## We show how to quantify uncertainties while applying several computational geometry, spatial statistics, and clustering tasks for post-processing APT datasets as large as two billion ions.

On strong-scaling and open-source tools for analyzing atom probe tomography data

## Exploiting several computational geometry techniques, we reduce the openloop controller synthesis problem to satisfiability over quantifierfree linear real arithmetic.

Controller synthesis for linear system with reach-avoid specifications

## For increased efficiency, the core package is written in C++, works in parallel, and uses the Computational Geometry Algorithms Library (Hert & Seel, 2020).

SeismicMesh: Triangular meshing for seismology

GeoGraph

## Considering that not only throughput capacity of airspace but also complexity of path planning is highly dependent on the topology of a navigable space, we propose a new airspace assessment approach to extract the topology of airspace using computational geometry techniques.

Extracting the topology of urban airspace through graph abstraction

## Using image processing and computational geometry techniques to calculate the orientation.

A Method for Measuring the Orientation of Carbon Fiber Weave

## The narrowed down list of constituents from Tinospora cordifolia paved way for further tuning their ability to inhibit COVID-19 by modifying the chemical structures and by employing computational geometry optimization and docking methods.

Computationally approached inhibition potential of Tinospora cordifolia towards COVID-19 targets

## We present and solve a new computational geometry optimization problem in which a set of circles with given radii is to be arranged in unspecified area such that the length of the boundary, i.

Packing circles into perimeter-minimizing convex hulls

## With the proposed GNA design framework, we provide mathematical analysis and efficient heuristic algorithms that are built on the latest computational geometry tools and combinatorial optimization techniques.

On Network Topology Augmentation for Global Connectivity under Regional Failures

## The methods scalability are currently limited by the computational requirements for performing the necessary set operations by current computational geometry tools.

Lagrangian Approximations for Stochastic Reachability of a Target Tube

## Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing.

On Morphing 1-Planar Drawings

## This article is an introduction to fine-grained lower bounds in computational geometry, with a focus on lower bounds for polynomial-time problems based on the Orthogonal Vectors Hypothesis.

Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry

## The neighborhood problem appears in many applications of computational geometry, computational mechanics, etc.

Strategy and algorithms for the parallel solution of the nearest neighborhood problem in shared-memory processors

## Second, the block system model of rockfall is reconstructed by using 3D computational geometry theory and taking these geometric characteristic parameters as an input.

Reproduction Method of Rockfall Geologic Hazards Based on Oblique Photography and Three-Dimensional Discontinuous Deformation Analysis

## In this study, a coronary arterial computational geometry was constructed using magnetic resonance angiography (MRA) data acquired in a patient with moderate CAD.

Effect of Patient-Specific Coronary Flow Reserve Values on the Accuracy of MRI-Based Virtual Fractional Flow Reserve

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Data structures design and analysis.

Space Efficient Two-Dimensional Orthogonal Colored Range Counting

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Computing methodologies → Motion path planning.

Shadoks Approach to Low-Makespan Coordinated Motion Planning

## We also develop an efficient algorithm to compute the WT map based on computational geometry.

Cortical Morphometry Analysis based on Worst Transportation Theory

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

An Output-Sensitive Algorithm for Computing the Union of Cubes and Fat Boxes in 3D

## In order to preserve the privacy of both LBS providers and users, according to computational geometry and Asymmetric Scalar-product Preserving Encryption (ASPE) approach, we design a novel algorithm for accurately determining whether a segment intersects with a rectangle on ciphertext.

Privacy-Preserving Linear Region Search Service

## This model, inspired by the smoothed complexity analysis introduced in computational geometry \cite{DGGT,ST}, is a perturbation of the classical random polytope.

Convex hulls of perturbed random point sets

## As there exist an infinite number of tension distributions, this paper presents a novel computational geometry-based method to calculate a tension feasible region (TFR)—a preimage of tension distribution—for multi-redundant CDPRs.

Direct method for tension feasible region calculation in multi-redundant cable-driven parallel robots using computational geometry

## Considering that not only throughput capacity of airspace but also complexity of path planning is highly dependent on the topology of a navigable space, we propose a new airspace assessment approach to extract the topology of airspace using computational geometry techniques.

Extracting the topology of urban airspace through graph abstraction

## Using image processing and computational geometry techniques to calculate the orientation.

A Method for Measuring the Orientation of Carbon Fiber Weave

## This paper presents a set of related methods for performing a computational geometry analysis of a cone crusher shape that provides geometric information for use in understanding cone crusher flows and breakage and their variation with key crusher geometric parameters.

