Showing papers on "Tangent published in 2012"
TL;DR: A novel shape descriptor for matching and recognizing 2D object silhouettes that is not only invariant to geometric transformations such as translation, rotation and scaling but also insensitive to nonlinear deformations due to noise and occlusion is proposed.
178 citations
TL;DR: Numerical benchmark tests including transport of moving interface and incompressible interfacial flows are presented to validate the numerical accuracy for interface capturing and to show the capability for practical problems such as a stationary circular droplet, a drop oscillation, a shear-induced drop deformation and a rising bubble.
128 citations
01 Mar 2012
TL;DR: In this paper, the existence of smooth time functions on connected time-oriented Lorentzian manifolds is studied in a more general abstract setting, namely in a manifold M where is just dened a eld of tangent convex cones (Cx)x2M enjoying mild continuity properties.
Abstract: We are concerned with the existence of smooth time functions on connected time{oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just dened a eld of tangent convex cones ( Cx)x2M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on the denition of an intrinsic length for curves indicating how a curve is far from being an integral trajectory ofCx. We nd connections with topics pertaining to Hamilton{Jacobi equations, and make use of tools and results issued from weak KAM theory.
110 citations
TL;DR: It is proved that the center of the ball constructed by the algorithm converges to a true medial axis point as the sampling density increases to infinity, and a simple heuristic to handle noisy samples is proposed.
Abstract: We present a novel method to approximate medial axis points given a set of points sampled from a surface and the normal vectors to the surface at those points. For each sample point, we find its maximal tangent ball containing no other sample points, by iteratively reducing its radius using nearest neighbor queries. We prove that the center of the ball constructed by our algorithm converges to a true medial axis point as the sampling density increases to infinity. We also propose a simple heuristic to handle noisy samples. By simple extensions, our method is applied to medial axis point simplification, local feature size estimation and feature-sensitive point decimation. Our algorithm is simple, easy to implement, and suitable for parallel computation using GPU because the iteration process for each sample point runs independently. Experimental results show that our method is efficient both in time and in space.
71 citations
TL;DR: The results showed an increase in look-ahead fixations in the direction of the bend exit and a small but consistent reduction in the time spent looking in the area of the tangent point when steering was passive, which supports the idea that drivers look at the boundary of a safe trajectory envelop near the inside edge line.
Abstract: Current theories on the role of visuomotor coordination in driving agree that active sampling of the road by the driver informs the arm-motor system in charge of performing actions on the steering wheel. Still under debate, however, is the nature of visual cues and gaze strategies used by drivers. In particular, the tangent point hypothesis, which states that drivers look at a specific point on the inside edge line, has recently become the object of controversy. An alternative hypothesis proposes that drivers orient gaze toward the desired future path, which happens to be often situated in the vicinity of the tangent point. The present study contributed to this debate through the analyses of the distribution of gaze orientation with respect to the tangent point. The results revealed that drivers sampled the roadway in the close vicinity of the tangent point rather than the tangent point proper. This supports the idea that drivers look at the boundary of a safe trajectory envelop near the inside edge line. Furthermore, the study investigated for the first time the reciprocal influence of manual control on gaze control in the context of driving. This was achieved through the comparison of gaze behavior when drivers actively steered the vehicle or when steering was performed by an automatic controller. The results showed an increase in look-ahead fixations in the direction of the bend exit and a small but consistent reduction in the time spent looking in the area of the tangent point when steering was passive. This may be the consequence of a change in the balance between cognitive and sensorimotor anticipatory gaze strategies. It might also reflect bidirectional coordination control between the eye and arm-motor systems, which goes beyond the common assumption that the eyes lead the hands when driving.
68 citations
TL;DR: The empirical results reveal that the proposed paradigm frames the classification scheme as a nearest neighbor based on the intrinsic distance, prior training is unnecessary and the method is highly competitive with the current state-of-the-art methods, robust to small alignment errors, and yet simpler.
