تمثيل الإطار الخارجي للكلمات العربية بكفاءة من خلال الدمج بين نموذج الكنتور النشط وتحديد ونقاط الزوايا

Graphical curves and surfaces fitting are hot areas of research studies and application, such as artistic applications, analysis applications and encoding purposes. Outline capture of digital word images is important in most of the desktop publishing systems. The shapes of the characters are stored in the computer memory in terms of their outlines, and the outlines are expressed as Bezier curves. Existing methods for Arabic font outline description suffer from low fitting accuracy and efficiency. In our research, we developed a new method for outlining shapes using Bezier curves with minimal set of curve points. A distinguishing characteristic of our method is that it combines the active contour method (snake) with corner detection to achieve an initial set of points that is as close to the shape's boundaries as possible. The method links these points (snake + corner) into a compound Bezier curve, and iteratively improves the fitting of the curve over the actual boundaries of the shape. We implemented and tested our method using MATLAB. Test cases included various levels of shape complexity varying from simple, moderate, and high complexity depending on factors, such as: boundary concavities, number of corners. Results show that our method achieved average 86% of accuracy when measured relative to true shape boundary. When compared to other similar methods (Masood & Sarfraz, 2009; Sarfraz & Khan, 2002; Ferdous A Sohel, Karmakar, Dooley, & Bennamoun, 2010), our method performed comparatively well. Keywords: Bezier curves, shape descriptor, curvature, corner points, control points, Active Contour Model.تعتبر المنحنيات والأسطح الرسومية موضوعاً هاماً في الدراسات البحثية وفي التطبيقات البرمجية مثل التطبيقات الفنية، وتطبيقات تحليل وترميز البيانات. ويعتبر تخطيط الحدود الخارجية للكلمات عملية أساسية في غالبية تطبيقات النشر المكتبي. في هذه التطبيقات تخزن أشكال الأحرف في الذاكرة من حيث خطوطها الخارجية، وتمثل الخطوط الخارجية على هيئة منحنيات Bezier. الطرق المستخدمة حالياً لتحديد الخطوط الخارجية للكلمات العربية تنقصها دقة وكفاءة الملاءمة ما بين الحدود الحقيقية والمنحنى الرسومي الذي تقوم بتشكيله. في هذا البحث قمنا بتطوير طريقة جديدة لتخطيط الحدود الخارجية للكلمات تعتمد على منحنيات Bezier بمجموعة أقل من المنحنيات الجزئية. تتميز طريقتنا بخاصية مميزة وهي الدمج بين آلية لاستشعار الزوايا مع آلية نموذج الكنتور النشط (الأفعى). يتم الدمج بين نقاط الزوايا ونقاط الأفعى لتشكيل مجموعة موحدة من النقاط المبدئية قريبة قدر الإمكان من الحدود الحقيقية للشكل المراد تحديده. يتشكل منحنى Bezier من هذه المجموعة المدمجة، وتتم عملية تدريجية على دورات لملاءمة المنحنى على الحدود الحقيقية للشكل. قام الباحث بتنفيذ وتجربة الطريقة الجديدة باستخدام برنامج MATLAB. وتم اختيار أشكال رسومية كعينات اختبار تتصف بمستويات متباينة من التعقيد تتراوح ما بين بسيط إلى متوسط إلى عالي التعقيد على أساس عوامل مثل تقعرات الحدود، عدد نقاط الزوايا، الفتحات الداخلية، إلخ. وقد أظهرت نتائج الاختبار أن طريقتنا الجديدة حققت دقة في الملائمة تصل نسبتها إلى 86% مقارنة بالحدود الحقيقية للشكل المستهدف. وكذلك فقد كان أداء طريقتنا جيداً بالمقارنة مع طرق أخرى مماثلة