Geometric analysis of cone crusher liner shape: Geometric measures, methods for their calculation and linkage to crusher behaviour

## We treat the DHOP as a computational geometry function over stochastic BB user locations which requires careful adjustment in the deployment parameters to ensure MTC service at all times.

Standalone Deployment of a Dynamic Drone Cell for Wireless Connectivity of Two Services

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

More Dynamic Data Structures for Geometric Set Cover with Sublinear Update Time

## Given two points s and t in the plane and a set of obstacles defined by closed curves, what is the minimum number of obstacles touched by a path connecting s and t? This is a fundamental and well-studied problem arising naturally in computational geometry, graph theory (under the names Min-Color Path and Minimum Label Path), wireless sensor networks (Barrier Resilience) and motion planning (Minimum Constraint Removal).

A Constant Factor Approximation for Navigating Through Connected Obstacles in the Plane

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Data structures design and analysis.

Dynamic Colored Orthogonal Range Searching

## We revisit a classical problem in computational geometry: finding the largest-volume axisaligned empty box (inside a given bounding box) amidst n given points in d dimensions.

Faster Algorithms for Largest Empty Rectangles and Boxes

## For increased efficiency, the core package is written in C++, works in parallel, and uses the Computational Geometry Algorithms Library (Hert & Seel, 2020).

SeismicMesh: Triangular meshing for seismology

## 2012 ACM Subject Classification General and reference → Performance; General and reference → Experimentation; Theory of computation → Computational geometry; Mathematics of computing → Matroids and greedoids; Mathematics of computing → Mathematical software performance; Computing methodologies → Combinatorial algorithms; Computing methodologies → Algebraic algorithms.

Combinatorial Resultants in the Algebraic Rigidity Matroid

## In this study, a systematic tool is developed based on computing techniques, including deep learning and computational geometry.

A Mask R-CNN based particle identification for quantitative shape evaluation of granular materials

## Thus the problem of motion approximation is transformed into a curve approximation problem, where concepts and techniques in the field of Computer Aided Geometric Design and Computational Geometry may be applied.

Algebraic Motion Approximation With NURBS Motions and its Application to Spherical Mechanism Synthesis

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

Chasing Puppies: Mobile Beacon Routing on Closed Curves

## Computational geometry and mesh are generated in ANSYS.

Computational fluid dynamics simulation of a stirred tank reactor

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

On Undecided LP, Clustering and Active Learning

## We show how to quantify uncertainties while applying several computational geometry, spatial statistics, and clustering tasks for post-processing APT datasets as large as two billion ions.

On strong-scaling and open-source tools for analyzing atom probe tomography data

## The framework, built on level set method and variational multi-scale formulation (VMS), features three major contributions: (1) a simple computational geometry-based re-initialization approach, which maintains excellent signed distance property on unstructured meshes, re-constructs an explicit representation of gas-metal interface from the level set, and facilitates the treatment of the multiple laser reflections during keyhole evolution in AM processes; (2) a fully coupled VMS formulation for thermal multi-phase governing equations, including Navier-Stokes, level set convection, and thermodynamics with melting, solidification, evaporation, and interfacial force models; and (3) a three-level recursive preconditioning technique to enhance the robustness of linear solvers.

A mixed interface-capturing/interface-tracking formulation for thermal multi-phase flows with emphasis on metal additive manufacturing processes

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

A Stepping-Up Lemma for Topological Set Systems

## This is a classic problem in computational geometry, known as point location.

Well-testing based turbidite lobes modeling using the ensemble smoother with multiple data assimilation

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Models of learning.

Obstructing Classification via Projection

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

On Greedily Packing Anchored Rectangles

## Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively.

Shortest Paths Among Obstacles in the Plane Revisited

## The aim of our project is computational geometry reconstruction for blood flow simulations to make it suitable for comparison with plaque image analysis performed by commercially available software.

Comparison of Manual versus Semi-Automatic Segmentations of the Stenotic Carotid Artery Bifurcation

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Design and analysis of algorithms.

A 4-Approximation of the $\frac{2\pi }{3}$-MST

## We hope this work leads to the further study of the intersection of differential privacy and computational geometry.

Private Approximations of a Convex Hull in Low Dimensions

## 2012 ACM Subject Classification Information systems → Geographic information systems; Theory of computation → Computational geometry.

Volume from Outlines on Terrains

## The greatest challenges of rigorously modeling coupled hydro-mechanical processes in fractured rocks at different scales are associated with computational geometry.

