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Reducing the triangle count in complex 3D models is a basic geometry preprocessing step in graphics pipelines such as efficient rendering and interactive editing. However, most existing mesh simplification methods exhibit a few issues.…
In this work, we focus on synthesizing high-quality textures on 3D meshes. We present Point-UV diffusion, a coarse-to-fine pipeline that marries the denoising diffusion model with UV mapping to generate 3D consistent and high-quality…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Solving image inverse problems (e.g., super-resolution and inpainting) requires generating a high fidelity image that matches the given input (the low-resolution image or the masked image). By using the input image as guidance, we can…
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…
Given a 3D mesh with a UV parameterization, we introduce a novel approach to generating textures from text prompts. While prior work uses optimization from Text-to-Image Diffusion models to generate textures and geometry, this is slow and…
We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Generating visual instructions in a given context is essential for developing interactive world simulators. While prior works address this problem through either text-guided image manipulation or video prediction, these tasks are typically…
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include…
Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional…
We present a new meshing algorithm called guided and augmented meshing, GAMesh, which uses a mesh prior to generate a surface for the output points of a point network. By projecting the output points onto this prior and simplifying the…
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…