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In recent years, an ever-increasing number of remote satellites are orbiting the Earth which streams vast amount of visual data to support a wide range of civil, public and military applications. One of the key information obtained from…

Accurate and dense mapping in large-scale environments is essential for various robot applications. Recently, implicit neural signed distance fields (SDFs) have shown promising advances in this task. However, most existing approaches employ…

With the recent advances in hardware and rendering techniques, 3D models have emerged everywhere in our life. Yet creating 3D shapes is arduous and requires significant professional knowledge. Meanwhile, Deep learning has enabled…

Simplifying polygonal curves at different levels of detail is an important problem with many applications. Existing geometric optimization algorithms are only capable of minimizing the complexity of a simplified curve for a single level of…

Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner --…

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage. When the source data is noisy or…

The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting…

Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field…

The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…

We present a pipeline for parametric wireframe extraction from densely sampled point clouds. Our approach processes a scalar distance field that represents proximity to the nearest sharp feature curve. In intermediate stages, it detects…

We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or…

Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…

We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…

Automatic mesh-based shape generation is of great interest across a wide range of disciplines, from industrial design to gaming, computer graphics and various other forms of digital art. While most traditional methods focus on primitive…

This paper presents a novel post-processing methodology for extracting high-quality geometries from density-based topology optimization results. Current post-processing approaches often struggle to simultaneously achieve smooth boundaries,…

This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…

We propose an algorithm to reconstruct explicit polygonal meshes from discretely sampled Signed Distance Function (SDF) data, which is especially effective at recovering sharp features. Building on the traditional Dual Contouring of Hermite…