Related papers: Controlling Meshes via Curvature: Spin Transformat…
We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers,…
In this paper, we explore the evolution of plane curves and surfaces governed by the hyperbolic mean curvature flow. We propose a mesh-free approach based on the physics-informed neural networks (PINNs), which eliminates the need for…
Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
We study the mean curvature flow of smooth $m$-dimensional compact submanifolds with quadratic pinching in the Riemannian manifold $\mathbb{C}P^n$. Our main focus is on the case of high codimension, $k\geq 2$. We establish a codimension…
We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from…
This paper deals with flow-induced shape transitions of elastic capsules. The state of the art concerning both theory and experiments is briefly reviewed starting with dynamically induced small deformation of initially spherical capsules…
Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multipoint stress…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however,…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
In this paper we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms. Particularly, we prove that the mean curvature flow deforms a closed submanifold satisfying a…
The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is…
The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…