the exact viewing of a 3D scene in mind. The situation is even worse for computer animation, in which a continuous The through-the-lens camera control technique originally proposed by M. Gleicher and A. Witkin [Comput. Graphics camera motion is often required to generate a smooth 26(2), 1992, 331–340], provides a powerful user interface for scene change. With a poor camera model, the computer t...

We establish a connection between knot theory and cluster algebras via representation theory. To every diagram (or link diagram), we associate algebra by constructing quiver with potential. The rank of the is 2n, where n number crossing points in diagram. then construct 2n indecomposable modules T(i) over Jacobian For each T(i), show that submodule lattice isomorphic to corresponding Kauffman s...

Abstract Let J g be the Jacobian locus and let P +1 Prym locus, in moduli space A of principally polarized abelian varieties dimension , for ≥ 7. We study extrinsic geometry ⊂ under inclusion provided by theory generalized introduced Beauville. More precisely, we address problem if certain geodesic curves, defined with respect to Siegel metric starting at a variety [ JC ] ∈ curve C M direction ...

Robertson in 1988 suggested a model for the realization space of convex d-dimensional polytope and an approach via implicit function theorem, which—in case full rank Jacobian—proves that is manifold dimension NG ( P ) : = d f 0 + ? 1 , . This natural guess given by number variables minus quadratic equations are used definition space. While this indeed holds many classes polytopes (including sim...

Decoupling of multivariate functions is an important problem in block-structured system identification. In the literature, different tensor-based solutions have been proposed to solve this using a canonical polyadic decomposition (CPD) Jacobian tensor. recent work, it has add polynomial constraint on model, which leads constrained CPD model with two factors depending nonlinearly each other. we ...

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the...

We give an explicit rational parameterization of the surface $$\mathcal {H}_3$$ over $${\mathbb Q}$$ whose points parameterize genus 2 curves $$C$$ with full $$\sqrt{3}$$ -level structure on their Jacobian J. use this model to construct abelian surfaces A property that for a positive proportion quadratic twists $$A_d$$ . In fact, $$100\%$$ $$x \in \mathcal {H}_3({\mathbb Q})$$ , holds $$A = {\t...