Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Quasi-Bezier curves integrating localised information

Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods

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

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries