Results 61 to 70 of about 514 (177)

The Pontryagin Forms of Hessian Manifolds [PDF]

, 2016
We show that Hessian manifolds of dimensions 4 and above must have vanishing Pontryagin forms. This gives a topological obstruction to the existence of Hessian metrics. We find an additional explicit curvature identity for Hessian 4-manifolds. By contrast, we show that all analytic Riemannian 2-manifolds are Hessian.
Armstrong, J.; id_orcid 0000-0002-4232-9555, Amari, S.   +1 more
openaire  

Fast Injective Mesh Parameterization via Beltrami Coefficient Prolongation

Computer Graphics Forum, EarlyView.
Abstract We present a highly efficient and robust method for free boundary injective parameterization of disk‐like triangle meshes with low isometric distortion. Harmonic function–based approaches, grounded in a strong mathematical framework, are widely employed.
G. Fargion, O. Weber
wiley   +1 more source

Interpolated Adaptive Linear Reduced Order Modeling for Deformation Dynamics

Computer Graphics Forum, EarlyView.
Abstract Linear reduced‐order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that allows the reduced mapping to vary dynamically in response to the evolving deformation state ...
Y. Tao, M. Chiaramonte, P. Fernandez
wiley   +1 more source

Affinification: A Fine Approximation of Deformations

Computer Graphics Forum, EarlyView.
Abstract We introduce affinification, a novel method for accelerating physics‐based animation of elastic solids. During a time‐dependent simulation, our method automatically partitions the space into affine and elastic regions depending on the deformation.
A. Mercier‐Aubin, T. Schneider, P.G. Kry, S. Andrews   +3 more
wiley   +1 more source

Progressively Projected Newton's Method

Computer Graphics Forum, EarlyView.
Abstract Newton's Method is widely used to find the solution of complex non‐linear simulation problems. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to assembly—a strategy known as Projected Newton (PN)—but this perturbation often hinders convergence.
J. A. Fernández‐Fernández, F. Löschner, J. Bender   +2 more
wiley   +1 more source

Survey on differential estimators for 3d point clouds

Computer Graphics Forum, EarlyView.
Abstract Recent advancements in 3D scanning technologies, including LiDAR and photogrammetry, have enabled the precise digital replication of real‐world objects. These methods are widely used in fields such as GIS, robotics, and cultural heritage. However, the point clouds generated by such scans are often noisy and unstructured, posing challenges for ...
Léo Arnal–Anger, Thibault Lejemble, David Coeurjolly, Loïc Barthe, Nicolas Mellado   +4 more
wiley   +1 more source

Local solvability of degenerate Monge-Ampere equations and applications to geometry

Electronic Journal of Differential Equations, 2007
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in $mathbb{R}^{3}$, and the local
Marcus A. Khuri
doaj  

The derivation of phase-space metric in a geometric quantization approach: General relativity with quantized phase-space metric and relative spacetime

Nuclear Physics B
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static) spacetime ...
Kareem Mubaidin, Debarshi Mukherjee, Saleh O. Allehabi, Azzah A. Alshehri, Mahmoud Nasar, Ashraf F. El-Sherif, Abdel Nasser Tawfik   +6 more
doaj   +1 more source

Establishing Shape Correspondences: A Survey

Computer Graphics Forum, EarlyView.
Abstract Shape correspondence between surfaces in 3D is a central problem in geometry processing, concerned with establishing meaningful relations between surfaces. While all correspondence problems share this goal, specific formulations can differ significantly: Downstream applications require certain properties that correspondences must satisfy ...
A. Heuschling, H. Meinhold, L. Kobbelt
wiley   +1 more source

Projective Vector Fields on Semi-Riemannian Manifolds

Mathematics
This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector ...
Norah Alshehri, Mohammed Guediri
doaj   +1 more source