Related papers: Smooth Surfaces via Nets of Geodesics

Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only…

In this paper, we address the problem of texture representation for 3D shapes for the challenging and underexplored tasks of texture transfer and synthesis. Previous works either apply spherical texture maps which may lead to large…

A projective hypersurface is nodal if it does not have singularities worse than simple nodes. We calculate the rational cohomology of the spaces of equations of nodal cubic and quartic plane curves and also nodal cubic surfaces in the…

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…

A general definition of the curves and geodesics associated with a given connection on a quantized manifold is given. In the particular case of the functional quantization we define geodesics in the same way as in the classical case and we…

We propose a new approach for constructing a 3D representation from a 2D wireframe drawing. A drawing is simply a parallel projection of a 3D object onto a 2D surface; humans are able to recreate mental 3D models from 2D representations…

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…

Network science explores intricate connections among objects, employed in diverse domains like social interactions, fraud detection, and disease spread. Visualization of networks facilitates conceptualizing research questions and forming…

This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…

Humans possess an exceptional ability to imagine 4D scenes, encompassing both motion and 3D geometry, from a single still image. This ability is rooted in our accumulated observations of similar scenes and an intuitive understanding of…

For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…

Designing a network on 3D surface for non-rigid shape analysis is a challenging task. In this work, we propose a novel spectral transform network on 3D surface to learn shape descriptors. The proposed network architecture consists of four…

This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local…

Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…

Point clouds obtained from 3D scans are typically sparse, irregular, and noisy, and required to be consolidated. In this paper, we present the first deep learning based edge-aware technique to facilitate the consolidation of point clouds.…

The emergence of explainability methods has enabled a better comprehension of how deep neural networks operate through concepts that are easily understood and implemented by the end user. While most explainability methods have been designed…

Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision…

We prove that a smooth projective surface of degree $d$ in $\mathbb P^3$ contains at most $d^2(d^2-3d+3)$ lines. We characterize the surfaces containing exactly $d^2(d^2-3d+3)$ lines: these occur only in prime characterize $p$ and, up to…

We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we…

Understanding the 3D structure of a scene is of vital importance, when it comes to developing fully autonomous robots. To this end, we present a novel deep learning based framework that estimates depth, surface normals and surface curvature…