Query processing of geometric objects with free form boundaries in spatial databases

Bezier and B-spline curves are among the most powerful tools used for complex graphical approximation. In this paper, we will use them to recreate the hydrographic map of the Republic of Macedonia. The results obtained in this paper show that cubic spline curves have smaller average deviation in respect to B-spline curves, in contrast to Bezier curves. The results and the images are obtained by using the software package Wolfram Mathematica. Key words: Bezier curves; B-spline; cubic spline REFERENCES [1] Vera B. Anand: Computer Graphics and Geometric Modeling for Engineers, John Wiley & Sons Inc. 1996. [2] V. Andova, S. Atanasova, K. Bacev, Gj. Peev, G.Kostov: Approximation of map borders using Mathematica, ETAI (2015). [3] R. H. Bartels, J. C. Beatty, B. A. Barsky: An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann Publishers Inc. 1987. [4] R. C. Beach: An Introduction to the Curves and Surfaces of Computer-Aided Design, Van Nostrand Reinhold, 1991. [5] E. Cohen: Discrete B-splines and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics, International Association for Bridge and Structural Engineering, 1979. [6] C. De Boor: A Practical Guide to Splines, Revised Edition, Springer, 1978. [7] G. Farin: Curves and Surfaces for CAGD. A Practical Guide, fifth edition, Academic Press, 2002. [8] G. Farin, J. Hoschek, M.-S. Kim: Handbook of Computer Aided Geometric Design, Elsevier, 2002. [9] G. Farin: NURBS: From Projective Geometry to Practical Use, 2nd edition, AK Peters, 1999. [10] J. Fiorot, P. Jeannin: Rational Curves and Surfaces, Wiley, 1992. [11] J. Gallier: Curves and Surfaces. In: Geometric Modeling:Theory and Algorithms, Morgan Kofman Publishers,2000. [12] G. G. Lorentz: Bernstein Polynomials, University of Toronto Press, 1953. [13] R. F. Riesenfeld: Applications of B-spline Approximation to Geometric Problems of Computer-Aided Design, Syracuse University, 1973. [14] D. Rogers: An Introduction to NURBS with Historical Perspective, Elsevier, 2001. [15] W. Rudin: Real and Complex Analysis, McGraw-Hill Higher Education, 1986. [16] D. Salomon: Curves and Surfaces for Computer Graphic, Springer, 2006. [17] S. Wagon: Mathematica in Action Problem Solving Through Visualization and Computation, Springer, 2010. [18] S. Wolfram: The Mathematica Book, Fifth Edition, Wolfram Media, 2003.

Nowadays, with the advancement of database information technology, databases has led to large-scale distributed databases. According to this study, database management systems are improved and optimized so that they provide responses to customer questions with lower cost. Query processing in database management systems is one of the important topics that grabs attentions. Until now, many techniques have been implemented for query processing in database system. The purpose of these methods is to optimize query processing in the database. The main topics that is interested in query processing in the database makes run-time adjustments of processing or summarizing topics by using the new approaches. The aim of this research is to optimize processing in the database by using adaptive methods. Ant Colony Algorithm (ACO) is used for solving optimization problems. ACO relies on the created pheromone to select the optimal solution. In this article, in order to make adaptive hybrid query processing. The proposed algorithm is fundamentally divided into three parts: separator, replacement policy, and query similarity detector. In order to improve the optimization and frequent adaption and correct selection in queries, the Ant Colony Algorithm has been applied in this research. In this algorithm, based on Versatility (adaptability) scheduling, Queries sent to the database have been attempted be collected. The simulation results of this method demonstrate that reduce spending time in the database. According to the proposed algorithm, one of the advantages of this method is to identify frequent queries in high traffic times and minimize the time and the execution time. This optimization method reduces the system load during high traffic load times for adaptive query Processing and generally reduces the execution runtime and aiming to minimize cost. The rate of reduction of query cost in the database with this method is 2.7%. Due to the versatility of high-cost queries, this improvement is manifested in high traffic times. In the future Studies, by adapting new system development methods, distributed databases can be optimized.

Temporal databases and data warehouses are essential components of intelligent information systems in cyberworlds. We describe a geometric model for querying time-dependent data in databases and warehouses. An implementation and application of the model for querying of results of numerical simulation in molecular dynamics is discussed. Data are interpreted geometrically as multidimensional points with time dimension. A geometric query is a query solid of any shape specified by its parameters, location and time. These queries are formulated with geometric objects and operations over them to form the query solid. The geometric objects and operations are described with implicit functions. With the uniform geometric model for querying time-dependent data, 3D visualization tools can be naturally incorporated into the molecular dynamics visualization system to pose the queries.