Algebraic level sets for CAD/CAE integration and moving boundary problems

Boundary representation (B-rep) of CAD models obtained from solid modeling kernels are commonly used in design, and analysis applications outside the CAD systems. Boolean operations between interacting B-rep CAD models as well as analysis of such multi-body systems are fundamental operations on B-rep geometries in CAD/CAE applications. However, the boundary representation of B-rep solids is, in general, not a suitable representation for analysis operations which lead to CAD/CAE integration challenges due to the need for conversion from B-rep to volumetric approximations. The major challenges include intermediate mesh generation step, capturing CAD features and associated behavior exactly and recurring point containment queries for point classification as inside/outside the solid. Thus, an ideal analysis technique for CAD/CAE integration that can enable direct analysis operations on B-rep CAD models while overcoming the associated challenges is desirable. ^ Further, numerical surface intersection operations are typically necessary for boolean operations on B-rep geometries during the CAD and CAE phases. However, for non-linear geometries, surface intersection operations are non-trivial and face the challenge of simultaneously satisfying the three goals of accuracy, efficiency and robustness. In the class of problems involving multi-body interactions, often an implicit knowledge of the boolean operation is sufficient and explicit intersection computation may not be needed. Such implicit boolean operations can be performed by point containment queries on B-rep CAD models. However, for complex non-linear B-rep geometries, the point containment queries may involve numerical iterative point projection operations which are expensive. Thus, there is a need for inexpensive, non-iterative techniques to enable such implicit boolean operations on B-rep geometries. ^ Moreover, in analysis problems with evolving boundaries (ormoving boundary problems), interfaces or cracks, blending functions are used to enrich the underlying domain with the known behavior on the enriching entity. The blending functions are typically dependent on the distance from the evolving boundaries. For boundaries defined by free form curves or surfaces, the distance fields have to be constructed numerically. This may require either a polytope approximation to the boundary and/or an iterative solution to determine the exact distance to the boundary. ^ In this work a purely algebraic, and computationally efficient technique is described for constructing signed distance measures from Non-Uniform Rational B-Splines (NURBS) boundaries that retain the geometric exactness of the boundaries while eliminating the need for iterative and non-robust distance calculation. The proposed technique exploits the NURBS geometry and algebraic tools of implicitization. Such a signed distance measure, also referred to as the Algebraic Level Sets, gives a volumetric representation of the B-rep geometry constructed by purely non-iterative algebraic operations on the geometry. This in turn enables both the implicit boolean operations and analysis operations on B-rep geometries in CAD/CAE applications. Algebraic level sets ensure exactness of geometry while eliminating iterative numerical computations. Further, a geometry-based analysis technique that relies on hierarchical partition of unity field compositions (HPFC) theory and its extension to enriched field modeling is presented. The proposed technique enables direct analysis of complex physical problems without meshing, thus, integrating CAD and CAE. The developed techniques are demonstrated by constructing algebraic level sets for complex geometries, geometry-based analysis of B-rep CAD models and a variety of fracture examples culminating in the analysis of steady state heat conduction in a solid with arbitrary shaped three-dimensional cracks. ^ The proposed techniques are lastly applied to investigate the risk of fracture in the ultra low-k (ULK) dies due to copper (Cu) wirebonding process. Maximum damage induced in the interlayer dielectric (ILD) stack during the process steps is proposed as an indicator of the reliability risk. Numerical techniques based on enriched isogeometric approximations are adopted to model damage in the ULK stacks using a cohesive damage description. A damage analysis procedure is proposed to conduct damage accumulation studies during Cu wirebonding process. Analysis is carried out to identify weak interfaces and potential sites for crack nucleation as well as damage nucleation patterns. Further, the critical process condition is identified by analyzing the damage induced during the impact and ultrasonic excitation stages. Also, representative ILD stack designs with varying Cu percentage are compared for risk of fracture

Quasi 3D Multi-stage Turbomachinery Pre-optimizer

A pre-optimizer has been developed which modifies existing turbomachinery blades to create new geometries with improved selected aerodynamic coefficients calculated using a linear panel method. These blade rows can then be further refined using a Navier-Stokes method for evaluation. This pre-optimizer was developed in hopes of reducing the overall CPU time required for optimization when using only Navier-Stokes evaluations. The primary method chosen to effect this optimization is a parallel evolutionary algorithm. Variations of this method have been analyzed and compared for convergence and degree of improvement. Test cases involved both single and multiple row turbomachinery. For each case, both single and multiple criteria fitness evaluations were used

