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... 

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... 

In many applications of multi view 3D reconstruction, image mosaicing is one of the most important processes. Image mosaicing is the action of stitching some pictures of a scene so that a complete picture of the scene is constructed. The proposed method is such that for PTZ cameras by extracting features from frame, the homography matrix between frames will be computed. Then by converting plane coordinate into spherical coordinate, a complete picture of the scene will be constructed and forground will be removed. For fixed cameras sufficient corresponding points will be selected for computing the homography matrix between cameras. Using the homography, the frames without forground will be... 

Finding a path between two specified points is one of the most common problem in computational geometry. The minimum-link path problem is in this category. The minimum-link path between two points is the path between these points with the minimum number of segments. Minimum-link paths have application in areas such as computer graphic, geographic information systems, robotics, image processing, cryptography and VLSI.In this thesis we study variations of the minimum link path problem. Specifically we consider the constrained minimum-link paths in which the path must passes through some given
regions. We detected a flaw in a previously presented algorithm and propose a method to fix this... 

In this thesis we introduce Tropical Geometry and It’s Application in Arithmetic Geometry  

Without optimization, it is impossible to reduce the cost of power generation from an efficient megawatt wind turbine. In this work, we present a multi-objective algorithm to optimize the megawatt blade geometry. In this algorithm, the mass of blade and the wind turbine annual energy production (AEP) are considered as the objective functions. The design variables are blade chord, blade twist, airfoil thickness, spar geometry and blade curvature distribution.The constraints are maximum allowable strain for the chosen materials, maximum tip deflection and maximum tip speed. For the internal geometry, we consider two spars and four panels. The blade element momentum method (BEM) is used for... 

Visibility is an important topic in computational geometry, computer graphics, and motion planning. Two points inside a polygon are visible to each other if their connecting segment remains completely inside the polygon. Visibility polygon of a point in a simple polygon P is the set of points inside P that are visible from the point. The visibility problem has also been considered for line segments. A point v is said to be weakly visible to a line segment pq if there exists a point w 2 pq, such that w and v are visible to each other. The problem of computing the weak visibility polygon (or WVP) of pq inside a polygon P is to compute all points of P that are weakly visible from pq. In this... 

Semiconductor-based photo catalysts, titanium dioxide (TiO2) especially, have been extensively studied for the oxidative photo destruction of organic pollutants in wastewaters and hydrogen production as a green energy source. Much effort has been made to remove the restrictions on the use of TiO2 and challenges related to the recovery of powdery photocatalysts. In this study, copper oxide (CuO) and Zirconium oxide (ZrO2) were used to synthesize nanocomposites. Composition of TiO2/CuO and TiO2/ZrO2 with different weight percentages of second dioxide was synthesized by chemical methods and structural properties of samples were studied by X-ray diffraction and scanning electron microscopy.... 

In the competitive facility location problem, two service providers fight over winning consumers by establishing a series of well-located facilities on the line. The consumers seek their required services from the facility which is closest to them. The order in which service providers locate and build their facilities is as follows: the first service provider establishes k facilities after which the second service provider locates another k facilities and this goes on for m rounds. The payoff of each service provider equals the number of consumers that choose that provider’s facilities to seek service from. In this dissertation, we address different types of this problem and try to analyze... 

Code-based cryptosystems could be a suitable alternative to the cryptosystems based on number theory. It is shown that cryptosystems based on descrete logarithm and factoring is vulnerable to the Shor’s algorithm running on quantum computers, while code-based cryptosystemsare thought to be secure against this cryptanalysis. Despite its security, large key size and low transmission rate keep thesecryptosystems impractical. Reliability is one of our inevitable desires in communication systems along with security.In order to fulfill these desires, joint encryption-encoding schemes has been released.Using LDPC codes in joint encryption-encoding schemes, as an alternative to classical linear... 