Multi-scale Coupled Processes Modeling of Fractures as Porous, Interfacial and Granular Systems from Rock Images with the Numerical Manifold Method

## Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization.

A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm

## Typically, we adapt methods from other communities like mathematics, data science, computational geometry, artificial intelligence, or scientific computing.

Community-Driven Methods for Open and Reproducible Software Tools for Analyzing Datasets from Atom Probe Microscopy.

## This problem is a variant of three well-studied problems that have arisen in computational geometry, data structures, and network design: (i) It is a node-cost variant of the classical Manhattan network problem, (ii) it is an extension of the binary search tree problem to arbitrary demands, and (iii) it is a special case of the directed Steiner forest problem.

On Minimum Generalized Manhattan Connections

## Solving nonlinear equations is an important problem which appears in various models of science and engineering such as computer vision, computational geometry, signal processing, computational chemistry, and robotics.

A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations

## 2012 ACM Subject Classification Theory of computation → Data structures design and analysis; Theory of computation → Computational geometry; Information systems → Information retrieval.

Locality Sensitive Hashing for Efficient Similar Polygon Retrieval

## 2012 ACM Subject Classification Theory of computation → Design and analysis of algorithms; Theory of computation → Computational geometry; Applied computing → Operations research.

Minimum Scan Cover and Variants - Theory and Experiments

## We develop a computational geometry-based tractography representation that aims to simplify the connectivity of white matter fibers.

A computational geometry approach for modeling neuronal fiber pathways

## In Cheng, Devillers (eds), 30th Annual Symposium on Computational Geometry, SOCG’14, Kyoto, Japan, June 08–11, p 328, ACM, 2014).

Dimensionality reduction for k-distance applied to persistent homology

## But with the help of image processing techniques and computational geometry, this problem can be handled with ease.

Computationally efficient approach to quantify 2D particle morphological descriptors

## Terrain visibility graphs are a well-known graph class in computational geometry.

A Fast Shortest Path Algorithm on Terrain-like Graphs

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

On Ray Shooting for Triangles in 3-Space and Related Problems

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

Computing the Fréchet Distance Between Uncertain Curves in One Dimension

## Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity.

Multipatch Isogeometric Analysis for electrophysiology: Simulation in a human heart

## Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods.

Structured inversion of the Bernstein-Vandermonde Matrix

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Mathematics of computing.

Two-Sided Kirszbraun Theorem

## 2012 ACM Subject Classification Mathematics of computing → Approximation algorithms; Mathematics of computing → Paths and connectivity problems; Theory of computation → Computational geometry.

On Euclidean Steiner (1+ε)-Spanners

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

Uncertain Curve Simplification

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Mathematics of computing → Algebraic topology.

Computing Zigzag Persistence on Graphs in Near-Linear Time

## Dimensionality reduction tools from computational geometry are applied to learn the intrinsic manifold on which the latent, temporal topics reside.

A Geometry-Driven Longitudal Topic Model

## The key contribution made in this paper is the complete automation of the design of a PSCI based on the skull’s unique geometry using a combination of image-processing and computational geometry techniques.

Image Processing-based Method for Automatic Design of Patient-Specific Cranial Implant for Additive Manufacturing

## In this paper machine learning methods for automatic classification problems using computational geometry are considered.

Machine learning algorithm based on convex hull analysis

## , in embedding an undirected graph into hyperbolic space with minimum distortion (Verbeek and Suri, in Symposium on Computational Geometry, ACM, New York, 2014).

Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

The Visibility Center of a Simple Polygon

## The point inclusion tests for polygons, in other words the point in polygon (PIP) algorithms are fundamental tools for many scientific fields related to computational geometry and they have been studied for a long time.

A Novel Point Inclusion Test for Convex Polygons Based on Voronoi Tessellations

## 2012 ACM Subject Classification Theory of computation → Packing and covering problems; Theory of computation → Computational geometry.

Packing Squares into a Disk with Optimal Worst-Case Density

## We propose an extension of Art Galleries in Computational Geometry towards a more real world application related definition, well suited for Evolutionary Algorithms.

The Sectional Art Gallery and an Evolutionary Algorithm for Approaching Its Minimum Point Guard Problem

GeoGraph

## Wavelet trees are compact data structures in computational geometry.

Wavelet Tree ensembles with Machine Learning and its classification

## The simulator is based on a generic computational geometry algorithm which estimates the exact volume of rock removed by each cutter while making minimal assumptions on the geometry of the cutter.

