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Related papers: On the Spline-Based Parameterisation of Plane Grap…

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An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…

Data Structures and Algorithms · Computer Science 2022-08-29 Ahammed Ullah

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

Algebraic Geometry · Mathematics 2016-03-24 Bernard Mourrain , Raimundas Vidunas , Nelly Villamizar

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Computational Geometry · Computer Science 2018-03-06 Samy Ait-Aoudia , Adel Moussaoui , Khaled Abid , Dominique Michelucci

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…

Data Structures and Algorithms · Computer Science 2014-02-18 Michael Lampis

In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for…

Computational Geometry · Computer Science 2025-05-19 Gunnar Brinkmann

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…

Artificial Intelligence · Computer Science 2009-09-25 S. Bhansali , G. A. Kramer , T. J. Hoar

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

Computational Geometry · Computer Science 2024-10-25 Juan Juan Gerardo Alcázar , Carlos Hermoso , Hüsnü Anıl Çoban , Uğur Gözütok

Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…

Algebraic Geometry · Mathematics 2025-04-02 Thierry Dana-Picard , Daniel Tsirkin

Graphene, the one-atom-thick sp2 hybridized carbon crystal, displays unique electronic, structural and mechanical properties, which promise a large number of interesting applications in diverse high tech fields. Many of these applications…

Mesoscale and Nanoscale Physics · Physics 2016-09-27 Tommaso Cavallucci , Khatuna Kakhiani , Riccardo Farchioni , Valentina Tozzini

Graph-based representations such as Scene Graphs enable localization in structured indoor environments by matching a locally observed graph, constructed from sensor data, to a prior map. This process is particularly challenging in…

Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm…

Computational Geometry · Computer Science 2020-02-10 Gary Pui-Tung Choi , Lok Ming Lui

We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…

Numerical Analysis · Mathematics 2015-07-15 Maria-Laura Torrente , Stefano Anzellotti , Chiara Finocchiaro , Claudio Fontanari

Parameterized algebraic curves and surfaces are widely used in geometric modeling and their manipulation is an important task in the processing of geometric models. In particular, the determination of the intersection loci between points,…

Commutative Algebra · Mathematics 2021-08-02 Laurent Busé , Marc Chardin

Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…

Numerical Analysis · Mathematics 2023-02-16 Hiba Nassar , Krzysztof Podgórski

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…

Computational Geometry · Computer Science 2013-10-28 Vikash Gupta , Hari K. Voruganti , Bhaskar Dasgupta

Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard…

Computational Geometry · Computer Science 2020-12-16 Marco Livesu

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…

Soft Condensed Matter · Physics 2012-01-18 Aaron S. Keys , Christopher R. Iacovella , Sharon C. Glotzer

The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first…

Differential Geometry · Mathematics 2012-05-28 David Pérez Fernández

A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…

Combinatorics · Mathematics 2011-11-01 Gábor Tardos

In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is…

Optimization and Control · Mathematics 2019-10-25 Fabian Wein , Peter Dunning , Julián A. Norato