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geometry
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On the topological properties of grid-based interconnection networks: Surface area and volume of radial spheres
, Article Computer Journal ; Vol. 54, issue. 5 , 2011 , p. 726-737 ; ISSN: 00104620 ; Khonsari, A ; Ould-Khaoua, M ; Sharif University of Technology
Abstract
Grid-based networks (or grids for short), such as meshes and tori, have been the underlying topology for many multicomputers, and have been extensively studied in the past as a graph topology. In this paper, we investigate some topological properties of grids without boundary wrap-around (meshes) and with boundary wrap-around (tori). In particular, we study the problem of finding the number of nodes located at/within a given distance from a given node (surface area/volume) in the network and derive some expressions for computing such a number. Furthermore, we provide similar expressions that improve on previous results already reported in the literature for some special cases of grids,...
Computing the smallest color-spanning axis-parallel square
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Volume 8283 , 2013 , Pages 634-643 ; 03029743 (ISSN) ; 9783642450297 (ISBN) ; Mohades, A ; Abam, M. A ; Kazemi, M. R ; Sharif University of Technology
2013
Abstract
For a given set of n colored points with k colors in the plane, we study the problem of computing the smallest color-spanning axis-parallel square. First, for a dynamic set of colored points on the real line, we propose a dynamic structure with O(log2 n) update time per insertion and deletion for maintaining the smallest color-spanning interval. Next, we use this result to compute the smallest color-spanning square. Although we show there could be Ω(kn) minimal color-spanning squares, our algorithm runs in O(nlog2 n) time and O(n) space
Spanning colored points with intervals
, Article CCCG 2013 - 25th Canadian Conference on Computational Geometry ; 2013 , Pages 265-270 ; Mohades, A ; Abam, M. A ; Kazemi, M. R ; Sharif University of Technology
Canadian Conference on Computational Geometry
2013
Abstract
We study a variant of the problem of spanning colored objects where the goal is to span colored objects with two similar regions. We dedicate our attention in this paper to the case where objects are points lying on the real line and regions are intervals. Precisely, the goal is to compute two intervals together spanning all colors. As the main ingredient of our algorithm, we first introduce a kinetic data structure to keep track of minimal intervals spanning all colors. Then we present a novel algorithm using the proposed KDS to compute a pair of intervals which together span all the colors with the property that the largest one is as small as possible. The algorithm runs in O(n2 log n)...
The dynamics of wettability driven droplets in smooth and corrugated microchannels
, Article Journal of Statistical Mechanics: Theory and Experiment ; Volume 2012, Issue 10 , 2012 ; 17425468 (ISSN) ; Moosavi, A ; Mazloomi, A ; Sharif University of Technology
IOP
2012
Abstract
A multi-component lattice Boltzmann scheme is used to investigate the dynamics of a wettability driven droplet within a microchannel. The driving force for the motion is created by a stepwise change in the wettability of the channel walls. Moreover, an analytical solution is developed for evaluation of the dynamics of the droplet inside the channel. The effects of various parameters such as the height of the channel, the wetting pattern of the channel walls, the viscosity and the density ratio on the dynamics are studied. Also, the effect of grooves of different sizes on the channel surfaces on the dynamics of the droplet is investigated for both hydrophilic and hydrophobic surfaces....
How particle shape affects the flow through granular materials
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 85, Issue 3 , 2012 ; 15393755 (ISSN) ; Ahmadi, M. M ; Mohammadi, S
2012
Abstract
Flow through the pores of granular materials has many instances in practice. Therefore, it is interesting to realize how some parameters, such as the shape of the particles affect the passing flow. Following the recent mathematical theory proposed by the authors, this paper deals with the issue of how tortuosity and permeability are influenced by the particle shape. Comparison of the results with the experimental data reveals the competency of the theory in predicting the impact of particle geometry
Staying close to a curve
, Article Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, 10 August 2011 through 12 August 2011 ; 2011 ; Sack, J. R ; Shahbaz, K ; Zarrabi Zadeh, H ; Sharif University of Technology
Abstract
Given a point set S and a polygonal curve P in Rd, we study the problem of finding a polygonal curve through S, which has minimum Fréchet distance to P. We present an efficient algorithm to solve the decision version of this problem in O(nk2) time, where n and k represent the sizes of P and S, respectively. A curve minimizing the Fréchet distance can be computed in O(nk2 log(nk)) time. As a by-product, we improve the map matching algorithm of Alt et al. by an O(log k) factor for the case when the map is a complete grap
Euclidean movement minimization
, Article Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, 10 August 2011 through 12 August 2011 ; February , 2011 ; Fazli, M ; Ghodsi, M ; Khalilabadi, P. J ; Safari, M ; Sharif University of Technology
2011
Abstract
We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of nodes on the plane, the aim is to achieve some spe- cific property by minimum movement of the nodes. We consider two specific properties, namely the connectiv- ity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems. We obtain an O(m)-factor approximation for ConMax and ConSum and an O( p m=OPT)-factor approximation for Con- Max. We also extend some known result on graphical grounds in [1, 2] and...
