Related papers: A review on geometric constraint solving
The concept of comprehensive triangular decomposition (CTD) was first introduced by Chen et al. in their CASC'2007 paper and could be viewed as an analogue of comprehensive Grobner systems for parametric polynomial systems. The first…
Version control is critical in mechanical computer-aided design (CAD) to enable traceability, manage product variation, and support collaboration. Yet, its implementation in modern CAD software as an essential information infrastructure for…
Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Computer Aided Control System Design (CACSD) allows to analyze complex interconnected systems and design controllers achieving challenging control requirements. We extend CACSD to systems with time delays and illustrate the functionality of…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
3D Gaussian Splatting has emerged as an alternative 3D representation for novel view synthesis, benefiting from its high-quality rendering results and real-time rendering speed. However, the 3D Gaussians learned by 3D-GS have ambiguous…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…
Heterogeneous object design is an active research area in recent years. The conventional CAD modeling approaches only provide geometry and topology of the object, but do not contain any information with regard to the materials of the object…
Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete…
3D Gaussian Splatting (3DGS) has emerged as a powerful explicit representation enabling real-time, high-fidelity 3D reconstruction and novel view synthesis. However, its practical use is hindered by the massive memory and computational…
Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects' surfaces with their corresponding edges and nodes are…
Stereophotogrammetry is an established technique for scene understanding. Its origins go back to at least the 1800s when people first started to investigate using photographs to measure the physical properties of the world. Since then,…
We introduce CADSpotting, an effective method for panoptic symbol spotting in large-scale architectural CAD drawings. Existing approaches often struggle with symbol diversity, scale variations, and overlapping elements in CAD designs, and…
We consider large-scale, implicit-search-based solutions to Shortest Path Problems on Graphs of Convex Sets (GCS). We propose GCS*, a forward heuristic search algorithm that generalizes A* search to the GCS setting, where a…
Control Co-Design (CCD) considers the coupled effects of both the plant and control parameters to optimize a system's closed-loop transient performance during the design stage. This paper presents a new method for CCD with guarantees on…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
We tackle a new problem: generating geometrically consistent multi-view scenes from a single freehand sketch. Freehand sketches are the most geometrically impoverished input one could offer a multi-view generator. They convey scene intent…
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…