Bibliographies thématiques / Singular Curve Topology

Littérature scientifique sur le sujet « Singular Curve Topology »

Auteur : Grafiati
Publié le 8 juin 2024

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Articles de revues sur le sujet "Singular Curve Topology"

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Montaldi, James, et Duco van Straten. « One-forms on singular curves and the topology of real curve singularities ». Topology 29, no 4 (1990) : 501–10. http://dx.doi.org/10.1016/0040-9383(90)90018-f.

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Kleiman, Steven Lawrence, et Renato Vidal Martins. « The canonical model of a singular curve ». Geometriae Dedicata 139, no 1 (11 février 2009) : 139–66. http://dx.doi.org/10.1007/s10711-008-9331-4.

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Castañeda, Ángel Luis Muñoz. « On the moduli spaces of singular principal bundles on stable curves ». Advances in Geometry 20, no 4 (27 octobre 2020) : 573–84. http://dx.doi.org/10.1515/advgeom-2020-0003.

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AbstractWe prove the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of δ-(semi)stable singular principal G-bundles over families of reduced projective and connected nodal curves, and to reduce the construction of the universal moduli space over 𝓜g to the construction of the universal moduli space of swamps.
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Golla, Marco, et Laura Starkston. « The symplectic isotopy problem for rational cuspidal curves ». Compositio Mathematica 158, no 7 (juillet 2022) : 1595–682. http://dx.doi.org/10.1112/s0010437x2200762x.

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We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex projective plane. We prove that every such curve is isotopic to a complex curve in degrees up to five, and for curves with one singularity whose link is a torus knot. Classification results of symplectic isotopy classes rely on pseudo-holomorphic curves together with a symplectic version of birational geometry of log pairs and techniques from four-dimensional topology.
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Menegon Neto, Aurélio. « Lê's polyhedron for line singularities ». International Journal of Mathematics 25, no 13 (décembre 2014) : 1450114. http://dx.doi.org/10.1142/s0129167x14501146.

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We study the topology of line singularities, which are complex hypersurface germs with non-isolated singularity given by a smooth curve. We describe the degeneration of its Milnor fiber to the singular hypersurface by means of a vanishing polyhedron in the Milnor fiber. As a milestone, we also study the topology of the degeneration of a complex isolated singularity hypersurface under a nonlocal point of view.
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Yang, Jieyin, Xiaohong Jia et Dong-Ming Yan. « Topology Guaranteed B-Spline Surface/Surface Intersection ». ACM Transactions on Graphics 42, no 6 (5 décembre 2023) : 1–16. http://dx.doi.org/10.1145/3618349.

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The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.
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Nishimura, Takashi. « Normal forms for singularities of pedal curves produced by non-singular dual curve germs in S n ». Geometriae Dedicata 133, no 1 (30 janvier 2008) : 59–66. http://dx.doi.org/10.1007/s10711-008-9233-5.

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Fomin, Sergey, et Eugenii Shustin. « Expressive curves ». Communications of the American Mathematical Society 3, no 10 (28 août 2023) : 669–743. http://dx.doi.org/10.1090/cams/12.

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We initiate the study of a class of real plane algebraic curves which we call expressive. These are the curves whose defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of a curve. This concept can be viewed as a global version of the notion of a real morsification of an isolated plane curve singularity. We prove that a plane curve C C is expressive if (a) each irreducible component of C C can be parametrized by real polynomials (either ordinary or trigonometric), (b) all singular points of C C in the affine plane are ordinary hyperbolic nodes, and (c) the set of real points of C C in the affine plane is connected. Conversely, an expressive curve with real irreducible components must satisfy conditions (a)–(c), unless it exhibits some exotic behaviour at infinity. We describe several constructions that produce expressive curves, and discuss a large number of examples, including: arrangements of lines, parabolas, and circles; Chebyshev and Lissajous curves; hypotrochoids and epitrochoids; and much more.
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Pinsky, Tali. « On the topology of the Lorenz system ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 473, no 2205 (septembre 2017) : 20170374. http://dx.doi.org/10.1098/rspa.2017.0374.

