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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Error measurement for 100 data points

From: Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

Test function

Method

α

β

γ

Max. Error

COD, \(r^{2}\)

\(F_{1}\)

Proposed scheme

0

0

0

0.01327875

0.999912128

0.5

0.5

0.5

0.012703223

0.999965192

1

1

1

0.012527293

0.999969234

1.5

1.5

1.5

0.012972964

0.999956775

2

2

2

0.013307217

0.999939037

RBF

Linear

0.045764175

0.999020404

Thin plate

0.02673708

0.999781811

Gaussian

0.016490476

0.999901308

Multiquadric

0.018715584

0.999944503

\(F_{2}\)

Proposed scheme

0

0

0

0.004299433

0.999888327

0.5

0.5

1

0.001704035

0.999981796

1

1

1

0.000423733

0.999998995

1.5

1.5

2

0.001262135

0.999989182

2

2

2

0.002189063

0.999969739

RBF

Linear

0.007574866

0.99956425

Thin plate

0.002558841

0.999952891

Gaussian

0.001716047

0.999979641

Multiquadric

0.001518386

0.99998958

F3

Proposed scheme

0

0

0

0.006227877

0.999833076

0.5

0.5

0.5

0.002603843

0.999957872

1

1

1

0.00242092

0.999974602

1.5

1.5

1.5

0.002923569

0.999953996

2

2

2

0.003911407

0.999920738

RBF

Linear

0.019392135

0.998325827

Thin plate

0.004887544

0.999887104

Gaussian

0.001008888

0.999995475

Multiquadric

0.000371279

0.99999926

\(F_{4}\)

Proposed scheme

0

0

0

0.006370899

0.999779457

0.5

0.5

0.5

0.002586925

0.999963996

1

1

1

0.000130732

0.99999994

1.5

1.5

1.5

0.001748691

0.99998296

2

2

2

0.00310011

0.9999469

RBF

Linear

0.011647112

0.999181379

Thin plate

0.007628386

0.999786938

Gaussian

0.014452639

0.999286921

Multiquadric

0.006187163

0.999869078

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