Related papers: Controlling Meshes via Curvature: Spin Transformat…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
An extrinsic curvature surface model is investigated by Monte Carlo simulations on a disk. We found that the model undergoes a first-order transition separating the smooth phase from the collapsed phase. The results in this paper together…
Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
Soft materials with layered structure such as membranes, block copolymers, and smectics exhibit intriguing morphologies with nontrivial curvatures. We report on restructuring the Gaussian and mean curvatures of smectic A films with free…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that…
Diffusion MRI (dMRI) is sensitive to microstructural barriers, yet most existing methods either assume impermeable boundaries or estimate voxel-level parameters without recovering explicit interfaces. We present Spinverse, a…
We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…
We consider pattern formation using reaction-diffusion equation on various non-uniformly curved surfaces. We explore how, in general, curvature and, in particular the domain shape would affect the pattern formation in these geometries. As…
Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value…
In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete…
Coordinated cellular movements are key processes in tissue morphogenesis. Using a cell-based modeling approach we study the dynamics of epithelial layers lining surfaces with constant and varying curvature. We demonstrate that extrinsic…
In the realm of 3D computer vision, parametric models have emerged as a ground-breaking methodology for the creation of realistic and expressive 3D avatars. Traditionally, they rely on Principal Component Analysis (PCA), given its ability…
Curvature plays a central role in the proper function of many biological processes. With active matter being a standard framework for understanding many aspects of the physics of life, it is natural to ask what effect curvature has on the…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
In this work, we study theoretical models of \emph{programmable matter} systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or…