A New Pdc Bit Selection Method Based on 3d Realistic Cutter Damage Simulation Aimed at Maximizing Product Life–Cycle

## Our main technical result is a practical and provable approximation algorithm to compute it for any p≥1, based on modern techniques in computational geometry.

No Fine-Tuning, No Cry: Robust SVD for Compressing Deep Networks

## Where robotics middleware is focused on communication, these software tools focus primarily on computational geometry within design software, with the goal of enabling mass-customization and individualization by linking parametric design with toolpath generation and robot simulation.

Towards Real-Time Interaction with Industrial Robots in the Creative Industries

## This hypothesis was first used in Computational Geometry by Gajentaan and Overmars [4] 1 who built a web of reductions showing that many geometric problems are hard, assuming that 3SUM is hard.

3SUM and Related Problems in Fine-Grained Complexity (Invited Talk)

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

On rich points and incidences with restricted sets of lines in 3-space

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

An Instance-optimal Algorithm for Bichromatic Rectangular Visibility

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

Counting Cells of Order-k Voronoi Tessellations in ℝ³ with Morse Theory

## A numerical example of an advection diffusion PDE is presented to provide an understanding of this computational geometry based partitioning of feedback kernels.

Employing mobile sensor density to approximate state feedback kernels in static output feedback control of PDEs

## ) 2012 ACM Subject Classification Theory of computation → Computational geometry.

No Krasnoselskii Number for General Sets

## With the proposed GNA design framework, we provide mathematical analysis and efficient heuristic algorithms that are built on the latest computational geometry tools and combinatorial optimization techniques.

On Network Topology Augmentation for Global Connectivity under Regional Failures

## 2012 ACM Subject Classification Theory of computation → Computational geometry; Security and privacy → Formal methods and theory of security.

Approximate Range Counting Under Differential Privacy

## In recent works—both experimental and theoretical—it has been shown how to use computational geometry to efficiently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by discretizing one of the measures.

Convergence Rates for Discretized Monge–Ampère Equations and Quantitative Stability of Optimal Transport

## Using JSXGraph, a state-of-the-art JavaScript library for geometry, we have implemented seven of these sophisticated algorithms so that they can be used for further research and teaching computational geometry.

An Interactive Tool for Experimenting with Bounded-Degree Plane Geometric Spanners (Media Exposition)

## Our simulation makes use of an improved computational geometry algorithm XenoSweep, which predicts sweep collision in a particularly simple way.

Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles.

## 2012 ACM Subject Classification Theory of computation → Computational geometry.

Fréchet Mean and p-Mean on the Unit Circle: Decidability, Algorithm, and Applications to Clustering on the Flat Torus

## However, obtaining sharp bounds on H Dd(p, q), known as 'the Hadwiger-Debrunner numbers', is still a major open problem in discrete and computational geometry.

A new lower bound on Hadwiger-Debrunner numbers in the plane

## The experimental plan addressed: (i) the evaluation of the particle shape from a large number of particles using a computational geometry algorithm and statistical procedures; (ii) the estimation of the minimum and maximum void ratio through two standard methods; (iii) the assessment of the stress–strain behaviour by triaxial tests using lubricated end platens and an embedded connection piston, and void ratio measurements using end-of-test soil freezing; and (iv) the stress-dependency assessment of seismic wave velocities using bender elements.

Key geomechanical properties of the historically liquefiable TP-Lisbon sand

## In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls.

Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

## The analysis of metabolic networks is a computational geometry oriented field as one of the main operations they depend on is sampling uniformly points from polytopes; the latter provides a representation of the steady states of the metabolic networks.

Geometric Algorithms for Sampling the Flux Space of Metabolic Networks

## gif"/></alternatives></inline-formula> values by building upon results from computational geometry to replace HDBSCAN*’s complete graph with a smaller equivalent graph.

Efficient Computation and Visualization of Multiple Density-Based Clustering Hierarchies

## We revisit classical problems about searching in totally monotone and Monge matrices, which have many applications in computational geometry and other areas.

(Near-)Linear-Time Randomized Algorithms for Row Minima in Monge Partial Matrices and Related Problems

## The narrowed down list of constituents from Tinospora cordifolia paved way for further tuning their ability to inhibit COVID-19 by modifying the chemical structures and by employing computational geometry optimization and docking methods.

Computationally approached inhibition potential of Tinospora cordifolia towards COVID-19 targets

## Machine learning methods for automatic classification problems using computational geometry are considered.

Nearest Convex Hull Classification Based on Linear Programming