Optimized NURBS Curve and Surface Fitting Using Simulated Annealing

Zhang, Jing; Feng, Shui; Hanguo, Cui

doi:10.1109/iscid.2009.227

Cited by 5 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to find a good NURBS model from large amount of data, Erkan Ulker (2012) applied the heuristic of artificial immune system for global optimization to find a smooth curve and the optimization of the NURBS weights and the knot vector. Jing et al (2009) used a simulated annealing method to optimize weights and knot parameters of NURBS for curve and surface fitting. The genetic algorithm (GA) is a common multi-variables optimization method.…”

Section: Optimization Methodsmentioning

confidence: 99%

Optimal NURBS conversion of PDE surface-represented high-speed train heads

et al. 2019

View full text Add to dashboard Cite

The head shape of high-speed trains has become a critical factor in boosting the speed further. Aerodynamic simulation-based optimization is a dominant method to obtain the optimal head shape which relies on detailed train head models defined by a lot of design variables. Since aerodynamic simulation-based optimization involves heavy calculations, too many design variables not only causes high computational costs, but also makes the optimal solution difficult to obtain. Therefore, how to use few design variables to define detailed train head model is the key to success. Partial differential equation (PDE)-based geometric modelling which creates a complicated PDE patch with few design variables provides an effective solution to this problem. In addition, it also has the advantage of naturally maintaining any high-order continuities between two adjacent surfaces which is very important in designing highly smooth train heads to achieve excellent aerodynamic performance. At the present time, PDE-based geometric modelling cannot be directly applied in computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) since it has not become an industrial standard. In contrast, non-uniform rational B-splines (NURBS) are commonly used in CAD, CAM, CAE, and many other engineering fields. They have already become part of industry wide standards. In order to apply PDE-based geometric modelling in shape design of high-speed train heads for CAD etc., how to optimally convert PDE surfaces into NURBS surfaces must be addressed. In this paper, a new method of achieving optimal conversion of PDE surfaces representing high-speed train heads into NURBS surfaces is developed. It takes control points and weight deformations of NURBS surfaces to be design variables, and the error between NURBS surfaces and PDE surfaces as the objective function. The least squares fitting and the genetic algorithm are combined to obtain the optimal conversion between PDE surfaces and NURBS surfaces. The application examples demonstrate the effectiveness of the developed method.

show abstract

Section: Optimization Methodsmentioning

confidence: 99%

Optimal NURBS conversion of PDE surface-represented high-speed train heads

et al. 2019

View full text Add to dashboard Cite

show abstract

“…NURBS curves have been used as building blocks in CAD software for decades. Some works in optimizing the NURBS representation in certain inverse problems, including reverse engineering, fitting strategies, and recovering shapes from photographs, have been done in [1,4,12,14,18,26,32,31]. Other works in X-ray tomography that readily provide segmented images can be found in [19,20,15].…”

Section: Introductionmentioning

confidence: 99%

Shape recovery for sparse‐data tomography

Haario

Kallonen²,

Laine

et al. 2017

Math Methods in App Sciences

View full text Add to dashboard Cite

A two-dimensional sparse-data tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A nonuniform rational basis splines (NURBS) curve is used as a computational representation of the boundary. This approach conveniently provides the result in a format readily compatible with computer-aided design software. However, the linear tomography task becomes a nonlinear inverse problem because of the NURBS-based parameterization. Therefore, Bayesian inversion with Markov chain Monte Carlo sampling is used for calculating an estimate of the NURBS control points. The reconstruction method is tested with both simulated data and measured X-ray projection data. The proposed method recovers the shape and the attenuation coefficient significantly better than the baseline algorithm (optimally thresholded total variation regularization), but at the cost of heavier computation.

show abstract

“…As mentioned above, a proper and precise curve fitting requires an unavoidable optimization mission. The nonlinear nature of sophisticated geometries, like turbomachinery blades' shape, and availability of high-speed parallel computers for massive computation have resulted in the use of non-gradient-based and guided random search methodologies in curve/surface fitting problems [11][12][13][14]. On the other hand, a vast variety of population-based optimization techniques have been formulated in recent decades, some of which are inspired by natural processes taking place in our environment.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of Nature-Inspired Optimization Approaches to 2D Geometric Modelling for Turbomachinery Applications

Safari

Lemu

Jafari

et al. 2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

A vast variety of population-based optimization techniques have been formulated in recent years for use in different engineering applications, most of which are inspired by natural processes taking place in our environment. However, the mathematical and statistical analysis of these algorithms is still lacking. This paper addresses a comparative performance analysis on some of the most important nature-inspired optimization algorithms with a different basis for the complex high-dimensional curve/surface fitting problems. As a case study, the point cloud of an in-hand gas turbine compressor blade measured by touch trigger probes is optimally fitted using B-spline curves. In order to determine the optimum number/location of a set of Bezier/NURBS control points for all segments of the airfoil profiles, five dissimilar population-based evolutionary and swarm optimization techniques are employed. To comprehensively peruse and to fairly compare the obtained results, parametric and nonparametric statistical evaluations as the mathematical study are presented before designing an experiment. Results illuminate a number of advantages/disadvantages of each optimization method for such complex geometries’ parameterization from several different points of view. In terms of application, the final appropriate parametric representation of geometries is an essential, significant component of aerodynamic profile optimization processes as well as reverse engineering purposes.

show abstract

Optimized NURBS Curve and Surface Fitting Using Simulated Annealing

Cited by 5 publications

References 6 publications

Optimal NURBS conversion of PDE surface-represented high-speed train heads

Optimal NURBS conversion of PDE surface-represented high-speed train heads

Shape recovery for sparse‐data tomography

A Comparative Analysis of Nature-Inspired Optimization Approaches to 2D Geometric Modelling for Turbomachinery Applications

Contact Info

Product

Resources

About