Our bodies are made from billions of individual cells and DNA is the control central of each cell. In addition to linear DNAs, there are circular DNAs in nature. Circular DNAs cause new topological structures such as knots and catenanes. These topological structures form during biological proccesses such as replication. For example during replication, two daughter circular DNAs may link together and form catenanes. Anzymes named topoisomerases can simplify the topology of circular DNAs. Type 2 topoisomerases is used for simplification of catenanes. These anzymes do it with breaking a double-strand DNA and passing through another one. In comparison with DNAs, topoisomerases are very small and... 

We consider two variations of shortest paths problem inside a poly-gon. In the first variation, we want to find a shortest path from asource to view a destination inside a polygon with holes. We pro-pose two algorithms for this problem with the time complexity of O (hn log n) and O(n log n) in which the second one is optimal. In the second variation, we want to place a center policeman inside a sim-ple polygon so that the longer of the two shortest paths from two existing guards to the visibility polygon of the center policeman is minimized. We propose an algorithm for this problem with the time complexity of O(n 3)  

Near Horizon Extremal Geometries (NHEG), are geometries which may appear in the near horizon region of the extremal black holes. These geometries have SL(2;R)U(1)n isometry, and constitute a family of solutions to the theory under consideration. In the first part of this report,their thermodynamic properties are reviewed, and their three universal laws are derived. In addition, at the end of the first part, the role of these laws in black hole thermodynamics is presented. In the second part of this thesis, we review building their classical phase space in the Einstein-Hilbert theory. The elements in the NHEG phase space manifold are built by appropriately chosen coordinate transformations of... 

More than 70 weight percentage of using parts in diverse industries (such as military, civil, automobile productions and etc.) are produceed by the casting processes. For each one of the casting procceses, mold cavity is requisite for arrived molten metal in the mold cavity to get eventuated as a solidified part. Based on mold ilk, if the mold is permanent, the cast part must be capable to be remoeved from the the mold inside. For the non-permanent mold (asssuming multi-piece and non-monolithic), if the model requires to be removed from the mold inside after molding and before casting, only model (no cast part) has to be moldable (why for removing the solidified cast part from the... 

The phase space of the Near Horizon of Extremal Geometries has been studied in ”arXiv:1506.07181”. The phase space for the NHEGs consists of the space of all near horizon geometries with a given symmetry. Utilizing covariant phase space method we will build the symplectic two form on the phase space and will use it to define the notion of symplectic symmetry. The conserved charges corresponding to this symmetries form a symmetry algebra which is called NHEG algebra. It turns out that this algebra is a generalization of the celebrated Virasoro algebra. In this thesis we will first review necessary concepts for construction of the phase space of a Lagrangian field theory and will build the... 

This thesis is devoted to study some asymptotic behaviors of Poisson Voronoi tessellation in the Euclidean space as dimension of the space tends to infinity. First we use Blaschke-Petkantschin formula to prove that the variance of volume of the typical cell tends to zero exponentially in dimension. It is also shown that the volume of intersection of the typical cell with the co-centered ball of volume converges in distribution to the constant . Next we consider the linear contact distribution function of the Poisson Voronoi tessellation and compute the limit when dimension goes to infinity. As a byproduct, the chord length distribution and the geometric covariogram of the typical cell are... 

In this research, path planning in unknown environment is considered. It is assumed that the robot’s sensors are the only tools to collect information from the scene. Volume of the information gathered from the environment depends on the capability of the sensor. So, a detour from the optimal path is unavoidable. In this research, the basic robot is equipped with a minimal sensing system that only detects the iscontinuities in depth information (gaps). We present some online search strategies that guide such a robot to navigate unknown streets from a start point s to reach a target point t. Then, we empower the robot by adding a compass to patrol more general classes of polygons. We present... 

Approximately, 60 percent of the world's populations are living at the distance of 60 kilometers of the coasts. In coastal zones, coastal aquifers are the most important resources of the available freshwater while expected that the short-term or long-term impacts of the climate changes threat such aquifers. In general, it is predicted that climate changes e.g. sea-level rise (SLR) cause to increase seawater intrusion (SWI) in the coastal aquifers. In this study, both continental and island coastal aquifers are considered. The objective of this research is the investigation of SWI behavior occurred in the coastal aquifers due to climatic change parameters and aquifer properties. For...