A bi-level object-oriented data model together with a user query language called OFQL is designed which can support applications like GIS (geographic information systems). The data model is divided into two layers, the higher-level data model and the lower-level data model. The higher-level data model or the geographic object data model primarily consists of the geographic objects and a set of semantic spatial functions through which the topological relationships of the geographic objects are defined or derived. The lower-level data model or the geometric object data model has geometric objects which are the actual spatial representations of the geographic objects in the higher-level data model. It also has a set of geometric functions that retrieve, manipulate, and compute for geometric objects. The general architecture of a GIS system using this data modeling approach consists of two modules: the query processor and the function implementor. With the OFQL user-interface, the user is able to pose queries of a geographic nature without knowing the details of the spatial representation and computation of the geographic objects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper has been considered the main content and distinctive features of the “Geometric Modeling” training course for the “Mathematics and Computer Science” training program 02.03.01 (“Mathematical and Computer Modeling” specialization).&#x0D; The goal of the “Geometric Modeling” course study is the assimilation of mathematical methods for construction of geometric objects with complex curved shapes, and techniques for their computer visualization by using polygons of curves and surfaces. Methods for construction of structures’ curved shapes using spline representations, as well as techniques for construction of surfaces and volumetric geometries using motion operations and basic logical operations on geometric objects are considered. The spline representations include linear and bilinear splines, Hermite cubic splines and Hermite surfaces, natural cubic and bicubic interpolation splines, Bezier curves and surfaces, rational Bezier splines, B-splines and B-spline surfaces, NURBS-curves and NURBS-surfaces, transfinite interpolation methods, and splines of surfaces with triangular form. Logical operations for intersection of two spline curves, and intersection of two parametric surfaces are considered. The principles of scientific visualization and computer animation are considered in this course as well.&#x0D; Some examples for visualization of initial data and results of curves and surfaces construction in two- and three-dimensional spaces through the software shell developed by authors and used by students while doing tests have been demonstrated. The software shell has a web interface with the WebGL library graphic support. Tasks for four practical studies in a computer classroom, as well as several variations of homework are represented.&#x0D; The problems occurring in preparation materials for some course sections are discussed, as well as the practical importance of acquired knowledge for the further progress of students.&#x0D; The paper may be interesting for teachers of “Geometric Modeling” and “Computer Graphics” courses aimed to students with a specialization in mathematics and information, as well as to those who independently develop software interfaces for algorithms of geometric modeling.

Multiple Representation, Multiple Definition and Object Oriented Representation

The similarity ainong elemcnts emerges naturally as the most adequate to ask about complex data (such as, multimdia and genomic sequenees among others). There are two basie similarity queries: Range Query and k-Nearest Neighbor Query. The increasing volume of complex data stored in Database Management Systems (DBMS), makes it neeessary to provide support for these data tvpes. One way to support complex data types in current DBMS is to include similarity queries in its query processor, and consequently, in the relational algebra. This fact leacls to produce ways to express such queries in the DBMS language as predicates in select operations. As a consequence, the two basic similarity queries cari be combined in more complex expressions involving boolean conjunctions and disjunctions among them, i.e., complex similarity queries. However, for complex similarity queries to be processed efhciently in a DBMS, it is neeessary to provide support in the optimization and runtime laycrs of the; query proeessing. There are many works involving the development, of algorithms to ariswer specific and simple similarity query whereas there is not a generic algorithm efficiently able to handle complex similarity queries. Furthermore, the similarity query optimization is a topic not frequently explored in the literature. This work establishes a structured rnethod 011 how to analyze complex similarity queries. This method is used to extend the relational algebra through algebraic rules and to determine a small set of algorithms that can be used to answer any complex similarity query. In addition, the proposed method makes it possible to formalize rules for selectivity estimai,ion of these. queries thus assisting cost estimation. To validate the concepts presented, exjjeriments are being performed on real and synthetic data sets that highlight meaningful results. The algebraic rules. algorithms and metrics to est-imate the selectivity can be employed in the optimization process of a DBMS in order to derive efficient complex similarity query execution plans. Therefore, this work deals with essential poiuts that enable the practical use of similarity (jueries in Relational Database Management Systems.

Spatial query processing using a spatial access method (SAM) faces the problem of having to examine a large number of candidate objects during the CPU-time intensive refinement step. This is due to the minimum bounding rectangle (MBR) filter in the first step of query processing which is rough by nature. In order to overcome this problem, the multi-step filtering method that takes a series of spatial filters with higher filtering ratios than that of the MBR in a cascade fashion for the object set already filtered by an MBR has been introduced. Most of the spatial filters were only able to manage areal objects. In this paper, we propose the minimum maximum points (MMP) filter, a spatial filter that can manage not only areal objects but also linear objects. In addition, we propose a multi-step filtering processor using the MMP filter, which is designed for the well-known spatial operator respectively. We also show the superiority of our multistep filtering by extensive experiments.