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We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theory as a way to remove the singularities. Specifically, we claim: (i) for certain parameters, the Lorenz system has an invariant one-dimensional curve, which is a trefoil knot. The knot is a union of invariant manifolds of the singular points. (ii) The flow is topologically equivalent to an Anosov flow on the complement of this curve, and moreover to a geodesic flow. (iii) When varying the parameters, the system exhibits topological phase transitions, i.e. for special parameter values, it will be topologically equivalent to an Anosov flow on a knot complement. Different knots appear for different parameter values and each knot controls the dynamics at nearby parameters.
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Guo, Feng, Gang Cheng et Zunzhong Zhao. « Interior singularity analysis for a 2(3HUS+S) parallel manipulator with descending matrix rank method ». International Journal of Advanced Robotic Systems 16, no 1 (1 janvier 2019) : 172988141982684. http://dx.doi.org/10.1177/1729881419826841.

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Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.
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Thèses sur le sujet "Singular Curve Topology"

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Krait, George. « Isolating the Singularities of the Plane Projection of Generic Space Curves and Applications in Robotics ». Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0092.

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L’isolation des points singuliers d'une courbe plane est la première étape vers le calcul de sa topologie. Pour cela, les méthodes numériques sont efficaces mais non certifiées en général. Nous sommes intéressés par le développement d'algorithmes numériques certifiés pour isoler les singularités. Pour ce faire, nous limitons notre attention au cas particulier des courbes planes qui sont des projections de courbes lisses en dimensions supérieures. Ce type de courbes apparaît naturellement dans les applications robotiques et la visualisation scientifique. Dans ce cadre, nous montrons que les singularités peuvent être encodées par un système carré et régulier dont les solutions peuvent être isolées avec des méthodes numériques certifiées. Notre analyse est conditionnée par des hypothèses que nous démontrons comme étant génériques en utilisant la théorie de la transversalité ; nous fournissons également un semi-algorithme pour vérifier leur validité. Enfin, nous présentons des expériences de visualisation et de robotique, dont certaines ne sont pas accessibles par d'autres méthodes, et discutons de l'efficacité de notre méthode
Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory. We also provide a semi-algorithm to check their validity. Finally, we present experiments in visualization and robotics, some of which are not reachable by other methods, and discuss the efficiency of our method
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Blažková, Eva. « Struktura a aproximace reálných rovinných algebraických křivek ». Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-389639.

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Finding a topologically accurate approximation of a real planar algebraic curve is a classic problem in Computer Aided Geometric Design. Algorithms describing the topology search primarily the singular points and are usually based on algebraic techniques applied directly to the curve equation. In this thesis we propose a more geometric approach, taking into account the subsequent high-precision approximation. Our algorithm is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. To find the characteristic points we use not only the primary algebraic equation of the curve but also, and more importantly, its implicit support function representation. Using the rational Puiseux series, we describe local properties of curve branches at the points of interest and exploit them to find their connectivity. The support function representation is also used for an approximation of the segments. In this way, we obtain an approximate graph of the entire curve with several nice properties. It approximates the curve within a given Hausdorff distance. The actual error can be measured efficiently. The ap- proximate curve and its offsets are piecewise rational. And the question of topological equivalence of the...
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Chapitres de livres sur le sujet "Singular Curve Topology"

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Wolpert, Nicola. « Jacobi Curves : Computing the Exact Topology of Arrangements of Non-singular Algebraic Curves ». Dans Algorithms - ESA 2003, 532–43. Berlin, Heidelberg : Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39658-1_49.

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« Topology of the singularity link ». Dans Singular Points of Plane Curves, 103–30. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511617560.006.

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« Singular Points of Plane Curves ». Dans Differential Geometry and Topology of Curves, 41–47. CRC Press, 2001. http://dx.doi.org/10.1201/9781420022605.ch9.

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Actes de conférences sur le sujet "Singular Curve Topology"

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LIBGOBER, A. « PROBLEMS IN TOPOLOGY OF THE COMPLEMENTS TO PLANE SINGULAR CURVES ». Dans Proceedings of the Trieste Singularity Summer School and Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706812_0011.

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