Envelope Of Surfaces Research Articles

Investigating the relationship between surface roughness and reflectance properties of building materials

Materials used in the exterior envelope of buildings and open urban surfaces, in general, strongly affect the urban thermal balance, determining the general magnitude of urban overheating. The surface temperature of reflective materials varies as a function of physical and geometrical properties. Quantifying the influence of surface roughness on reflectance properties has crucial relevance since reflectance can significantly affect the reduction of the absorbed solar radiation and, in turn, the energy demand for cooling. Through an experimental and statistical investigation, this research aims to analytically assess the impact of surface roughness on the reflectance and thermal performances of building materials and, in turn, the role that roughness could play towards urban cooling and mitigation. Results show that the surface’s different roughness affects the sample’s reflectance coefficient, leaving it basically unchanged in the Ultraviolet and Visible ranges but with appreciable differences in the Near-Infrared wavelengths. This outcome confirms the correlation between the surface roughness and the optical and thermal characteristics of the building materials, making evident the importance of the study of superficial topography towards the mitigation of Urban Heat Island phenomena.

Mechanical response of AZ31B magnesium alloy: Experimental characterization and material modeling considering proportional loading at room temperature

Tension and compression experiments have been performed to characterize the mechanical response of 1.57mm AZ31B-O sheet at room temperature. Five different sheet orientations were used to characterize the in-plane anisotropy under tensile loading conditions while cubic samples consisting of adhesively-bonded layers of sheet samples were used for compression testing along four sheet directions. During uniaxial tensile testing, the axial and transverse strain components were measured using two independent extensometers. A digital image correlation system was used to measure the strain components during compression testing. Both instantaneous and cumulative r-values were measured as they evolved with plastic strain. A strong, evolving asymmetry is observed. An evolving anisotropic/asymmetric continuum-based material model based on a Cazacu–Plunkett–Barlat (CPB)-type yield function is proposed to fit the material behavior as a continuous function of plastic strain. Considerable improvement in the representation of the material behavior is achieved as the number of stress transformations used in the CPB yield surface formulation is increased. To capture the evolution of the envelope of the subsequent yield surfaces, the anisotropy and asymmetry parameters are replaced with functions expressed in terms of plastic strain. The evolution parameters are found by minimizing the difference between the model predictions and the experiments at discrete plastic strain levels, using gradient search methods. A strain rate-independent elastic–plastic material model incorporating the evolving envelope of subsequent yield surface formulation has been developed and implemented within a commercial finite element package. The model reproduces the experiments initially used for fitting. The predictions of the developed material model are compared with the measured load–displacement and strain distributions from a three-point bending experiment. Improvement in the prediction of strain and forming forces is observed compared to the previously available non-evolving material models.

Envelopes and nonconvex Hamilton–Jacobi equations

This paper introduces a new representation formula for viscosity solutions of nonconvex Hamilton–Jacobi PDE using “generalized envelopes” of affine solutions. We study as well envelope and singular characteristic constructions of equivocal surfaces and discuss also differential game theoretic interpretations. In memory of Arik A. Melikyan.

