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The paper presents an optimal synthesis of overconstrained linkages, based on the factorization of rational curves (representing one parametric motions) contained in Study's quadric. The group of Euclidean displacements is embedded in a…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
Performances of an adaptive optics (AO) system are directly linked with the quality of its alignment. During the instrument calibration, having open loop fast tools with a large capture range are necessary to quickly assess the system…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
This paper presents a numerical optimization algorithm for generating approach and landing trajectories for a six-degree-of-freedom (6-DoF) aircraft. We improve on the existing research on aircraft landing trajectory generation by…
An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of…
We present a novel non-iterative learnable method for partial-to-partial 3D shape registration. The partial alignment task is extremely complex, as it jointly tries to match between points and identify which points do not appear in the…
We study metric data structures for curves in doubling spaces, such as trajectories of moving objects in Euclidean $\mathbb{R}^d$, where the distance between two curves is measured using the discrete Fr\'echet distance. We design data…
A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this paper, we consider the…
The most commonly used method for addressing 3D geometric registration is the iterative closet-point algorithm, this approach is incremental and prone to drift over multiple consecutive frames. The Common strategy to address the drift is…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "simple" in the sense that any three curves have no common…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
Commercial off the shelf (COTS) 3D scanners are capable of generating point clouds covering visible portions of a face with sub-millimeter accuracy at close range, but lack the coverage and specialized anatomic registration provided by more…
We formulate mold filling in metal casting as a 2D neural operator learning problem that maps geometry and boundary data on an unstructured mesh to time resolved flow quantities, replacing expensive transient CFD. In the proposed method, a…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…