On the capture and representation of fonts

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The commercial need to capture, process and represent the shape and form of an outline has lead to the development of a number of spline routines. These use a mathematical curve format that approximates the contours of a given shape. The modelled outline lends itself to be used on, and for, a variety of purposes. These include graphic screens, laser printers and numerically controlled machines. The latter can be employed for cutting foil, metal. plastic and stone. One of the most widely used software design packages has been the lKARUS system. This, developed by URW of Hamburg (Gennany), employs a number of mathematical descriptions that facilitate the process of both modelling and representation of font characters. It uses a variety of curve formats, including Bezier cubics, general conics and parabolics. The work reported in this dissertation focuses on developing improved techniques, primarily. for the lKARUS system. This includes two algorithms which allow a Bezier cubic description, two for a general conic representation and, yet another, two for the parabolic case. In addition, a number of algorithms are presented which promote conversions between these mathematical forms; for example, Bezier cubics to a general conic form. Furthennore, algorithms are developed to assist the process of rasterising both cubic and quadratic arcs.This study was partly funded by the Science and Education Research Council (SERC)

Design and Modeling of Tool Trajectory in C0 Continuity Concept by Importing the IGES Neutral File

A common task in geometric modeling is to interpolate a sequence of points or derivatives, sampled from a curve, with a parametric polynomial or spline curve. To do this the first step is to choose parameter values corresponding to the interpolation points. In a parametric environment, user can completely define a geometric feature with some parameters. This paper has an aim to generate a smooth tool trajectory spline for machining a workpiece. With the spline technique MATLAB program has been proposed for simulation of cutter contact points in the trajectory. The author has gone through C0 continuity concept and at last the simulated result has been shown by MATLAB program in its output. Keywords: Spline, Approximation technique, C++, IGES, MATLA

