Related papers: Meshing of High-Dimensional Toroidal Manifolds fro…
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…
Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincar\'e maps to search for a suitable path through the interconnected web of periodic…
The automatic semantic segmentation of the huge amount of acquired remote sensing data has become an important task in the last decade. Images and Point Clouds (PCs) are fundamental data representations, particularly in urban mapping…
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most…
Existing 3D mask learning methods encounter performance bottlenecks under limited data, and our objective is to overcome this limitation. In this paper, we introduce a triple point masking scheme, named TPM, which serves as a scalable…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…
Existing learning-based methods for point cloud rendering adopt various 3D representations and feature querying mechanisms to alleviate the sparsity problem of point clouds. However, artifacts still appear in rendered images, due to the…
A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply…
When the planar circular restricted 3-body problem (PCRTBP) is periodically perturbed, as occurs in many useful astrodynamics models, most unstable periodic orbits persist as whiskered tori. Intersections between stable and unstable…
The matching of 3D shapes has been extensively studied for shapes represented as surface meshes, as well as for shapes represented as point clouds. While point clouds are a common representation of raw real-world 3D data (e.g. from laser…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
This paper employs an alternate dynamical model of the circular restricted three body problem to quantify uncertainties associated with spacecraft thrusting maneuvers. A non-product quadrature scheme known as Conjugate Unscented Transform…
In the preliminary design of space missions it can be useful to identify regions of dynamics that drive the system's behaviour or separate qualitatively different dynamics. The Lagrangian Coherent Structure (LCS) has been widely used in the…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…
Current 3D representations like meshes, voxels, point clouds, and NeRF-based neural implicit fields exhibit significant limitations: they are often task-specific, lacking universal applicability across reconstruction, generation, editing,…
We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations,…