Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

Dupont, Laurent; Hemmer, Michael; Petitjean, Sylvain; Schömer, Elmar

doi:10.1007/978-3-540-75520-3_56

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…In [12] solved the problem of efficient and accurate parametric representation of the curve of intersection of two quadrics. These results led to further development in [13], in which an effective, accurate and complete algorithm was proposed for constructing the graph of contiguity of ordering quadrics.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Developing an algorithm with improved relevance for the localization of vector’s coordinates for intelligent sensors

Marusenkova

2016

EEJET

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Досліджено проблему недостатнього розвитку алгоритмів, реалізованих у мікропрограмному забезпеченні для пошуку точок перетину квадрик. Розроблено, реалізовано та досліджено алгоритм локалізації точок перетину квадрик на основі властивостей неперервних диференційовних функцій у замкнутій області. Новим алгоритмом досягається вища релевантність результатів, ніж його єдиним аналогом. Результати призначені для інтелектуальних сенсорів векторних величин Ключові слова: інтелектуальні сенсори векторних величин, локалізація точок перетину квадрик, мікроконтролер ARM Исследована проблема недостаточного развития алгоритмов, применимых для реализации в микропрограммном обеспечении для поиска точек пересечения квадрик. Разработан, реализован и изучен алгоритм локализации точек пересечения квадрик на основе свойств непрерывных дифференцируемых функций в замкнутой области. Новым алгоритмом достигается релевантность результатов выше, чем у его единственного аналога. Результаты предназначены для интеллектуальных сенсоров Ключевые слова: интеллектуальные сенсоры векторных величин, локализация точек пересечения квадрик, микроконтроллер ARM

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Developing an algorithm with improved relevance for the localization of vector’s coordinates for intelligent sensors

Marusenkova

2016

EEJET

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“…In this section we focus on new geometric applications that are build on top of our bivariate algebraic kernel. Further applications (that used experimental versions of the kernel) have been discussed in previous work [12,4,6,7,23].…”

Section: Geometric Applicationsmentioning

confidence: 99%

“…Its prototypical version has already been an essential building block for numerous geometric applications. While its univariate part was used to exactly handle parameterized curves defined over extension fields of degree 2 [12], the bivariate part enabled computing arrangements of algebraic curves in the plane (see next paragraph), computing arrangements on quadrics [4] and on ring Dupin cyclides [6], triangulating algebraic surfaces of arbitrary degree [7], and, most recently, computing Voronoi diagrams for lines in space [23].…”

Section: Introductionmentioning

confidence: 99%

A generic algebraic kernel for non-linear geometric applications

Berberich

Hemmer

Kerber

2011

Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry

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“…Practical exact computation of complexes whose cells are delimited by general second order surfaces is still the subject of active research [16,11], not to mention the queries required by our surface reconstruction step. To circumvent this major problem, an approximation of the cell complex induced by the BSP tree is computed by using an adaptive multi-domain volume mesh generator [25] which extends the surface meshing algorithm of [6].…”

Section: Approximation Of the Induced Cell Complexmentioning

confidence: 99%

Hierarchical shape-based surface reconstruction for dense multi-view stereo

Labatut¹,

Pons²,

Keriven³

2009

2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops

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The recent widespread availability of urban imagery has lead to a growing demand for automatic modeling from multiple images. However, modern image-based modeling research has focused either on highly detailed reconstructions of mostly small objects or on human-assisted simplified modeling. This paper presents a novel algorithm which automatically outputs a simplified, segmented model of a scene from a set of calibrated input images, capturing its essential geometric features. Our approach combines three successive steps. First, a dense point cloud is created from sparse depth maps computed from the input images. Then, shapes are robustly extracted from this set of points. Finally, a compact model of the scene is built from a spatial subdivision induced by these structures: this model is a global minimum of an energy accounting for the visibility of the final surface. The effectiveness of our method is demonstrated through several results on both synthetic and real data sets, illustrating the various benefits of our algorithm, its robustness and its relevance for architectural scenes.

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Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

Cited by 8 publications

References 14 publications

Developing an algorithm with improved relevance for the localization of vector’s coordinates for intelligent sensors

Developing an algorithm with improved relevance for the localization of vector’s coordinates for intelligent sensors

A generic algebraic kernel for non-linear geometric applications

Hierarchical shape-based surface reconstruction for dense multi-view stereo

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