Sharif Digital Repository

In this thesis, we considered several types of the visibility problem. These problems include computing the visibility polygon of a point observer inside a polygonal domain, maintaining visibility polygon of a moving point observer, visibility coherence in space, maintaining visibility polygon of a moving segment observer and visibility dependent simplification. Furthermore, we considered these problems in both offline and streaming settings. These problems arise in different practical areas, such as computer graphics, machine vision, robotics, motion planning, geographic information systems (GIS) and computational geometry. We obtained effective theoretical results as well as superior... 

An interesting theoretical and practical set of problems in computer science is concerned with the study of spatial relations among objects in a geometric space. Examples of such problems for a set of points P are finding the closest pair of the points P, partitioning space into regions such that all points of a region have minimum distance to the same point in P, and computing the Euclidean minimum spanning tree on P. Moreover, we need mechanisms to efficiently update these properties when the points P are allowed to move or may be inserted or deleted. This is to avoid re-computation of these properties from scratch. Here, we consider the Euclidean minimum spanning tree (EMST) of a set of... 

Planar visibility computing is defined as determining the region of the plane that is visible from a specific observer. This concept has many applications in computer graphics, robotic and computer games. In this thesis we consider two visibility problems: the visibility testing problem which checks the inter-visibility of two objects and the visibility counting problem which counts the number of visible objects from an observer. For these problems we propose new algorithms which have some improvements compare to the previous ones  

A basic technique in data reduction is to approximate a collection of data by another collection of smaller size. Then, the resulted data are easier to be processed or maintained. An example of such large scale data is the ordered sequence of n points describing a path or a region boundary. We are given a sequence of points p , p , ..., p , and we consider the 1 2 n problem of approximating these points by a path with k < n line segments which error of this path is not greater than special value. Various criterions are defined to compute the path simplification error.This problem can be used in GIS, Image Processing and Computer Graphics problems. In this thesis, we consider special case... 

Disconnections in neural paths from the central nervous system to the muscles or vice versa cause different neuropathies, thus paralysis in different limbs may occur. As a result of the lack of muscular activity and the decrease in blood perfusion in paralyzed limbs, problems like osteoporosis, increase in the risk of breaking, decline in muscle size, cardiovascular diseases, renal dysfunction, bedsores, etc may happen. In order to induce movement in paralyzed limbs, thus preventingmentioned problems, rowing exercise through Functional Electrical Stimulation (FES) may be utilized. In FES, electrical Stimulation using current stimulating pulses is applied to contracting and relaxing muscles,... 

Moving data is becoming more and more important in different areas such as air traffic control, mobile communications, geographical information systems, GPS and other advanced technologies. In most cases, the path trajectory of such moving data is not known in advance. Moreover, they can change the direction and their speed of motion. Recently, a moving model, called black box model, has been proposed for such environments. In this model, there is a sequence of time stamps in which the position of each object is reported and the maximum displacement of each object in a time step is bounded by a known constant, dmax. In this thesis, we use this model to solve some computational... 

Separating colored points is one of the important problems in computational geometry. In separating colored points problems a set of colored points in Euclidean space are given that each color designates a set of certain data.Different problems can be defined in the colored points subject. Among them,separating colored points is studied in this thesis. It is supposed that two sets of blue and red points are given. It is desired to find the minimum number of rectangles that separate the blue points from the red points. It is demonstrated hat if P ̸= NP then there is no polynomial time algorithm for solving this problem. Then, a constant factor approximation algorithm is introduced and applied... 

3D-object modeling and its representation in computers are one of the interested fields in computer science and engineering and problems like object and environment modeling, representation, storage and physical interactions are some of the important problems in this field. Increasing the applications of the technologies like localization, machine vision and virtual reality made the 3D-object modeling and its related problems, like 3D-model extraction and reconstruction, a nowadays interested challenges and a variety of solutions such as time of flight sensors,
structured light, sonar sensors and multi-camera reconstruction are presented for it. Multi-camera solutions, just like the... 

