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We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is…
We present a model for computing the surface force density on a fluid ellipsoid in simple shear flow, which we derive by coupling existing models for the shape of a fluid droplet and the surface force density on a solid ellipsoid. The…
With the recent development of high-end LiDARs, more and more systems are able to continuously map the environment while moving and producing spatially redundant information. However, none of the previous approaches were able to effectively…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds.…
3D Gaussian Splatting (3DGS) represents a significant advancement in the field of efficient and high-fidelity novel view synthesis. Despite recent progress, achieving accurate geometric reconstruction under sparse-view conditions remains a…
Multi-view 3D surface reconstruction using neural implicit representations has made notable progress by modeling the geometry and view-dependent radiance fields within a unified framework. However, their effectiveness in reconstructing…
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero…
In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
We propose DeMapGS, a structured Gaussian Splatting framework that jointly optimizes deformable surfaces and surface-attached 2D Gaussian splats. By anchoring splats to a deformable template mesh, our method overcomes topological…
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.…