Related papers: A review on geometric constraint solving
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by…
Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…
Mechanical product engineering often must comply with manufacturing or geometric constraints related to the shaping process. Mechanical design hence should rely on robust and fast tools to explore complex shapes, typically for design for…
In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex…
Computer-Aided Design (CAD) plays a pivotal role in industrial manufacturing, yet 2D Parametric Primitive Analysis (PPA) remains underexplored due to two key challenges: structural constraint reasoning and advanced semantic understanding.…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
While Dynamic Gaussian Splatting enables high-fidelity 4D reconstruction, its deployment is severely hindered by a fundamental dilemma: unconstrained densification leads to excessive memory consumption incompatible with edge devices,…
Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
Sketch-based shape modeling aims to bridge the gap between 2D drawing and 3D modeling by providing an intuitive and accessible approach to create 3D shapes from 2D sketches. However, existing methods still suffer from limitations in…
Single-view 3D object reconstruction is a challenging fundamental problem in computer vision, largely due to the morphological diversity of objects in the natural world. In particular, high curvature regions are not always captured…
Performance variability management is an active research area in high-performance computing (HPC). We focus on input/output (I/O) variability. To study the performance variability, computer scientists often use grid-based designs (GBDs) to…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: asymptotic parameters, improved estimates on the minimum…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…