We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P=NP, it is not possible to get Fully Polynomial Time Approximation Algorithms (FPTAS) for such problems. We give the first PTAS for this problem when the geometric objects are half-spaces in Re3 and when they are an r-admissible set regions in the plane (this includes pseudo-disks as they are 2-admissible). Quite surprisingly, our algorithm is a very simple local search algorithm which iterates over local improvements only.

Database management systems have become the most important process since millions and billions of data transactions taking place every second. It comes as surprise that database optimization and tuning has become the main key research. If the database processes are not handled properly, it will lead to a slow system and it might cause a lot of errors and there is a possibility for the system to crash. Since database main task is storing and accessing the data according to the user needs through SQL operations, therefore there is a need to optimize the database operations by reducing their response times. There are many ways to optimize database operations, but among those; database tuning seems the most challenging area. There are many studies done on the improvement of database tuning approach however they are still suffer from a slow query processing time. Factors causing slow processing time normally are due to small-shared pool size and improper execution plans used during queries. This study focused on improving database indexing to overcome these two factors. A combination of clustered index, non-clustered index and bitmap is proposed as an integrated approach in query processing. These combinations of indexes are tested using complex and simple queries. The results of this experiment are being compared with the result from the existing indexing approaches when using the same datasets. The result shows that these combinations are able to optimize the database systems. The proposed solution able to provide a database system that is fast in data retrieval and an improved performance percentage of 10&#x0025; to 20&#x0025; depending on the query, and the dataset used. Indirectly, this proposed solution enables companies&#x0027; database systems to achieve its highest potential with maximum performance.

This study examines the performance of a bio-inspired micro-air vehicle’s wing planforms at a low Reynolds number. The shape of the manta ray’s wing was extracted from the real image of a manta ray and a B-spline curve was generated. The Zimmerman planform was taken as the base for the model. Using Bezier curve, the planform was extended on the sides to create two models with differing curvatures which were named Manta A and Manta B. Numerical simulations were conducted using ANSYS FLUENT 15.0 at a Reynolds number of 1×105, and the aerodynamic characteristics of the planforms were studied. It was clear from the results that the manta ray-inspired planforms provided better lift characteristics at all angles of attack between 0° and 20° when compared to the base Zimmerman planform. It can also be observed that both the manta planforms provide better CL/CD ratios by around 11–23% between angles of attack 10° and 20°.

Closed (C 2- and C 3-continuous) Bézier and B-spline curves with given tangent polygons

A new curve matching method is proposed to generate non-self-intersecting and non-twisted ruled layers for application in diverse fields such as layered manufacturing, offsetting and multi-axis CNC machining. The method establishes point-to-point correspondence represented by a set of ruling lines between two directrices of the ruled surface. The directrices are given as non-self-intersecting, closed, at least C1 continuous, planar, B-spline curves. To match the points on the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the ruling lines and minimize the sum of the lengths of connecting ruling lines. The generated ruling lines can be used as cutter location data for multi-axis NC machining of ruled surfaces. Moreover, by subdividing the ruling lines into equal number of segments, one can construct a series of intermediate piecewise linear curves that represent the metamorphosis between the directrices. Implementation and examples are also presented.

The upcoming generation of computer hardware poses several new challenges for database developers and engineers. Software in general and database management systems (DBMSs) in particular will no longer benefit from performance gains of future hardware due to increase clock speed, as it was the case for the last 35 years; instead, the number of cores per CPU will increase steadily. Today’s approach is to run each query on a single core or only a few different cores using parallel query execution. This approach suffers from several problems (e.g. contention problem) and therefore leads to poor speed up and scale up behavior. These observations open several important research questions on how to use the new multi-core CPU architecture for improving the overall performance of DBMSs. This paper outlines our approach for query processing on multi-core CPU architectures. We present an abstract architecture view for multi-core CPUs, meta operators to control and to interact with the hardware, and a new query operator model that makes use of the meta operators to control the parallel execution of a query over different cores. We illustrate how each of these parts fits in our framework for query processing on multi-core architectures.

An algorithm that creates planar and arbitrarily curved sections of free-form volumes is presented. The definition of free-form volumes generalizes techniques from free-form curves and surfaces to trivariate representation. The definition is given for volumes in the Bernstein-Bezier representation. The author illustrates an intersection algorithm that can be used to perform intersection operations on free-form volumes. Some calculated examples are given. The algorithm can be used as a subroutine for algorithms which are able to perform more general intersections of free-form volumes, e.g. Boolean operations on two free-form volumes. >