Weak visibility queries in simple polygons
, Article Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 ; 2011 ; Ghodsi, M ; Sharif University of Technology
Abstract
In this paper, we consider the problem of computing the weak visibility (WV ) of a query line segment in- side a simple polygon. Our algorithm first preprocesses the polygon and creates data structures from which any WV query is answered efficiently in an output sensitive manner. In our solution, the preprocessing is performed in time O(n3 log n) and the size of the constructed data structure is O(n3). It is then possible to report the WV polygon of any query line segment in time O(log n+k), where k is the size of the output. Our algorithm im- proves the current results for this problem
A heuristic homotopic path simplification algorithm
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 20 June 2011 through 23 June 2011 ; Volume 6784 LNCS, Issue PART 3 , June , 2011 , Pages 132-140 ; 03029743 (ISSN) ; 9783642219306 (ISBN) ; Ghodsi, M ; Sharif University of Technology
2011
Abstract
We study the well-known problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set of extra points in the plane. We present a heuristic method for homotopy-preserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O( mlog(n + m) + nlogn log(nm) + k) time, where k is the number of homotopic shortcuts. Using this method, we obtain an O(n 2 + mlog(n + m) + nlogn log(nm)) time algorithm for simplification under the Hausdorff...
Visibility maintenance of a moving segment observer inside polygons with holes
, Article Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, 9 August 2010 through 11 August 2010, Winnipeg, MB ; 2010 , Pages 117-120 ; Ghodsi, M ; Sharif University of Technology
2010
Abstract
We analyze how to efficiently maintain and update the visibility polygons for a segment observer moving in a polygonal domain. The space and time requirements for preprocessing are O(n2) and after preprocessing, visibil- ity change events for weak and strong visibility can be handled in O(log VP) and O(log(VP1 + VP2)) re- spectively, or O(log n) in which VP is the size of the line segment's visibility polygon and VP 1 and VP2 represent the number of vertices in the visibility poly- gons of the line segment endpoints
Monte Carlo simulation of spine geometry from T12 to sacrum in males
, Article ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, 12 July 2010 through 14 July 2010, Istanbul ; Volume 1 , 2010 , Pages 813-820 ; 9780791849156 (ISBN) ; Asghari, M ; Junno, J. A ; Parnianpour, M ; Sharif University of Technology
2010
Abstract
In biomechanical modeling of spine, the prediction of spinal loading during occupational activities is crucial in assessment of the risk of low back pain and injury of spine. Current biomechanical models are based on the average data. Hence, they are unable to predict the effects of the observed natural anatomical variations on muscles moment arms and lines of action, while these variations ultimately influence the required muscular forces for balancing the external moments of any given task. In this work, a methodology based on the Monte Carlo technique has been developed to simulate spine geometry from T12 to S1 vertebrae for males. The lordosis of the assembled spine ranged between 21° to...
Aerosol nano-particle charger simulations and optimizations
, Article Scientia Iranica ; Volume 23, Issue 5 , 2016 , Pages 2220-2229 ; 10263098 (ISSN) ; Saidi, M. S ; Sani, M ; Sharif University of Technology
Sharif University of Technology
Abstract
Size distribution of aerosol particles is prevalently obtained through electrical characterization techniques and study of charged particles' dynamics in the presence of electric field. In this work, a wire-cylinder corona charger is presented, redesigned, and aero dynamically optimized. An initial 2D axisymmetric geometry of the charger was employed for the simulations using the Computational Fluid Dynamics (CFD) commercial code FLUENT 6.3.26. Through successive attempts, a new geometry was obtained by streamlining the walls to eliminate the undesired vortices produced in the flow field of the previous ones. The process optimized the charger by minimizing losses and dilutions of the...
How to extend visibility polygons by mirrors to cover invisible segments
, Article 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017, 29 March 2017 through 31 March 2017 ; Volume 10167 LNCS , 2017 , Pages 42-53 ; 03029743 (ISSN); 9783319539249 (ISBN) ; Ghodsi, M ; Sharif University of Technology
Springer Verlag
2017
Abstract
Given a simple polygon P with n vertices, the visibility polygon (V P) of a point q (V P(q)), or a segment (formula present) (V P(pq)) inside P can be computed in linear time. We propose a linear time algorithm to extend V P of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment (formula present) can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge such that, when converted to a mirror, makes (formula present) visible to our viewer. We find out exactly which interval of (formula present) becomes visible, by...
Efficient computational design of a scaffold for cartilage cell regeneration
, Article Bioengineering ; Volume 5, Issue 2 , 24 April , 2018 ; 23065354 (ISSN) ; Abdekhodaie, M. J ; Gernaey, K. V ; Kruhne, U ; Sharif University of Technology
MDPI AG
2018
Abstract
Due to the sensitivity of mammalian cell cultures, understanding the influence of operating conditions during a tissue generation procedure is crucial. In this regard, a detailed study of scaffold based cell culture under a perfusion flow is presented with the aid of mathematical modelling and computational fluid dynamics (CFD). With respect to the complexity of the case study, this work focuses solely on the effect of nutrient and metabolite concentrations, and the possible influence of fluid-induced shear stress on a targeted cell (cartilage) culture. The simulation set up gives the possibility of predicting the cell culture behavior under various operating conditions and scaffold designs....
SC-RANSAC: spatial consistency on RANSAC
, Article Multimedia Tools and Applications ; 2018 ; 13807501 (ISSN) ; Hekmatian, H ; Kashani Nezhad, M. A ; Kasaei, S ; Sharif University of Technology
Springer New York LLC
2018
Abstract
The goal of robust parameter estimation is developing a model which can properly fit to data. Parameter estimation of a geometric model, in presence of noise and error, is an important step in many image processing and computer vision applications. As the random sample consensus (RANSAC) algorithm is one of the most well-known algorithms in this field, there have been several attempts to improve its performance. In this paper, after giving a short review on existing methods, a robust and efficient method that detects the gross outliers to increase the inlier to outlier ratio in a reduced set of corresponding image points is proposed. It has a new hypothesis and verification scheme which...
Visibility of a moving segment
, Article Proceedings of the 2009 International Conference on Computational Science and Its Applications, ICCSA 2009, 29 June 2009 through 2 July 2009, Yongin ; 2009 , Pages 169-176 ; 9780769537016 (ISBN) ; Ghodsi, M ; Sharif University of Technology
2009
Abstract
In this paper we define topological segment visibility, and show how to compute and maintain it as the observer moves in the plane. There are n non-intersecting line segment objects in the plane, and we have a segment observer among them. As the topological visibility of a line segment has not been studied before, we first consider static case of the problem, in which the observer and objects are static, and then we study dynamic case of the problem, in which the observer can move among obstacles
A practical approach for planar visibility maintenance
, Article Journal for Geometry and Graphics ; Volume 13, Issue 1 , 2009 , Pages 75-90 ; 14338157 (ISSN) ; Ghodsi, M ; Sharif University of Technology
2009
Abstract
In this paper, we propose a method for maintaining the region visible from a moving point observer inside a planar scene. In this method, we check the observer position in discrete time-stamps to detect and apply changes to the visible or illuminated region of a moving point observer q, or VP(q). We efficiently maintain a list C(q) of edges in VP(q) which are subject to change during the motion. In each time-stamp that VP(q) is to be updated, we only refine and redraw the view against the edges of C(q) that indicate the positions of the visibility changes. We build an enriched representation of the visibility graph in a preprocessing step to apply the required updates on C(q) efficiently and...
An improved upper bound on dilation of regular polygons
, Article Computational Geometry: Theory and Applications ; Volume 80 , 2019 , Pages 53-68 ; 09257721 (ISSN) ; Izadi, M ; Sharif University of Technology
Elsevier B.V
2019
Abstract
Dilation of a set of points on the plane is the lowest possible dilation of a plane spanner on the point set. We show that dilation of vertices of any regular polygon is less than 1.4482. We introduce a method for constructing a triangulation of a regular polygon and prove this bound on its dilation. The upper bound on dilation is shown using mathematical proofs and experimental results. The new upper bound improves the previously known bound of 1.48454. © 2019 Elsevier B.V
SC-RANSAC: Spatial consistency on RANSAC
, Article Multimedia Tools and Applications ; Volume 78, Issue 7 , 2019 , Pages 9429-9461 ; 13807501 (ISSN) ; Hekmatian, H ; Kashani Nezhad, M. A ; Kasaei, S ; Sharif University of Technology
Springer New York LLC
2019
Abstract
The goal of robust parameter estimation is developing a model which can properly fit to data. Parameter estimation of a geometric model, in presence of noise and error, is an important step in many image processing and computer vision applications. As the random sample consensus (RANSAC) algorithm is one of the most well-known algorithms in this field, there have been several attempts to improve its performance. In this paper, after giving a short review on existing methods, a robust and efficient method that detects the gross outliers to increase the inlier to outlier ratio in a reduced set of corresponding image points is proposed. It has a new hypothesis and verification scheme which...
A simple randomized algorithm for all nearest neighbors
, Article 31st Canadian Conference on Computational Geometry, CCCG 2019, 8 August 2019 through 10 August 2019 ; 2019 , Pages 94-98 ; Zarrabi Zadeh, H ; Sharif University of Technology
Canadian Conference on Computational Geometry
2019
Abstract
Given a set P of n points in the plane, the all nearest neighbors problem asks for finding the closest point in P for each point in the set. The following folklore algorithm is used for the problem in practice: Pick a line in a random direction, project all points onto the line, and then search for the nearest neighbor of each point in a small vicinity of that point on the line. It is widely believed that the expected number of points needed to be checked by the algorithm in the vicinity of each point is O(pn) on average. We confirm this conjecture in affirmative by providing a careful analysis on the expected number of comparisons made by the algorithm. We also present a matching lower...