NURBS Curve Approximation Using Particle Swarm Optimization

Adi, Delint Ira Setyo; Shamsuddin, Siti Mariyam; Hashim, Siti Zaiton Mohd

doi:10.1109/cgiv.2010.19

Cited by 6 publications

(16 citation statements)

References 10 publications

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“…Surface approximation is the process of approximating the generated surface towards original surface using mathematical modeling. Several parameterization methods along with the characteristic were discussed in the previous works [6,15,16]. Uniform method is the simplest method compared to others [16].…”

Section: Parameterization and Surface Approximationmentioning

confidence: 99%

“…Several parameterization methods along with the characteristic were discussed in the previous works [6,15,16]. Uniform method is the simplest method compared to others [16]. While chord length method will be performed using arc length approximation.…”

Section: Parameterization and Surface Approximationmentioning

confidence: 99%

“…After parameterization was performed, knot vector will be generated using knot vector generation method. Based on [16], equally spaced method is the simplest method to generate knot vector because parameters are not required to perform this method. Parameters from parameterization will be used in averaging knot vector method to generate the knot vector.…”

Section: Parameterization and Surface Approximationmentioning

confidence: 99%

“…Averaging knot vector method is used to generate the knot values for each surface. This method has been suggested and referred from [16] and [20]. Assume that n+1 parameter with u 0 , u 1 ,..., u n and the degree d. Therefore, m+1 knot will be generated where m = n+d+1.…”

Section: Parameterization and Knot Vector Generationmentioning

confidence: 99%

“…Based on [15], because rational form leads to nonlinear problem, therefore some researchers assigned the weight, h i = 1 to avoid from the problem. By doing so, the NURBS surface will be reduced to B-Spline surface [16]. According to [21], a curve or surface must used at least with cubic degree (order 4) to represent the generic 3D entities.…”

Section: Calculation Of Basis Functions Control Points and Surfaces mentioning

confidence: 99%

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Applying NURBS Surfaces Approximation with Different Parameterization Methods on CKSOM Model Closed Surfaces Data

Lim

Haron

2014

Lecture Notes in Computer Science

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Surface reconstruction towards 3D data is a popular case study in the field of computer graphics. Although many methods are able to solve surface reconstruction problems, but limitations are still appeared. The limitations of Kohonen Self Organizing Map (KSOM) model in closed surface was handled by introducing Cube KSOM (CKSOM) model. However, the CKSOM model output is not in industrial standard format because NURBS are mostly used as surface representation in computer aided geometric design. Furthermore, NURBS surface approximation result will be affected by the parameterization methods. Therefore, the aims are to test and apply NURBS surface approximation on the CKSOM model output and to obtain less surface errors using different parameterization methods. Based on the result, NURBS was proven to be able to apply on the CKSOM model output and uniform parameterization method was proven to be the best method compared to others based on the surfaces error obtained.

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Section: Parameterization and Surface Approximationmentioning

confidence: 99%

Section: Parameterization and Surface Approximationmentioning

confidence: 99%

Section: Parameterization and Surface Approximationmentioning

confidence: 99%

Section: Parameterization and Knot Vector Generationmentioning

confidence: 99%

Section: Calculation Of Basis Functions Control Points and Surfaces mentioning

confidence: 99%

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Applying NURBS Surfaces Approximation with Different Parameterization Methods on CKSOM Model Closed Surfaces Data

Lim

Haron

2014

Lecture Notes in Computer Science

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NURBS Parameterization: A New Method of Parameterization Using the Correlation Relationship between Nodes

Jalel¹,

Naouai²,

Hamouda³

et al. 2012

Lecture Notes in Computer Science

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NURBS (Non-uniform rational B-splines) has become the industry standard tools for the representation, design and data exchange of geometric information to be processed and used by computers because of their useful geometrical properties. The problem of the parameterization of data points in NURBS curve/surface has been considered by several of researchers. We propose in this paper a new parameterization method for NURBS approximation. The current methods of parameterization such as centripetal method uses only the previous knot vector to calculate the recent knot. In this paper, we give a new parameterization method based on the correlation of the nodes. This approach inherits the advantages of the relation and position of the knots.

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Curve approximation by adaptive neighborhood simulated annealing and piecewise Bézier curves

et al. 2020

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NURBS Curve Approximation Using Particle Swarm Optimization

Cited by 6 publications

References 10 publications

Applying NURBS Surfaces Approximation with Different Parameterization Methods on CKSOM Model Closed Surfaces Data

Applying NURBS Surfaces Approximation with Different Parameterization Methods on CKSOM Model Closed Surfaces Data

NURBS Parameterization: A New Method of Parameterization Using the Correlation Relationship between Nodes

Curve approximation by adaptive neighborhood simulated annealing and piecewise Bézier curves

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