Methods for constraint-based conceptual free-form surface design

Zusammenfassung Der constraint-basierte Entwurf von Freiformfl„chen ist eine m„chtige Methode im Computer gest�tzten Entwurf. Bekannte Realisierungen beschr„nken sich jedoch meist auf Interpolation von Rand- und isoparametrischen Kurven. In diesem Zusammenhang sind die sog. "Multi-patch" Methoden die am weitesten verbreitete Vorgehensweise. Hier versucht man Fl„chenverb„nde aus einem Netz von dreidimensionalen Kurven (oft gemischt mit unstrukturierten Punktewolken) derart zu generieren, dass die Kurven und Punkte von den Fl„chen interpoliert werden. Die Kurven werden als R„nder von rechteckigen oder dreieckigen bi-polynomialen oder polynomialen Fl„chen betrachtet. Unter dieser Einschr„nkung leidet die Flexibilit„t des Verfahrens. In dieser Dissertation schlagen wir vor, beliebige, d.h. auch nicht iso-parametrische, Kurven zu verwenden. Dadurch ergeben sich folgende Vorteile: Erstens kann so beispielsweise eine B-spline Fl„che entlang einer benutzerdefinierten Kurve verformt werden w„hrend andere Kurven oder Punkte fixiert sind. Zweitens, kann eine B-spline Fl„che Kurven interpolieren, die sich nicht auf iso-parametrische Linien der Fl„che abbilden lassen. Wir behandeln drei Arten von Constraints: Inzidenz einer beliebigen Kurve auf einer B-spline Fl„che, Fixieren von Fl„chennormalen entlang einer beliebigen Kurve (dieser Constraint dient zur Herstellung von tangentialen šberg„ngen zwischen zwei Fl„chen) und die sog. Variational Constrains. Letztere dienen unter anderem zur Optimierung der physikalischen und optischen Eigenschaften der Fl„chen. Es handelt sich hierbei um die Gausschen Normalgleichungen der Fl„chenfunktionale zweiter Ordnung, wie sie in der Literatur bekannt sind. Die Dissertation gliedert sich in zwei Teile. Der erste Teil befasst sich mit der Aufstellung der linearen Gleichungssysteme, welche die oben erw„hnten Constraints repr„sentieren. Der zweite Teil behandelt Methoden zum L”sen dieser Gleichungssysteme. Der Kern des ersten Teiles ist die Erweiterung und Generalisierung des auf Polarformen (Blossoms) basierenden Algorithmus f�r Verkettung von Polynomen auf Bezier und B-spline Basis: Gegeben sei eine B-spline Fl„che und eine B-spline Kurve im Parameterraum der Fl„che. Wir zeigen, dass die Kontrollpunkte der dreidimensionalen Fl„chenkurve, welche als polynomiale Verkettung der beiden definiert ist, durch eine im Voraus berechenbare lineare Tranformation (eine Matrix) der Fl„chenkontrollpunkte ausgedr�ckt werden k”nnen. Dadurch k”nnen Inzidenzbeziehungen zwischen Kurven und Fl„chen exakt und auf eine sehr elegante und kompakte Art definiert werden. Im Vergleich zu den bekannten Methoden ist diese Vorgehensweise effizienter, numerisch stabiler und erh”ht nicht die Konditionszahl der zu l”senden linearen Gleichungen. Die Effizienz wird erreicht durch Verwendung von eigens daf�r entwickelten Datenstrukturen und sorgf„ltige Analyse von kombinatorischen Eigenschaften von Polarformen. Die Gleichungen zur Definition von Tangentialit„ts- und Variational Constraints werden als Anwendung und Erweiterung dieses Algorithmus implementiert. Beschrieben werden auch symbolische und numerische Operationen auf B-spline Polynomen (Multiplikation, Differenzierung, Integration). Dabei wird konsistent die Matrixdarstellung von B-spline Polynomen verwendet. Das L”sen dieser Art von Constraintproblemen bedeutet das Finden der Kontrollpunkte einer B-spline Fl„che derart, dass die definierten Bedingungen erf�llt werden. Dies wird durch L”sen von, im Allgemeinen, unterbestimmten und schlecht konditionierten linearen Gleichungssystemen bewerkstelligt. Da in solchen F„llen keine eindeutige, numerisch stabile L”sung existiert, f�hren die �blichen Methoden zum L”sen von linearen Gleichungssystemen nicht zum Erfolg. Wir greifen auf die Anwendung von sog. Regularisierungsmethoden zur�ck, die auf der Singul„rwertzerlegung (SVD) der Systemmatrix beruhen. Insbesondere wird die L-curve eingesetzt, ein "numerischer Hochfrequenzfilter", der uns in die Lage versetzt eine stabile L”sung zu berechnen. Allerdings reichen auch diese Methoden im Allgemeinen nicht aus, eine Fl„che zu generieren, welche die erw�nschten „sthetischen und physikalischen Eigenschaften besitzt. Verformt man eine Tensorproduktfl„che entlang einer nicht isoparametrischen Kurve, entstehen unerw�nschte Oszillationen und Verformungen. Dieser Effekt wird "Surface-Aliasing" genannt. Wir stellen zwei Methoden vor um diese Aliasing-Effekte zu beseitigen: Die erste Methode wird vorzugsweise f�r Deformationen einer existierenden B-spline Fl„che entlang einer nicht isoparametrischen Kurve angewendet. Es erfogt eine Umparametrisierung der zu verformenden Fl„che derart, dass die Kurve in der neuen Fl„che auf eine isoparametrische Linie abgebildet wird. Die Umparametrisierung einer B- spline Fl„che ist keine abgeschlossene Operation; die resultierende Fl„che besitzt i.A. keine B-spline Darstellung. Wir berechnen eine beliebig genaue Approximation der resultierenden Fl„che mittels Interpolation von Kurvennetzen, die von der umzuparametrisierenden Fl„che gewonnen werden. Die zweite Methode ist rein algebraisch: Es werden zus„tzliche Bedingungen an die L”sung des Gleichungssystems gestellt, die die Aliasing-Effekte unterdr�cken oder ganz beseitigen. Es wird ein restriktionsgebundenes Minimum einer Zielfunktion gesucht, deren globales Minimum bei "optimaler" Form der Fl„che eingenommen wird. Als Zielfunktionen werden Gl„ttungsfunktionale zweiter Ordnung eingesetzt. Die stabile L”sung eines solchen Optimierungsproblems kann aufgrund der nahezu linearen Abh„ngigkeit des Gleichungen nur mit Hilfe von Regularisierungsmethoden gewonnen werden, welche die vorgegebene Zielfunktion ber�cksichtigen. Wir wenden die sog. Modifizierte Singul„rwertzerlegung in Verbindung mit dem L-curve Filter an. Dieser Algorithmus minimiert den Fehler f�r die geometrischen Constraints so, dass die L”sung gleichzeitig m”glichst nah dem Optimum der Zielfunktion ist.The constrained-based design of free-form surfaces is currently limited to tensor-product interpolation of orthogonal curve networks or equally spaced grids of points. The, so- called, multi-patch methods applied mainly in the context of scattered data interpolation construct surfaces from given boundary curves and derivatives along them. The limitation to boundary curves or iso-parametric curves considerably lowers the flexibility of this approach. In this thesis, we propose to compute surfaces from arbitrary (that is, not only iso-parametric) curves. This allows us to deform a B-spline surface along an arbitrary user-defined curve, or, to interpolate a B-spline surface through a set of curves which cannot be mapped to iso-parametric lines of the surface. We consider three kinds of constraints: the incidence of a curve on a B-spline surface, prescribed surface normals along an arbitrary curve incident on a surface and the, so-called, variational constraints which enforce a physically and optically advantageous shape of the computed surfaces. The thesis is divided into two parts: in the first part, we describe efficient methods to set up the equations for above mentioned linear constraints between curves and surfaces. In the second part, we discuss methods for solving such constraints. The core of the first part is the extension and generalization of the blossom-based polynomial composition algorithm for B-splines: let be given a B-spline surface and a B-spline curve in the domain of that surface. We compute a matrix which represents a linear transformation of the surface control points such that after the transformation we obtain the control points of the curve representing the polynomial composition of the domain curve and the surface. The result is a 3D B-spline curve always exactly incident on the surface. This, so-called, composition matrix represents a set of linear curve-surface incidence constraints. Compared to methods used previously our approach is more efficient, numerically more stable and does not unnecessarily increase the condition number of the matrix. The thesis includes a careful analysis of the complexity and combinatorial properties of the algorithm. We also discuss topics regarding algebraic operations on B-spline polynomials (multiplication, differentiation, integration). The matrix representation of B-spline polynomials is used throughout the thesis. We show that the equations for tangency and variational constraints are easily obtained re-using the methods elaborated for incidence constraints. The solving of generalized curve-surface constraints means to find the control points of the unknown surface given one or several curves incident on that surface. This is accomplished by solving of large and, generally, under-determined and badly conditioned linear systems of equations. In such cases, no unique and numerically stable solution exists. Hence, the usual methods such as Gaussian elimination or QR-decomposition cannot be applied in straightforward manner. We propose to use regularization methods based on Singular Value Decomposition (SVD). We apply the so-called L-curve, which can be seen as an numerical high-frequency filter. The filter automatically singles out a stable solution such that best possible satisfaction of defined constraints is achieved. However, even the SVD along with the L-curve filter cannot be applied blindly: it turns out that it is not sufficient to require only algebraic stability of the solution. Tensor-product surfaces deformed along arbitrary incident curves exhibit unwanted deformations due to the rectangular structure of the model space. We discuss a geometric and an algebraic method to remove this, so-called, Surface aliasing effect. The first method reparametrizes the surface such that a general curve constraint is converted to iso-parametric curve constraint which can be easily solved by standard linear algebra methods without aliasing. The reparametrized surface is computed by means of the approximated surface-surface composition algorithm, which is also introduced in this thesis. While this is not possible symbolically, an arbitrary accurate approximation of the resulting surface is obtained using constrained curve network interpolation. The second method states additional constraints which suppress or completely remove the aliasing. Formally we solve a constrained least square approximation problem: we minimize an surface objective function subject to defined curve constraints. The objective function is chosen such that it takes in the minimal value if the surface has optimal shape; we use a linear combination of second order surface smoothing functionals. When solving such problems we have to deal with nearly linearly dependent equations. Problems of this type are called ill-posed. Therefore sophisticated numerical methods have to be applied in order to obtain a set of degrees of freedom (control points of the surface) which are sufficient to satisfy given constraints. The remaining unused degrees of freedom are used to enforce an optically pleasing shape of the surface. We apply the Modified Truncated SVD (MTSVD) algorithm in connection with the L-curve filter which determines a compromise between an optically pleasant shape of the surface and constraint satisfaction in a particularly efficient manner

Hybrid Intelligent Optimization Methods for Engineering Problems

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles

Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods