an indication of the resulting deformation, but being extra...

Turbulence-degraded image frames are distorted by both turbulent deformations and space-timevarying blurs. To suppress these effects, we propose a multi-frame reconstruction scheme to recover a latent image from the observed image sequence. Recent approaches are commonly based on registering each frame to a reference image, by which geometric turbulent deformations can be estimated and a sharp ...

This paper develops a general approach for the efficient modeling and animation of non-rigid multibody objects. We develop a new family of physics-based modeling primitives that can undergo free motions as well as parameterized and free-form deformations. Starting with parameterized geometric primitives and adding global geometric deformations, local finite-element deformations, mass distributi...

– Motivated by the periodic ripples observed in bent multi-walled nanotubes, we use macroscopic ideas to derive geometric scaling laws for the wavelength and amplitude of ripples in elastic scrolls and multi-walled tubes. Remarkably, our predictions are essentially independent of material properties, and thus have a range of validity varying from the atomic to the macroscopic even for relativel...

Aeroelastic tailoring requires structural compliance and thus often conflicts with stiffness requirements to carry prescribed aerodynamic loads. Recently however, the application of cellular structural concepts has suggested the potential to achieve compliance while conserving required load-carrying capacity. Among the proposed concepts, a chiral geometry in particular is a novel configuration ...