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Boundary representation (B-rep) of geometric models is a fundamental format in Computer-Aided Design (CAD). However, automatically generating valid and high-quality B-rep models remains challenging due to the complex interdependence between…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
Consider a family of sets and a single set, called the query set. How can one quickly find a member of the family which has a maximal intersection with the query set? Time constraints on the query and on a possible preprocessing of the set…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
Driving scene understanding task involves detecting static elements such as lanes, traffic signs, and traffic lights, and their relationships with each other. To facilitate the development of comprehensive scene understanding solutions…
In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal…
In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…
The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper…
The U-shape structure has shown its advantage in salient object detection for efficiently combining multi-scale features. However, most existing U-shape based methods focused on improving the bottom-up and top-down pathways while ignoring…
The paper investigates the performance of state-of-the-art low-parameter deep neural networks for computer vision, focusing on bottleneck architectures and their behavior using superlinear activation functions. We address interference in…
Most superpixel algorithms compute a trade-off between spatial and color features at the pixel level. Hence, they may need fine parameter tuning to balance the two measures, and highly fail to group pixels with similar local texture…
In this paper, we propose a closed-form solution to the inverse problem in interpolation with periodic uniform B-spline curves. This solution is obtained by modifying the one we have established to a similar problem with relaxed uniform…