Related papers: Simplification of Multi-Scale Geometry using Adapt…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
This paper presents a new mesh segmentation method that integrates geometrical and topological features through a flexible Reeb graph representation. The algorithm consists of three phases: construction of the Reeb graph using the improved…
Recently, deep generative adversarial networks for image generation have advanced rapidly; yet, only a small amount of research has focused on generative models for irregular structures, particularly meshes. Nonetheless, mesh generation and…
This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…
Conventional production workflow of high-precision mesh assets necessitates a cumbersome and laborious process of manual sculpting by specialized 3D artists/modelers. The recent years have witnessed remarkable advances in AI-empowered 3D…
The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical…
Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the…
Point cloud surface reconstruction has improved in accuracy with advances in deep learning, enabling applications such as infrastructure inspection. Recent approaches that reconstruct from small local regions rather than entire point clouds…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
A new topography adapted mesh generation process tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and minimum surface mesh size, the size of the…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field…
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions…
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We consider the problem of extracting curve skeletons of three-dimensional, elongated objects given a noisy surface, which has applications in agricultural contexts such as extracting the branching structure of plants. We describe an…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…