Given a graph G with a set of terminals, two weight functions c and d defined on the edge set of G, and a bound D, a popular NP-hard problem in designing networks is to find the minimum cost Steiner tree (under function c) in G, to connect all terminals in such a way that its diameter (under function d) is bounded by D. Marathe et al. [1] proposed an (O(log2n);O(log2n)) approximation algorithm for this bicriteria problem, where n is the number of terminals. The first factor reflects the approximation ratio on the diameter bound D, and the second factor indicates the cost-approximation ratio. Later, Kapoor and Sarwat [2] introduced a parameterized approximation algorithm with performance... 

In this study, control and protection of low voltage microgrids have been analyzed. Studied microgrid takes the advantages of inverter based distributed generation. One of the most important issues in inverter based microgrids is the control of its distributed generation. Since, the low voltage networks have single phase loads and many imbalances, these imbalances can affect the control of IBDGs (inverter based distributed generations). This issue in the islanded mode of operation is the most important, because in this mode of operation, IBDGs control the network voltage and frequency.
In this thesis, the different control strategies of IBDGs are reviewed, and then modified to address... 

A hash function maps efficiently every finite length string to a fixed one. The output represents the entire content of the input, similar to digital fingerprint of input text. In order to be able to use a hash function in cryptography, it should be hard to find two distinct inputs with the same output (collision), because finding a collision in hash functions leads to malicious attacks on many security systems.We say a hash function is provably collision resistant, if finding a collision can be reduced to the known hard problems. Family of MD hash functions are one of the most famous applied hash functions which are considerably used in industrial applications. However, they are not... 

Pattern recognition in data streams using bounded memory and bounded time is a difficult task. There are many techniques for recognizing patterns but when we talk about data streams these algorithms became useless since there are no enough memory to store all data. In data stream model the entire data is not available at any time and we don’t have enough time processing each data.
In this thesis we consider current methods for recognizing patterns from a data streams. The goal pattern in this study was the minimum total area of k convex polygons encloses all data  

One of the methods to detect an unknown environment, is using the visual information about the environment. In this problem, we have an unknown two-dimensional environment consists of a set of edges and vertices that the geometric positions of vertices is not specified and only the combinatorial structure of the environment is available. In addition, certain information such as visibility of two vertices in the environment is known. The goal is to recognize the geometric shape of the environment with this information.This problem has many applications in Robotics particularly in dynamic envi- ronment where objects are moving.
In this thesis, we examine this problem in different conditions... 

We design a new algorithm for clustering data streams in any fixed di- mension, that use the framework of core-set to summarize data, in order to reduce the complexity of computation. Clustering is to separate data into distinct sets called clusters, which objects in the same cluster has the most similarity and objects in the different clusters has the least similarity.This problem has many application in the areas such as: machine learning,image processing, financial and stock transactions. Data stream has recently emerged as an important concept because in many applications, data is inherently streaming over a network or the data base is extremely large and sequential access is way faster... 

Due to recent advancements and wide usage of location detection devices, huge amount of data are collected by GPS and cellular technologies which exhibits moving objects trajectories. Using this information, it is possible to track a set of objects over a long period of time, as happens for instance in studying animal migration. Always, in these situations it is undesirable or even impossible (due to process and storage limits) to store the complete stream of positioning data. Then, simplifying a trajectory as a data reduction technique is the option for resolving such problems. Moreover, there is an increasing interest in queries capturing ”aggregate” behavior of trajectories as groups like... 

Visibility graph is a graph that comprises information about visibility of a set of objects in 2 or 3-dimensional space. By constructing this graph with respect to conditions of environment one can answer questions like minimum Euclidean distance. Inverse of this procedure is required too; i.e. knowing geometrical structure of objects and information about their visibility we want to guess their location in space and, as the saying goes, reconstruct the environment. For example some methods to reconstruct specific polygons knowing which vertices each vertex sees is proposed. In this dissertation we try to reconstruct a 2-dimensional environment that only has two x-monotone paths (chains)