The Approximation of Generalized Log-Aesthetic Curves with Cubic Trigonometric Bézier Function

Table 1

The error in approximation for various types of GLAC tested by the error measure .

#			Final			No of Itrs	Remarks
1	()	{((0, 1.17] × (0, 1.36]) ∥ ([1.17, 1.47] × (0, 1.07])}	(1, 1)		0.007	0
2	()	{((0, 1.36] × (0, 1.30]) ∥ ([1.36, 1.78] × (0, 0.96])}	(1, 1)		0.014	0
3	()	{((0, 1.08] × (0, 1.47]) ∥ ([1.08, 1.37] × (0, 1.16])}	(1, 1)		0.011	0
4	()	{((0, 1.11] × (0, 1.47]) ∥ ([1.11, 1.44] × (0, 1.14])}	(1, 1)		0.003	0
5	()	{((0, 1.06] × (0, 1.58]) ∥ ([1.06, 1.44] × (0, 1.18])}	(1, 1)		0.013	0
6	()	{((0, 1.05] × (0, 1.27]) ∥ ([1.05, 1.2] × (0, 1.11])}	(1, 1)		0.042	0	Circle involute
7	()	{((0, 1.18] × (0, 1.42]) ∥ ([1.18, 1.55] × (0, 1.07])}	(1, 1)		0.008	0	Circle involute
8	()	{((0, 1.10] × (0.1.35]) ∥ ([1.1, 1.32] × [0, 1.12])}	(1, 1)		0.008	0	Clothoid
9	()	{((0, 1.01] × (0, 1.77) ∥ ([1.01, 1.4] × (0, 1.31])}	(1, 1)		0.019	0	Clothoid
10	()	{((0, 3.2] × (0, 1.24])	(1, 1)		0.015	0	Logarithmic spiral
11	()	{((0, 1.05] × (0, 1.63]) ∥ ([1.05, 1.42] × (0, 1.21])}	(1, 1)		0.007	0	Logarithmic spiral
12	()	{((0, 1.03] × (0, 1.49]) ∥ ([1.03, 1.3] × (0, 1.2])}	(1, 1)		0.038	0	Neilsen’s spiral
13	()	{((0, 1.00 × (0, 1.74]) ∥ ([1.0, 1.37] × (0, 1.28])}	(1, 1)		0.006	0	Neilsen’s spiral
14	()	{((0, 1.25] × (0, 1.25]) ∥ ([1.25, 1.55] × (0, 0.98])}	()		0.045	1	Logarithmic spiral
15	()	{((0, 1.00] × (0, 1.59]) ∥ ([1.00, 1.33] × (0, 1.2 2])}	()		0.025	1	Logarithmic spiral