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Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…
The growing need for creating surfaces with specific wetting properties, such as superhyrdophobic behavior, asks for novel methods for their efficient design. In this work, a fast computational method for the evaluation of patterned…
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant…
We present a new method to bake classical facial animation blendshapes into a fast linear blend skinning representation. Previous work explored skinning decomposition methods that approximate general animated meshes using a dense set of…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…
Cutting thin-walled deformable structures is common in daily life, but poses significant challenges for simulation due to the introduced spatial discontinuities. Traditional methods rely on mesh-based domain representations, which require…
3D Gaussian Splatting (3DGS) has recently unlocked real-time, high-fidelity novel view synthesis by representing scenes using explicit 3D primitives. However, traditional methods often require millions of Gaussians to capture complex…
Closed queuing networks with finite capacity buffers and skip-over policies are fundamental models in the performance evaluation of computer and communication systems. This technical report presents the details of computational algorithms…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven…
In this paper, we present an advanced approach to solving the inverse rig problem in blendshape animation, using high-quality corrective blendshapes. Our algorithm introduces novel enhancements in three key areas: ensuring high data…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
3D representations of highly deformable 3D models, such as dynamic 3D meshes, have recently become very popular due to their wide applicability in various domains. This trend inevitably leads to a demand for storage and transmission of…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…