A Review on Approaches for Handling Bezier Curves in CAD for Manufacturing

Fitter, Hetal N.; Pandey, Akash; Patel, Divyang D.; Mistry, Jitendra M.

doi:10.1016/j.proeng.2014.12.394

Cited by 32 publications

(17 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Finally, we digitized West Bengal's highways using road maps from the National Highways Authority of India (Government of India, 2019). To improve cartographic quality, highways were smoothed out by creating Bezier curves to match the original input lines (Fitter et al, 2014). We used the Bezier interpolation smoothing algorithm without smoothing tolerance, and made sure no topological errors occurred after the smoothing operation.…”

Section: Design and Methodsmentioning

confidence: 99%

New urban geographies of West Bengal, East India

2020

View full text Add to dashboard Cite

This article is part of a larger research project on new urban geographies in India. Between the population censuses of 2001 and 2011, India witnessed a record increase of 2,532 new Census Towns, small settlements that meet the country's criteria to be considered 'urban'. This steep increase is intricately linked with decreases in agricultural jobs, but we know very little about the spatiality of these urban geographies, alternative local employment, or the nature of the local economies of Census Towns. Based on a tailored geodatabase, our Main Map visualizes the geography of these heretofore uncharted Census Towns in the state of West Bengal. We then draw on reconnaissance fieldwork to zoom in on a cluster of Census Towns in central Bengal where we find evidence of urban growth that appears linked to road infrastructure, what we described in earlier conceptual work as "emergent highway urbanization". The Main Map and reconnaissance fieldwork contribute to a better, albeit early-stage, understanding of the rapidly changing spatiality of contemporary urbanization in this region.

show abstract

Section: Design and Methodsmentioning

confidence: 99%

New urban geographies of West Bengal, East India

2020

View full text Add to dashboard Cite

show abstract

“…This approach is characterized by imposing the parametric curve to pass through all data points. However, most reverse engineering applications retrieve data from scanning, digitizing [1], or some mechanical device, such as pressure machines in the shoemaking industry [2], thus being subjected to measurement errors. In case of high-intensity noise, interpolation methods tend to fail since they force the curve to pass through all points, including the noisy outliers.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Therefore, our goal is to obtain the three sets of parameters { } =1 , { } =0 , and {b } =0 . It is obvious that since each blending function in (2) and (4) is nonlinear in , system (5) is also nonlinear. As a consequence, we have to deal with a multivariate continuous nonlinear minimization problem.…”

Section: The Fitting Problemmentioning

confidence: 99%

“…which corresponds to a curve on a torus. We consider a set of 202 three-dimensional data points with uniform sampling in the interval domain [0,2 ]. This dataset, labelled as torus in Table 1, is then perturbed with additive white noise of different intensities, modulated by a signal-to-noise ratio (SNR) ranging from 10 (very high intensity) to 90 (low intensity), with step-size 10.…”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Two Simulated Annealing Optimization Schemas for Rational Bézier Curve Fitting in the Presence of Noise

Iglesias

Gálvez

Loucera

2016

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Fitting curves to noisy data points is a difficult problem arising in many scientific and industrial domains. Although polynomial functions are usually applied to this task, there are many shapes that cannot be properly fitted by using this approach. In this paper, we tackle this issue by using rational Bézier curves. This is a very difficult problem that requires computing four different sets of unknowns (data parameters, poles, weights, and the curve degree) strongly related to each other in a highly nonlinear way. This leads to a difficult continuous nonlinear optimization problem. In this paper, we propose two simulated annealing schemas (the all-in-one schema and the sequential schema) to determine the data parameterization and the weights of the poles of the fitting curve. These schemas are combined with least-squares minimization and the Bayesian Information Criterion to calculate the poles and the optimal degree of the best fitting Bézier rational curve, respectively. We apply our methods to a benchmark of three carefully chosen examples of 2D and 3D noisy data points. Our experimental results show that this methodology (particularly, the sequential schema) outperforms previous polynomial-based approaches for our data fitting problem, even in the presence of noise of low-medium intensity.

show abstract

“…Finally, by means of a post-processor, a specific numerical control (NC) program is created [5]. Nevertheless, creating a complex curve in a CAD/CAM system is not always straightforward [6,7,8]. In CAD/CAM systems, complex curve trajectories are usually defined by curve fitting, having as input a set of points belonging to the nominal curve trajectory.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

et al. 2019

View full text Add to dashboard Cite

Nanotechnology applications demand high accuracy positioning systems. Therefore, in order to achieve sub-micrometer accuracy, positioning uncertainty contributions must be minimized by implementing precision positioning control strategies. The positioning control system accuracy must be analyzed and optimized, especially when the system is required to follow a predefined trajectory. In this line of research, this work studies the contribution of the trajectory definition errors to the final positioning uncertainty of a large-range 2D nanopositioning stage. The curve trajectory is defined by curve fitting using two methods: traditional CAD/CAM systems and novel algorithms for accurate curve fitting. This novel method has an interest in computer-aided geometric design and approximation theory, and allows high relative accuracy (HRA) in the computation of the representations of parametric curves while minimizing the numerical errors. It is verified that the HRA method offers better positioning accuracy than commonly used CAD/CAM methods when defining a trajectory by curve fitting: When fitting a curve by interpolation with the HRA method, fewer data points are required to achieve the precision requirements. Similarly, when fitting a curve by a least-squares approximation, for the same set of given data points, the HRA method is capable of obtaining an accurate approximation curve with fewer control points.

show abstract

A Review on Approaches for Handling Bezier Curves in CAD for Manufacturing

Cited by 32 publications

References 36 publications

New urban geographies of West Bengal, East India

New urban geographies of West Bengal, East India

Two Simulated Annealing Optimization Schemas for Rational Bézier Curve Fitting in the Presence of Noise

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

Contact Info

Product

Resources

About