Related papers: The Antipodal Method: Fast, Accurate, and Robust 3…

We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g.,…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Building good 3D maps is a challenging and expensive task, which requires high-quality sensors and careful, time-consuming scanning. We seek to reduce the cost of building good reconstructions by correcting views of existing low-quality…

We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings.…

We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward…

In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries…

Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…

We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the…

We present a method for fabricating general models with multi-directional 3D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm…

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…

Neural implicit surfaces have become an important technique for multi-view 3D reconstruction but their accuracy remains limited. In this paper, we argue that this comes from the difficulty to learn and render high frequency textures with…

With the emergence of data-driven approaches in science, there is growing interest in their application to manufacturing, particularly in surface precision engineering. However, generating large datasets required for model training is often…

A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element based mean curvature flow algorithm based on a coupled partial differential equation system which…

In this paper, we present a modular robotic system to tackle the problem of generating and performing antipodal robotic grasps for unknown objects from n-channel image of the scene. We propose a novel Generative Residual Convolutional…

A neural implicit outputs a number indicating whether the given query point in space is inside, outside, or on a surface. Many prior works have focused on _latent-encoded_ neural implicits, where a latent vector encoding of a specific shape…

Interfacial Stokes flow can be efficiently computed using the Boundary Integral Equation method. In 3D, the fluid velocity at a target point is given by a 2D surface integral over all interfaces, thus reducing the dimension of the problem.…

Robustness in terms of outliers is an important topic and has been formally studied for a variety of problems in machine learning and computer vision. Generalized median computation is a special instance of consensus learning and a common…