Cartoon animation, image warping, and several other tasks in two-dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, ...

The geometry of the Lubin-Tate space of deformations of a formal group is studied via anétale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.

A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact manifold with b2 > 7 admits only finitely many deformation types of holomorphic Lagrangian fibrations.

We present a review of methods for the construction and deformation of character models. We consider both state of the art research and common practice. In particular we review applications, data capture methods, manual model construction, polygonal, parametric and implicit surface representations, basic geometric deformations, free form deformations, subdivision surfaces, displacement map sche...

1. Given a map f :X→Y , show that there exists a map g :Y→X with gf ≃ 1 iff X is a retract of the mapping cylinder Mf . 2. (a) Suppose a CW complex X is the union of a finite number of subcomplexes Xi and that a subcomplex A of X is the union of subcomplexes Ai ⊂ Xi . Show that if each Xi deformation retracts onto Ai and each intersection of a subcollection of the Xi ’s deformation retracts ont...

In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the EulerPoincaré theory. In the metamorphosis of images, the Lie group of diffeomorphisms deforms a template image that is undergoing its own internal dynamics as it deforms. This type of deformation allows more freedom for image matching and has analogies ...

We use shear transformation zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a w...

This paper studies the effect of flexible linear torso on the dynamics of passive quadruped bounding. A reduced-order passive and conservative model with linear flexible torso and springy legs is introduced. The model features extensive spine deformation during high-speed bounding, resembling those observed in a cheetah. Fixed points corresponding to cyclic bounding motions are found and calcul...

A deformation of Einstein Gravity is constructed based on gauging the noncommutative ISO(3, 1) group using the Seiberg-Witten map. The transformation of the star product under diffeomorphism is given, and the action is determined to second order in the deformation parameter.

Let f : Σ1 → Σ2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in Σ1 × Σ2. This article discusses a canonical way to deform f along area preserving diffeomorphisms. This deformation process is realized through the mean curvature flow of the graph of f in Σ1 × Σ2. It is proved that the flow exi...