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3D Gaussian Splatting (3DGS) combines classic image-based rendering, pointbased graphics, and modern differentiable techniques, and offers an interesting alternative to traditional physically-based rendering. 3DGS-family models are far from…
Outdoor intelligent autonomous robotic operation relies on a sufficiently expressive map of the environment. Classical geometric mapping methods retain essential structural environment information, but lack a semantic understanding and…
This paper proposes a novel model fitting algorithm for 3D facial expression reconstruction from a single image. Face expression reconstruction from a single image is a challenging task in computer vision. Most state-of-the-art methods fit…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
Providing dry solid contacts with on-demand macroscale frictional behaviour remains a formidable challenge in tribology, haptics or robotics. Metainterfaces created from surfaces with engineered asperity-based topographies can achieve such…
Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
Using generative models for Inverse Graphics is an active area of research. However, most works focus on developing models for supervised and semi-supervised methods. In this paper, we study the problem of unsupervised learning of 3D…
The fundamental matrix and trifocal tensor are convenient algebraic representations of the epipolar geometry of two and three view configurations, respectively. The estimation of these entities is central to most reconstruction algorithms,…
The geometric phase requires the multivaluedness of solutions to Fuchsian second-order equations. The angle, or its complement, is given by half the area of a spherical triangle in the case of three singular points, or half the area of a…
A polyhedral surface~$\mathcal{C}$ in $\mathbb{R}^3$ with convex polygons as faces is a side-contact representation of a graph~$G$ if there is a bijection between the vertices of $G$ and the faces of~$\mathcal{C}$ such that the polygons of…
In this paper, we develop new methods for the analysis of decentralized control systems and we apply them to formation control problems. The basic set-up consists of a system with multiple agents corresponding to the nodes of a graph whose…
We describe a new approach to fit the polyhedron describing a 3D building model to the point cloud of a Digital Elevation Model (DEM). We introduce a new kinetic framework that hides to its user the combinatorial complexity of determining…
Octilinear graph drawings are a standard paradigm extending the orthogonal graph drawing style by two additional slopes (+1 and -1). We are interested in two constrained drawing problems where the input specifies a so-called representation,…
We report for the first time the intrinsically three-dimensional (3D) geometry of the magnetic reconnection process induced by ballooning instability in a generalized Harris sheet. The spatial distribution and structure of the…
Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…
Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…
The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…