Foreword

In the last years, the field of non-linear Computational Geometry has produced very relevant algorithmic advances, for instance, by adapting to low-degree curved objects techniques dealing with linear primitives. Moreover the introduction of new algorithms and approaches for dealing efficiently with curves and surfaces has shown a considerable impact in fields such as Computer-Aided Design where final users are continuously demanding more efficiency, accuracy, robustness, etc. New approaches for solving geometric problems, coming from Computer-Aided Geometric Design and involving curves and surfaces with a Computational Geometry flavour is the main focus of this special issue. Contributions were asked in areas such as: arrangements of low degree curves and surfaces; Voronoi diagrams and medial axes involving curved ob jects; offset computations and their topology; distance predicates for curves and surfaces; closed formulae for geometric queries involving curves and surfaces; intersection detection for moving curved ob jects; adapting algebraic or geometrical techniques for solving algorithmic problems involving curves and surfaces. This special issue is a direct consequence of the Second International Conference on Mathematical Aspects of Computer and Information Sciences - MACIS 2007 (see http:// www- spiral.lip6.fr/ MACIS2007) held in Paris in December 2007 and where Computational Geometry and Computer Aided Geometric Design were one of the main topics (among other two, Polynomial System Solving and Algorithms and Complexity). Finally six papers (out of eight papers submitted by the March 2009 deadline) were finally accepted. The two papers by C. D'Andrea et al. and I. Z. Emiris et al. deal with the problem of analyzing the Newton polygon of the implicit equation of a rational curve starting from its parameterization: both papers are devoted to study from different viewpoints the properties of the set of monomials appearing in the implicit equation of the considered curve without computing it. The two papers by E. Berberich et al. introduce a new approach to deal with the problem of determining the shape of an arrangement of curves on several classes of parametric surfaces which is then applied to compute, for example, the Minkowski sum of polytopes or the envelope of surfaces. The two papers by D. Lazard and J. Cheng et al. deal with the problem of computing the topology of a semialgebraic set (i.e. a set in $\mathbb{R}^n$ defined by polynomial equations and inequations): the first one shows how to deal with the general case by using the so called Cylindrical Algebraic Decomposition and the second one introduces an extremely fast algorithm computing the topology of a real algebraic plane curve defined implicitely. We would like finally to thank all the reviewers who definitively helped with their work to improve the papers that appear into this special issue.

Arrangements on Parametric Surfaces II: Concretizations and Applications

We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arrangements embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The fundamentals of the framework are described in a companion paper. Our work covers arrangements embedded on elliptic quadrics and cyclides induced by intersections with other algebraic surfaces, and a specialized case of arrangements induced by arcs of great circles embedded on the sphere. We also demonstrate how such arrangements can be used to accomplish various geometric tasks efficiently, such as computing the Minkowski sums of polytopes, the envelope of surfaces, and Voronoi diagrams embedded on parametric surfaces. We do not assume general position. Namely, we handle degenerate input, and produce exact results in all cases. Our implementation is realized using Cgal and, in particular, the package that provides the underlying framework. We have conducted experiments on various data sets, and documented the practical efficiency of our approach.

Unification of single‐configuration seismic imaging processes

ABSTRACTIn this paper we derive an integral formula that encompasses all linear processes on seismic data. These include migration, demigration and residual migration, as well as data mapping procedures such as transformation to zero offset, inverse transformation to zero offset, residual transformation to zero offset and offset continuation. The derivation of the equation is different from all previous approaches to unification. Here we do not use a cascaded operation between two operators, but rather the superposition principle. In this regard, the derivation is not only more fundamental, but also simpler and more general. We study the kinematics and the dynamics of these processes and show that the signals can be reconstructed asymptotically either by finding the envelope of particular surfaces or by stacking energy along “adjoint” surfaces. For example, in the case of migration, the first set of surfaces are isochrons, while the “adjoint” surfaces are diffraction responses. In practice, the distinction between these two types of surfaces is equivalent to choosing the order of the computational loops with regard to the input and output seismic traces.

The Area Method for Phase Stability Analysis Revisited: Further Developments. Formulation in Terms of the Convex Envelope of Thermodynamic Surfaces

The Area method for phase stability analysis is re-examined from the viewpoint of the topology of thermodynamic surfaces. A new generalization of the Area method objective function and the maximum area criterion is proposed in terms of the convex envelope of thermodynamic surfaces. Several special cases for two-component, single- and two-phase systems are analyzed and the results generalized to hypersurfaces, characteristic of the Gibbs energy of multicomponent, multiphase systems. It is shown conclusively that the area (or more generally hypervolume) between the free energy hypersurface and a hyperplane that intersects the hypersurface is maximal when the hyperplane coincides with the convex envelope of the hypersurface. Extension of the maximum area criterion to four basic thermodynamic surfaces for pure fluids and mixtures is discussed. The authors believe the approach adopted here sets the Area method on secure theoretical foundations, answers criticisms concerning its validity, and will stimulate fresh research.

