Computational Geometry Papers of the Week

We explain geometrically how the triangle $P$ rotates while continuously scaling and translating to be maximal inside $Q$, leading to a parameterized algorithm for containment problems.

However, identifying a structure near the zero-temperature convex hull or detecting its signature in a synthesis product does not, by itself, establish materials discovery. In this perspective, we argue that finite-temperature phase equilibria and transformation kinetics should guide these eff orts from the outset.

For every fixed dimension $d$, we give an algorithm for $m$ queries, $n$ key-value pairs, and additive error $\varepsilon$, with expected time $ \widetilde{\mathrm{O}}\bigl((mn)^{k/(k+1)}+m+n\bigr),\qquad k=\lfloor d/2\rfloor.

The research formalizes a parameter-driven design-to-fabrication framework bridging computational modeling and robotic metal deposition, providing a transferable methodology that can inform applications beyond prototype-scale fabrication while preserving architectural design intent.

This study addresses the research gap in quantifying fine-scale spatiotemporal urban transformations by employing the Normalized Difference Built-up Index (NDBI) from Sentinel-2 imagery over the period of 2019–2025.

Our algorithm introduces a new sweep-line paradigm that avoids explicitly constructing the diagram, together with a novel technique for point location in implicit subdivisions.

In this study, some types of convexity, like strictly (strongly) convexity, (λ,ψ)-convexity with different senses over fuzzy soft expert set, have been described with the numerical examples.

We study the problem of packing a given set of polygons into a minimum-area convex container, that is, placing them without overlap so as to minimize the area of their convex hull.

The purpose of this paper is to provide a human-written exposition of the algorithm.

We present a deterministic algorithm that approximates the Fréchet distance between two polygonal curves in $\mathbb{R}^d$ with $n$ and $m$ vertices within a constant factor in $O((m+n)^{1+\varepsilon})$ time, for every fixed $\varepsilon>0$ and fixed dimension $d$.

In this paper, we investigate Hamiltonian cycle construction in rectangular grid graphs containing a three-stacked right-triangular hole.

This study presents ES–TD3, an evolution strategy-assisted Twin Delayed Deep Deterministic Policy Gradient framework that combines population-based actor-parameter search with off-policy learning.

This article presents a novel proof-of-concept study that lays the foundation for objective tremor quantification based on inertial measurement unit (IMU) signals.

This study presents a design-intent-aware reverse-parametrization framework that converts history-free STEP parts into editable Grasshopper definitions and represents their assembly relations.

Its proof uses groups ordered in two coordinates, with neighbouring groups acting as barriers that preserve this invariant when one layer is removed. Combining these bounds with the existing interval-representation framework, we obtain a Las Vegas algorithm that, for every fixed integer $\Delta\ge1$, decides whether a graph given by $n$ cube centres has diameter at most $\Delta$ in expected $O_\Delta(n^{2-\varepsilon_\Delta})$ time, for an explicit constant $\varepsilon_\Delta>0$.

38 , 2007]. We prove that there are ball coverings of $$\mathbb {R}^n$$ R n attaining the asymptotically best known density $$\left( 1/2+ o(1)\right) n \ln n$$ 1 / 2 + o ( 1 ) n ln n such that, additionally, every point of $$\mathbb {R}^n$$ R n is covered at most $$\left( 1.79556... + o(1)\right) n \ln n$$ 1.79556 . . . + o ( 1 ) n ln n times.

Here, a rational approach to designing perovskite oxides with phase stability and oxygen storage capacity under thermodynamically favorable conditions is presented.

In order to formulate a reasonable defense plan, this paper uses the NBA tracking data and builds a defense scheduling model based on MIP.

We propose pair-relative partial equivariance, which measures equivariance under the empirical distribution of relative rotations in image pairs, and PaSteer, a relaxed descriptor-steering framework that allows the steering map to leave the exact representation manifold while retaining the lightweight, backbone-free design of steering.