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Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous…

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…

This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…

Recently, generalizable human Gaussian splatting from sparse-view inputs has been actively studied for the photorealistic human rendering. Most existing methods rely on explicit geometric constraints or predefined structural representations…

This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when…

One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…

While hand pose estimation is a critical component of most interactive extended reality and gesture recognition systems, contemporary approaches are not optimized for computational and memory efficiency. In this paper, we propose a tiny…

Reconstructing and processing the 3D objects are popular activities in the research field of computer graphics, image processing and computer vision. The 3D objects are processed based on the methods like geometric modeling, a branch of…

A fundamental problem in the texturing of 3D meshes using pre-trained text-to-image models is to ensure multi-view consistency. State-of-the-art approaches typically use diffusion models to aggregate multi-view inputs, where common issues…

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…

Geometric priors are often used to enhance 3D reconstruction. With many smartphones featuring low-resolution depth sensors and the prevalence of off-the-shelf monocular geometry estimators, incorporating geometric priors as regularization…

This research proposes a computation approach to address the evaluation of end product machining accuracy in elliptical surfaced helical pipe bending using 6dof parallel manipulator as a pipe bender. The target end product is wearable metal…

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…

Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated…

In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…