Quantum Computation in Computational Geometry

Next, as a showcase problem of our approach, we consider the problem of finding the lowest point in the intersection of n upper-halfspaces in the d-dimensional Euclidean space. The problem can be solved in �(n) time if d is a constant in RAM model. Regarding the problem as a parametric minimax problem [2], and by combining the quantum minimum finding algorithm and multidimensional searching technique, we can solve it in O( p nlog 2d 1 n) time. Then, we show some other geometric optimization problems such as the minimum enclosing ball problem and linear programming problems can be solved efficiently in quantum model if d is a constant. We can regard the minimum enclosing ball problem as a minimization of the parametric farthest-neighbor-query problem [2]; in other words, it is computation of the lowest point in the upper envelope of surfaces defined from the distance functions from points. Then it can be solved in O( p nlog 2d+1 n) time. Also, some output-sensitive convex-hull algorithms and the ellipsoid algorithm for solving a general dimensional convex programming problem can be accelerated by using the quantum model.

Interpreting a conformally flat pure radiation spacetime

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak-field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.

Getting around a lower bound for the minimum Hausdorff distance

We consider the following geometric pattern matching problem: find the minimum Hausdorff distance between two point sets under translation with L 1 or L ∞ as the underlying metric. Huttenlocher, Kedem and Sharir have shown that this minimum distance can be found by constructing the upper envelope of certain Voronoi surfaces. Further, they show that if the two sets are each of cardinality n then the complexity of the upper envelope of such surfaces is Ω(n 3) . We examine the question of whether one can get around this cubic lower bound, and show that under the L 1 and L ∞ metrics, the time to compute the minimum Hausdorff distance between two point sets is O( n 2log 2 n).

The upper envelope of voronoi surfaces and its applications

Given a setS ofsources (points or segments) in ?211C;d, we consider the surface in ?211C;d+1 that is the graph of the functiond(x)=minp?S?(x, p) for some metric?. This surface is closely related to the Voronoi diagram, Vor(S), ofS under the metric?. The upper envelope of a set of theseVoronoi surfaces, each defined for a different set of sources, can be used to solve the problem of finding the minimum Hausdorff distance between two sets of points or line segments under translation. We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the problems of finding the minimum Hausdorff distance under translation, between sets of points and segments.

THREE‐DIMENSIONAL KINEMATIC MIGRATION IN VARIABLE VELOCITY MEDIA*

ABSTRACTA three‐dimensional (3‐D) kinematic migration algorithm for media in which migration velocity varies linearly with depth is developed, implemented and tested. The algorithm is based on the concept that a single reflection or diffraction in a (zero‐ or finite‐offset) trace may have originated at any point on a constant traveltime surface within the Earth defined by the observed two‐way traveltime. The envelope of all such constant time surfaces, for all observed reflections and diffractions produced by one reflector, is the desired migrated 3‐D image. The optimal envelope position in depth is determined, beneath each point on a regular grid, by a statistical imaging condition; an incremental function of depth containing the number of constant time surfaces passing through that depth increment is cross‐correlated with a Gaussian function whose width is chosen to correspond to the vertical scale of the features of interest.The numerical procedures are based on the observation that, in a medium in which velocity varies linearly with depth, ray segments are circular so traveltimes can be computed analytically. Also, traveltimes are independent of azimuth so the 3‐D problem can be collapsed into an equivalent 2‐D problem.The algorithm is illustrated and tested by application to synthetic data and to scale‐model data from the Seismic Acoustics Laboratory at the University of Houston.

Über die Enveloppe von Zylinderflächen konstanter Breite

Über die Enveloppe von Zylinderflächen konstanter Breite

Über das Volumen des Körpers, dessen Randfläche die Enveloppe einer einparametrigen Familie von konvexen Zylinderflächen ist

Über das Volumen des Körpers, dessen Randfläche die Enveloppe einer einparametrigen Familie von konvexen Zylinderflächen ist