Related papers: Surface Approximation via Asymptotic Optimal Geome…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
We study partitions on three dimensional manifolds which minimize the total geodesic perimeter. We propose a relaxed framework based on a $\Gamma$-convergence result and we show some numerical results. We compare our results to those…
We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues over a given number of partitions of a surface. We consider…
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…
The concern of this work is the generalization of an Asymptotic Preserving method for the highly anisotropic elliptic equations presented in [P. Degond, A. Lozinski, J. Narski, and C. Negulescu. An asymptotic-preserving method for highly…
We propose a novel method for parameterizations of triangle meshes by finding an optimal quasiconformal map that minimizes an energy consisting of a relative entropy term and a quasiconformal term. By prescribing a prior probability measure…
We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
Normal integration reconstructs 3D surfaces from normal maps obtained e.g. by photometric stereo. These normal maps capture surface details down to the pixel level but require large computational resources for integration at high…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…
A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an…
We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…