Table 4 The result of optimization models for geodesic interpolation GHT-Bézier developable surfaces with developability degree values.

From: Engineering oriented shape optimization of GHT-Bézier developable surfaces using a meta heuristic approach with CAD/CAM applications

Iterations

Optimal shape

Fitness function

Developability

–

Parameters \((\lambda , \alpha , \beta )\)

(Arc length)

Degree

Iter 1

(0.3122,0.2246,0)

21.3475

0.0547

Iter 2

(0.0812,0.1533,0)

20.1796

0.1826

Iter 3

(0.0750,0.1416,0)

20.1131

0.2286

Iter 4

(0.0550,0.1039,0)

19.9014

0.3195

Iter 5

(0.1933,-0.0711,0)

19.8218

0.3964

Iter 6

(0.0440,0.0832,0)

19.7867

0.4230

Iter 7

(0.0382,0.0721,0)

19.7260

0.5415

Iter 8

(0.1312,-0.1222,0)

19.4193

0.6184

Iter 9

(0.0615,-0.1145,0)

19.1824

0.7324

Iter 10

(0.0873,0.0723,0)

19.1161

0.8760

Iterations

Optimal Shape

Fitness Function

Developability

-

parameters \((\lambda , \alpha , \beta )\)

Energy

Degree

Iter 1

(0.0812,0.1533,0)

123.842

0.0498

Iter 27

(0.0750,0.1416,0)

122.783

0.1294

Iter 3

(0.0550,0.1039,0)

119.486

0.2619

Iter 4

(0.0440,0.0832,0)

117.75

0.3128

Iter 5

(0.0397,0.0750,0)

117.081

0.4243

Iter 6

(0.0382,0.0721,0)

116.846

0.5829

Iter 7

(0.1263,-0.2057,0)

111.325

0.6583

Iter 8

(0.0597,-0.1940,0)

107.542

0.7528

Iter 9

(0.0018,-0.1139,0)

106.802

0.8429

Iter 10

(0.0133,-0.1753,0)

105.509

0.9121

Iterations

Optimal Shape

Fitness Function

Developability

-

parameters \((\lambda , \alpha , \beta )\)

(Curvature Variation Energy)

Degree

Iter 1

(-0.8291,-0.2126,0)

1330.85

0.1426

Iter 2

(-0.1748, -0.3794,0)

656.93

0.2142

Iter 3

(-0.3151, 0.0583,0)

428.694

0.3214

Iter 4

(-0.3015, 0.0482,0)

422.694

0.4963

Iter 5

(0.0199, -0.2126,0)

228.52

0.5429

Iter 6

(0.0482,-0.0326,0)

221.248

0.6248

Iter 7

(0.0099, -0.0126,0)

218.52

0.7534

Iter 8

(0.2482, -0.1316,0)

219.252

0.7912

Iter 9

(0.0482, -0.0326,0)

210.248

0.8246

Iter 10

(0.0114,0.1054,0)

172.13

0.9998

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