Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

ABSTRACT. The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task.The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. no. TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain)

Aerodynamic CFD Based Optimization of Police Car Using Bezier Curves

This paper investigates the optimization of the aerodynamic design of a police car, BMW 5-series which is popular police force across the UK. A Bezier curve fitting approach is proposed as a tool to improve the existing design of the warning light cluster in order to reduce drag. A formal optimization technique based on Computational Fluid Dynamics (CFD) and moving least squares (MLS) is used to determine the control points for the approximated curve to cover the light-bar and streamline the shape of the roof. The results clearly show that improving the aerodynamic design of the roofs will offer an important opportunity for reducing the fuel consumption and emissions for police vehicles. The optimized police car has 30% less drag than the non-optimized counter-part

Fit evaluation of virtual garment try-on by learning from digital pressure data

Presently, garment fit evaluation mainly focuses on real try-on, and rarely deals with virtual try-on. With the rapid development of E-commerce, there is a profound growth of garment purchases through the internet. In this context, fit evaluation of virtual garment try-on is vital in the clothing industry. In this paper, we propose a Naive Bayes-based model to evaluate garment fit. The inputs of the proposed model are digital clothing pressures of different body parts, generated from a 3D garment CAD software; while the output is the predicted result of garment fit (fit or unfit). To construct and train the proposed model, data on digital clothing pressures and garment real fit was collected for input and output learning data respectively. By learning from these data, our proposed model can predict garment fit rapidly and automatically without any real try-on; therefore, it can be applied to remote garment fit evaluation in the context of e-shopping. Finally, the effectiveness of our proposed method was validated using a set of test samples. Test results showed that digital clothing pressure is a better index than ease allowance to evaluate garment fit, and machine learning-based garment fit evaluation methods have higher prediction accuracies

Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm called cuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way

The Development Of Planar Curves With High Aesthetic Value

Penyelidikan terhadap lengkung satah bagi menghasilkan suatu produk yang can- tik dan pengubahsuaian lengkung bagi bidang tertentu telah dibangunkan sejak tahun 70-an. Pola penyelidikan dalam bidang ini boleh dibahagikan kepada lima cabang utama iaitu pembangungan algoritma adil, pembangunan lengkung satah melalui kaedah sintesis lengkung, pembangunan algoritma baru bagi mengubahsuai lingkaran asli untuk kegua- naan reka bentuk, pengubahsuaian lengkung °eksibel (B¶ezier dan NURBS) supaya pro¯l kelengkungan adalah monoton dan akhirnya, pembangungan algoritma dalam proses pe- myuaian dan penghampiran terhadap lingkaran asli menerusi lengkung °eksibel. The research on developing planar curves to produce visually pleasing products and modifying planar curves for special purposes has been progressing since the 1970s. The pattern of research in this ¯eld of study has branched to ¯ve major groups; the devel- opment of fairing algorithms; the development of planar curves via curve synthesis, the development of algorithms to modify natural spirals to suit design intent, the modi¯cation of °exible curves (B¶ezier and NURBS) so that the curvature pro¯le is strictly monotonic and ¯nally, the development of algorithms to ¯t natural spirals and approximation via °exible curves

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

Synthesis of aesthetics for ship design

In the search for consensus on a definition of beauty, fitting the task of appreciating a ship’s design, this research revealed that other components of visual appraisal and 3d pattern analysis are required for a systemic approach. The model process presented is built around local adaptation and Gestalt psychology and uses retrospective case studies to categorise and calculate proportions, and recognisable patterns. The number of results from each type of vessel were found to be different, due to each ship or boats various geometries and anatomy, which illuminated the importance of standardising a procedure of categorisation in the appreciative approach.The categorisation of functions around the philosophy of functional beauty and the maths of summation series, it is suggested here, will allow a library of algebraic patterns and parameters to penetrate further into the impending or emulated integrated systems of ship design. The process to derive physical parameters via the culturally focussed narrative of functional beauty, is deemed as a manageable and novel addition to the naval architect's role. However, for the results to have a decisive impact on commercial design or education, variance and validation through further case studies is required

FITTING A PARAMETRIC MODEL TO A CLOUD OF POINTS VIA OPTIMIZATION METHODS

Computer Aided Design (CAD) is a powerful tool for designing parametric geometry. However, many CAD models of current configurations are constructed in previous generations of CAD systems, which represent the configuration simply as a collection of surfaces instead of as a parametrized solid model. But since many modern analysis techniques take advantage of a parametrization, one often has to re-engineer the configuration into a parametric model. The objective here is to generate an efficient, robust, and accurate method for fitting parametric models to a cloud of points. The process uses a gradient-based optimization technique, which is applied to the whole cloud, without the need to segment or classify the points in the cloud a priori. First, for the points associated with any component, a variant of the Levenberg-Marquardt gradient-based optimization method (ILM) is used to find the set of model parameters that minimizes the least-square errors between the model and the points. The efficiency of the ILM algorithm is greatly improved through the use of analytic geometric sensitivities and sparse matrix techniques. Second, for cases in which one does not know a priori the correspondences between points in the cloud and the geometry model\u27s components, an efficient initialization and classification algorithm is introduced. While this technique works well once the configuration is close enough, it occasionally fails when the initial parametrized configuration is too far from the cloud of points. To circumvent this problem, the objective function is modified, which has yielded good results for all cases tested. This technique is applied to a series of increasingly complex configurations. The final configuration represents a full transport aircraft configuration, with a wing, fuselage, empennage, and engines. Although only applied to aerospace applications, the technique is general enough to be applicable in any domain for which basic parametrized models are available