Abstract: Increasingly, machines are interacting with people through human action recognition from video streams. Video data can naturally be represented as a third-order data tensor. Although many tensor-based approaches have been proposed for action recognition, the geometry of the tensor space is seldom regarded as an important aspect. In this paper, we stress that a data tensor is related to a tangent bundle on a special manifold. Using a manifold charting, we can extract discriminating information between actions. Data tensors are first factorized using high-order singular value decomposition, where each factor is projected onto a tangent space and the intrinsic distance is computed from a tangent bundle for action classification. We examine a standard manifold charting and some alternative chartings on special manifolds, particularly, the special orthogonal group, Stiefel manifolds, and Grassmann manifolds. Because the proposed paradigm frames the classification scheme as a nearest neighbor based on the intrinsic distance, prior training is unnecessary. We evaluate our method on three public action databases including the Cambridge gesture, the UMD Keck body gesture, and the UCF sport datasets. The empirical results reveal that our method is highly competitive with the current state-of-the-art methods, robust to small alignment errors, and yet simpler.
56 citations
Posted Content•
TL;DR: For Ricci-flat manifold with Euclidean volume growth, it was shown in this paper that local tangent cones are unique if one tangent cone has a smooth cross-section.
Abstract: We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.
55 citations
TL;DR: This study compute the quasi-periodic attractors together with their stable and tangent bundles and provides numerical evidence that, close to the breakdown, the angle between the invariant bundles has a linear behavior with respect to the perturbing parameter.
Abstract: We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical evidence that, close to the breakdown, the angle between the invariant bundles has a linear behavior with respect to the perturbing parameter. This linear behavior agrees with the universal asymptotics of the general framework of breakdown of hyperbolic quasi-periodic tori in skew product systems.
45 citations
TL;DR: In this paper, the Newmark time stepping methods and finite rotations for nonlinear finite element analysis of flexible beam structures are compared. And the numerical results show that these four formulations have the same numerical accuracy, but that the computational efficiency depends on the choice of the tangent inertia matrix.
45 citations
TL;DR: In this paper, the authors define coherent tangent bundles for wave front topology and geometry, and obtain new Gauss-Bonnet formulas for the third fundamental form of wave front.
Abstract: We give a definition of ‘coherent tangent bundles’, which is an intrinsic formulation of wave fronts. In our application of coherent tangent bundles for wave fronts, the first fundamental forms and the third fundamental forms are considered as induced metrics of certain homomorphisms between vector bundles. They satisfy the completely same conditions, and so can reverse roles with each other. For a given wave front of a 2-manifold, there are two Gauss–Bonnet formulas. By exchanging the roles of the fundamental forms, we get two new additional Gauss–Bonnet formulas for the third fundamental form. Surprisingly, these are different from those for the first fundamental form, and using these four formulas, we get several new results on the topology and geometry of wave fronts.
37 citations
TL;DR: This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints using knot insertion to satisfy constraints.
Abstract: This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.
TL;DR: CAD-inspired hierarchical partition of unity field compositions are extended to modeling explicitly defined enrichments within the isogeometric framework, enabling the modeling of material damage and the efficiency and robustness of distance computations is significantly improved.
TL;DR: In this paper, the authors studied the geometry of projective manifolds whose tangent bundles are nef on sufficiently general curves and showed that manifolds with anticanonical bundles are semi-ample.
Abstract: We study the geometry of projective manifolds whose tangent bundles are nef on sufficiently general curves (i.e. the tangent bundle is generically nef) and show that manifolds whose anticanonical bundles are semi-ample have this property. Furthermore we introduce a notion of sufficient nefness and investigate the relation with manifolds whose anticanonical bundles are nef.
TL;DR: In this paper, an infinite hierarchy of constraints on the body force were investigated, which, if satisfied, sequentially remove discontinuities or singularities in flow derivatives of progressively higher order.
Abstract: In a rotating spherical shell, an inviscid inertia-free flow driven by an arbitrary body force will have cylindrical components that are either discontinuous across, or singular on, the tangent cylinder, the cylinder tangent to the inner core and parallel to the rotation axis. We investigate this problem analytically, and show that there is an infinite hierarchy of constraints on this body force which, if satisfied, sequentially remove discontinuities or singularities in flow derivatives of progressively higher order. By splitting the solution into its equatorial symmetry classes, we are able to provide analytic expressions for the constraints and demonstrate certain inter-relations between them. We show numerically that viscosity smoothes any singularity in the azimuthal flow component into a shear layer, comprising inner and outer layers, either side of the tangent cylinder, of width O(E 2/7) and O(E 1/4), respectively, where E is the Ekman number. The shear appears to scale as O(E −1/3) in the equatorially symmetric case, although in a more complex fashion when considering equatorial antisymmetry, and attains a maximum value in either the inner or outer sublayers depending on equatorial symmetry. In the low-viscosity magnetohydrodynamic system of the Earth's core, magnetic tension within the fluid resists discontinuities in the flow and may dynamically adjust the body force in order that a moderate number of the constraints are satisfied. We speculate that it is violations of these constraints that excites torsional oscillations, magnetohydrodynamic waves that are observed to emanate from the tangent cylinder.
TL;DR: In this article, a two-point self-avoidance energy is defined for all rectifiable curves in ℝn as the double integral along the curve of 1/rq, where r stands for the radius of the (smallest) circle that the tangent to the curve at one point and passes through another point on the curve, with obvious natural modifications of this definition in the exceptional, non-generic cases.
Abstract: We study a two-point self-avoidance energy which is defined for all rectifiable curves in ℝn as the double integral along the curve of 1/rq. Here r stands for the radius of the (smallest) circle that the is tangent to the curve at one point and passes through another point on the curve, with obvious natural modifications of this definition in the exceptional, non-generic cases. It turns out that finiteness of for q ≥ 2 guarantees that γ has no self-intersections or triple junctions and therefore must be homeomorphic to the unit circle 𝕊1 or to a closed interval I. For q > 2 the energy evaluated on curves in ℝ3 turns out to be a knot energy separating different knot types by infinite energy barriers and bounding the number of knot types below a given energy value. We also establish an explicit upper bound on the Hausdorff-distance of two curves in ℝ3 with finite -energy that guarantees that these curves are ambient isotopic. This bound depends only on q and the energy values of the curves. Moreover, for all q that are larger than the critical exponent qcrit = 2, the arclength parametrization of γ is of class C1, 1-2/q, with Holder norm of the unit tangent depending only on q, the length of γ, and the local energy. The exponent 1 - 2/q is optimal.
TL;DR: This study focuses on the use of impulsive control to maintain formation flight in the circular restricted three-body problem and the proposal of a tangent targeting method-based formationkeeping strategy for handling uncertainty introduced by the thrust implementation error.
Abstract: The concept of formation flight of multiple spacecraft, near the libration points of the sun-Earth system, offers many possibilities for space exploration. This study focuses on the use of impulsive control to maintain formation flight in the circular restricted three-body problem. Two specific tasks are accomplished in this paper. First, the tangent targeting method, based on a two-level differential correction, is formulated to fully exploit the predetermined error bound. A comparison between the tangent targeting method and traditional targeting method shows that the number of maneuvers can be significantly reduced and the length of time between successive maneuvers can be greatly increased by using the tangent targetingmethod. The study of the practical convergence of the algorithm is also discussed. The second task is the proposal of a tangent targeting method-based formationkeeping strategy for handling uncertainty introduced by the thrust implementation error. A tradeoff between the formation-keeping accuracy and the number of maneuvers is achieved. Monte Carlo analysis, including 100 trials, demonstrates the effectiveness of this strategy.
TL;DR: A family of Class II RRMF quintics is thereby newly identified, that correspond to the case where a(t),b(t) are linear, and have five degrees of freedom, as with the Class I curves.
TL;DR: In this article, an efficient geometric parameterization technique for the continuation power flow was developed from the observation of the geometrical behavior of load flow solutions, which enables the complete tracing of P-V curves and the computation of maximum loading point of any electric power systems.
Abstract: This paper presents an efficient geometric parameterization technique for the continuation power flow. It was developed from the observation of the geometrical behavior of load flow solutions. The parameterization technique eliminates the singularity of load flow Jacobian matrix and therefore all the consequent problems of ill-conditioning. This is obtained by adding equations lines passing through the points in the plane determined by the loading factor and the total real power losses that is rewritten as a function of the real power generated by the slack bus. An automatic step size control is also provided, which is used when it is necessary. Thus, the resulting method enables the complete tracing of P-V curves and the computation of maximum loading point of any electric power systems. Intending to reduce the CPU time, the effectiveness caused by updating the Jacobian matrix is investigated only when the system undergoes a significant change. Moreover, the tangent and trivial predictors are compared with each other. The robustness and simplicity as well as the simple interpretation of the proposed technique are the highlights of this method. The results obtained for the IEEE 300-bus system and for real large systems show the effectiveness of the proposed method.
16 Jun 2012
TL;DR: An energy-based framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers, which uses higher-dimensional labels that allows modeling curvature with only pair-wise interactions.
Abstract: We propose an energy-based framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined by the tangent planes. In order to avoid the well-known ”shrinking” bias associated with first-order surface regularization, we choose a robust smoothing term that approximates curvature of the underlying surface. In contrast to a number of recent publications estimating curvature using discrete (e.g. binary) labellings with triple-cliques we use higher-dimensional labels that allows modeling curvature with only pair-wise interactions. Hence, many standard optimization algorithms (e.g. message passing, graph cut, etc) can minimize the proposed curvature-based regularization functional. The accuracy of our approach for representing curvature is demonstrated by theoretical and empirical results on synthetic and real data sets from multiview reconstruction and stereo.
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26 Jul 2012
TL;DR: In this article, the authors present an approach for the integration of Equilibrium Equations in the attached and Cartesian coordinate systems, based on the concept of Nondimensional Form of Equations (NFE).
Abstract: 1. Equilibrium Equations.- 1.1 Vector Equilibrium Equations.- 1.1.1 Basic Definitions and Hypothesis.- 1.1.2 Vector Equilibrium Equations.- 1.1.3 Relationship Between the Vectors M and ae.- 1.1.4 Relationship Between the Vectors ae and ?.- 1.1.5 Displacement of an Axial Line.- 1.1.6 Nondimensional Form of Equations.- 1.1.7 Boundary Conditions.- 1.2 External Loads.- 1.2.1 Types of External Loads.- 1.2.2 Increments of External Loads.- 1.3 Equilibrium Equations in the Attached and Cartesian Coordinate Systems.- 1.3.1 Vector Equilibrium Equations in the Attached Coordinate System.- 1.3.2 Equilibrium Equations in the Attached Coordinate Frame.- 1.3.3 Special Cases of Equilibrium Equations in the Attached Coordinate Frame.- 1.3.4 Vector Equilibrium Equations in the Cartesian Coordinate System.- 1.3.5 Equilibrium Equations in the Cartesian Coordinate System.- 1.4 Equilibrium Equations for Small Displacements and Angles of Rotation.- 1.4.1 Equilibrium Equations in the Attached Coordinate System.- 1.4.2 Equilibrium Equations of the Zeroth Approximation in the Attached Basis.- 1.4.3 Equilibrium Equations of the Zeroth Approximation in the Cartesian Coordinate System.- 1.4.4 Increments of External Loads.- 1.4.5 Equilibrium Equations of the First Approximation in the Attached Coordinate System.- 1.5 Problems.- 2. Integration of Equilibrium Equations.- 2.1 Integration of Linear Equilibrium Equations.- 2.1.1 Equilibrium Equations of the Zeroth Approximation.- 2.1.2 Picard Iteration Method for Determination of the Fundamental Matrix K (?).- 2.2 Equilibrium Equations for Rods with Lateral Supports.- 2.2.1 Rods with Lateral Hinge Supports.- 2.2.2 Rods with Lateral Elastic Supports.- 2.2.3 Rods with Predetermined Displacement of Some Cross Sections.- 2.3 Method of Step-by-Step Loading.- 2.3.1 Equilibrium Equations for One Step of Loading.- 2.3.2 Integration of the Equilibrium Equations.- 2.3.3 Method of Successive Approximations.- 3. Static Stability of Rods.- 3.1 Basic Concepts.- 3.1.1 State of Equilibrium.- 3.1.2 Examples.- 3.2 Equilibrium Equations for a Rod After Loss of Stability.- 3.2.1 Vector Equilibrium Equations in the Attached Coordinate System.- 3.2.2 Increments of Forces and Moments.- 3.2.3 Equations in the Form Suitable for Integration.- 3.3 Plane Curvilinear Rods.- 3.3.1 Rods of Plane Axial Line Before Loss of Stability.- 3.3.2 Stability of Plane Configuration of a Ring.- 3.3.3 Stability of a Plane Configuration of a Rod with Lateral Supports.- 3.4 Increments of Loads at Loss of Stability.- 3.4.1 Forces Directed at a Fixed Point.- 3.4.2 Forces Which Follow a Straight Line.- 3.4.3 Increments of Concentrated Forces Which Follow a Straight Line: Small Deflections of a Rod.- 3.4.4 Increments of Concentrated Forces Directed at a Fixed Point: Large Deflections of a Rod.- 3.4.5 Increments of Concentrated Forces Directed at a Fixed Point: Small Deflections of a Rod.- 3.5 Computer-Oriented Methods.- 3.5.1 Natural and Critical Configurations Coincide.- 3.5.2 Natural and Critical Configurations Differ.- 3.5.3 Concentrated Loads Applied to Arbitrary Cross Sections: Determination of Critical Loads..- 3.6 Problems.- 4. Straight Rods.- 4.1 Rods of Straight Natural Configuration.- 4.1.1 Traditional Routines of Derivation of Equilibrium Equations.- 4.1.2 General Equilibrium Equations in the Case of Straight Rods.- 4.2 Equilibrium Equations for Small Displacements and Angles of Rotation.- 4.2.1 Vector Equations.- 4.2.2 Equilibrium Equations in the Attached Coordinate System.- 4.2.3 Equilibrium Equations in the Cartesian Coordinate System.- 4.3 Naturally Twisted Straight Rods.- 4.3.1 Nonlinear Vector Equations of Equilibrium.- 4.3.2 Linear Vector Equations of Equilibrium.- 4.3.3 Equilibrium Equations in the Attached Coordinate System.- 4.4 Straight Rods on Elastic Foundation.- 4.4.1 Forces Acting on a Rod.- 4.4.2 Equilibrium Equations.- 4.4.3 Krylov's Functions.- 4.4.4 Equilibrium Equations for Rods of Constant Cross Section.- 4.4.5 Equilibrium Equations for Rods with Lateral Supports.- 4.4.6 Equilibrium Equations for Rods of Varying Cross Section.- 4.5 Application of Approximate Methods.- 4.5.1 Principle of Virtual Displacements.- 4.5.2 Principle of Minimum of Potential Energy.- 4.5.3 Ritz Method.- 4.5.4 Approximating Methods Based on Lagrangian Multipliers.- 4.6 Stability of Compressed-Twisted Rods.- 4.7 Stability of Straight Rods with Local Constraints.- 4.8 Problems.- 5. Curvilinear Rods.- 5.1 Plane Rods.- 5.1.1 Equilibrium Equations for a Rod Whose Axial Line Remains a Plane Curve During Deformation.- 5.1.2 Nonlinear Equilibrium Equations in the Cartesian Coordinate System.- 5.1.3 Equilibrium Equations for a Rod Whose Axial Line is a Spatial Curve in a Deformed Configuration.- 5.1.4 Equilibrium Equations in the Case of Small Displacement of Axial Points.- 5.2 Elementary Theory of Cylindrical Springs.- 5.2.1 Helical Rods.- 5.2.2 Linear Theory of Cylindrical Springs.- 5.2.3 Basics of Nonlinear Theory of Cylindrical Springs.- 5.3 General Theory of Cylindrical Springs.- 5.3.1 Linear Equilibrium Equations.- 5.3.2 Cylindrical Springs of Variable Angle of Helix.- 5.4 Flexible Rods in a Rigid Conduit.- 5.4.1 Statement of the Problem.- 5.4.2 Equilibrium Equations.- 5.4.3 Equilibrium Equations for Friction-Free Case.- 5.4.4 Specialization of Equilibrium Equations (5.151) for Rods of Different Bending Stiffnesses (A22 ? A33).- 5.4.5 Specialization of Equilibrium Equations for Rods with Equal Bending Stiffnesses (A22 = A33).- 5.4.6 Determination of Twisting Moments for Rods with Equal Bending Stiffnesses (A22 = A33).- 5.5 Stability of Plane Curvilinear Rods.- 5.6 Problems.- 6. Rods Interacting with Liquid or Air Flows.- 6.1 Introduction.- 6.2 Basic Concepts of Aerohydrodynamics.- 6.2.1 Eulerian and Lagrangian Representations.- 6.2.2 Basic Principles of Aerodynamics.- 6.3 Experimental Results.- 6.4 Aerodynamic Forces Acting on Rods of Circular Cross Section.- 6.5 Stress-Strain State of a Rod Interacting with an Air Flow.- 6.6 Aerodynamic Forces Acting on Rods of Noncircular Cross Section.- 6.6.1 Components of qn1 and q1 in the Cartesian Coordinate System.- 6.6.2 Components of qn1, and q1 in the Attached Coordinate System.- 6.7 Increments of Aerodynamic Forces at Small Displacements of Axial Points.- 6.7.1 Rods of Noncircular Cross Section.- 6.8 Rods Containing Internal Liquid Flows.- A. Appendices.- A.1 Elements of Vector Algebra.- A.1.1 Vector Bases Coordinates of Vectors.- A.1.2 Scalar Product.- A.1.3 Vector Product.- A.1.4 Scalar Triple Product.- A.1.5 Vector Triple Product.- A.1.6 Transformation of Base Vectors.- A.2 Basics of Differential Geometry.- A.2.1 The Derivative of a Radius Vector.- A.2.2 Spatial Curves.- A.2.3 Derivatives of the Base Vectors.- A.2.4 Geometrical Meaning of the Components of the Vector ae.- A.2.6 Derivatives of a Vector in the Attached Coordinate System.- A.3 Increments of the Components of a Vector under Transformation of the Attached Coordinate System.- A.4 Distributions.- A.4.1 The ?-function.- A.4.2 The Nondimensional ?-function.- A.4.3 The Heaviside Function.- A.4.4 Applications of the ?-function.- A.4.5 Integrals Containing Derivatives of the ?-function.- A.5 Direction Cosines of the Unit Vector Tangent to a Rod Axis.- A.5.1 Plane Curve.- A.5.2 Spatial Curve.- A.6 Equations of the First and Higher Approximation.- B. Solution of the Problems.- B.1 To Chapter 1.- B.2 To Chapter 3.- B.3 To Chapter 4.- B.4 To Chapter 5.- References.
TL;DR: In this article, the authors presented an analytical study of the two-body tangent orbit technique by providing solution-existence conditions, where the flight-direction angle was used to describe and solve this problem.
Abstract: This paper presents an analytical study of the two-body tangent orbit technique by providing solution-existence conditions. The flight-direction angle is used to describe and solve this problem. Closed-form solutions are obtained for three classic problems: specified arrival flight-direction angle, specified departure flight-direction angle, and cotangent transfers. Not all of the problems admit solutions; thus, closed-form conditions for solution existence are provided by imposing a positive semilatus rectum constraint and a negative transfer-orbit energy (elliptic orbit transfer) constraint. The final solution-existence condition is then provided in terms of the true anomaly range for initial or final orbit. The singularity problem of 180 deg orbit transfer is also analyzed. Several examples are provided to verify the proposed analytical methods.
01 May 2012
TL;DR: Global geometric estimators of area, length, moments, as well as local geometric estimator of tangent and curvature are presented, and their multigrid convergence is studied, a fundamental property which guarantees that the estimation tends toward the exact one as the sampling resolution gets finer and finer.
Abstract: The analysis of digital shapes requires tools to determine accurately their geometric characteristics. Their boundary is by essence discrete and is seen by continuous geometry as a jagged continuous curve, either straight or not derivable. Discrete geometric estimators are specific tools designed to determine geometric information on such curves. We present here global geometric estimators of area, length, moments, as well as local geometric estimators of tangent and curvature. We further study their multigrid convergence, a fundamental property which guarantees that the estimation tends toward the exact one as the sampling resolution gets finer and finer. Known theorems on multigrid convergence are summarized. A representative subsets of estimators have been implemented in a common framework (the library DGtal), and have been experimentally evaluated for several classes of shapes. Thus, the interested users have all the information for choosing the best adapted estimators to their applications, and readily dispose of an efficient implementation.
01 May 2012
TL;DR: This work provides the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner, and introduces advected stream lines as a parameter‐free variant of the time line metaphor.
Abstract: We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines. © 2012 Wiley Periodicals, Inc.
TL;DR: A new operator for detecting step edges is developed, which outperforms the existing edge detectors in terms of feature preservation and edge localization and can produce more attractive and impressive line illustrations with a variety of photographs.
TL;DR: Enough conditions are derived for a convergent interpolatory planar subdivision scheme to produce tangent continuous limit curves and these conditions as well as the proofs are purely geometric and do not rely on any parameterization.
TL;DR: In this paper, the peristaltic flow of a magnetohydrodynamic (MHD) Tangent hyperbolic fluid in an inclined asymmetric channel is investigated, and the governing equations for the proposed fluid model are derived in Cartesian coordinates system.
Abstract: The peristaltic flow of a magnetohydrodynamic (MHD) Tangent hyperbolic fluid in an inclined asymmetric channel is investigated. The governing equations for the proposed fluid model are derived in Cartesian coordinates system. Simultaneous effects of slip and heat transfer have been taken into account for the present analysis. Regular perturbation method is utilised to get the solutions for stream function, temperature, pressure gradient and heat transfer coefficients. The present solutions are compared with the existing work and comparison is shown through table. The presented graphical results analyse the variations of embedded parameters into the flow system.
TL;DR: In this article, the influence of highway geometric characteristics on capacity at tangents and horizontal curves as well as on capacity loss at the change from tangent to curve was assessed, and regression analysis was used to investigate the relationships between geometric characteristics and capacity.
TL;DR: In this article, the authors studied the geometry of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view.
Abstract: We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our field and show, as it is the case in the real setting, that, up to some multiplicities, the local density may be computed on this distinguished tangent cone. We also prove that these distinguished tangent cones stabilize for small enough subgroups. We finally obtain the p-adic counterpart of the Cauchy-Crofton formula for the density. To prove these results we use the Lipschitz decomposition of definable p-adic sets of (5) and prove here the genericity of the regularity conditions for stratification such as .wf/, .w/, .af/, .b/ and .a/ conditions. Mathematics Subject Classification (2010). Primary 03C10, 03C98, 12J10, 14B05, 32Sxx; Secondary 03C68, 11S80 14J17.
TL;DR: In this article, the authors presented an approach to modal analysis where the linear structural model is extracted directly from BHawC using the tangent system matrices when the turbine is in a steady state.
Abstract: The aeroelastic code BHawC for calculation of the dynamic response of a wind turbine uses a non-linear finite element formulation. Most wind turbine stability tools for calculation of the aeroelastic modes are, however, based on separate linearized models. This paper presents an approach to modal analysis where the linear structural model is extracted directly from BHawC using the tangent system matrices when the turbine is in a steady state. A purely structural modal analysis of the periodic system for an isotropic rotor operating at a stationary steady state was performed by eigenvalue analysis after describing the rotor degrees of freedom in the inertial frame with the Coleman transformation. For general anisotropic systems, implicit Floquet analysis, which is less computationally intensive than classical Floquet analysis, was used to extract the least damped modes. Both methods were applied to a model of a three-bladed 2.3 MW Siemens wind turbine model. Frequencies matched individually and with a modal identification on time simulations with the non-linear model. The implicit Floquet analysis performed for an anisotropic system in a periodic steady state showed that the response of a single mode contains multiple harmonic components differing in frequency by the rotor speed. Copyright © 2011 John Wiley & Sons, Ltd.
TL;DR: A remarkable and elementary fact that a locally compact set F of Euclidean space is a smooth manifold if (and only if) the lower and upper paratangent cones to F coincide at every point, is proved as mentioned in this paper.