Table 1 Relative curvature errors and CPU time consumption
From: A rational cubic trigonometric approximation scheme of the generalized Cornu spirals
Approximation schemes | Maximum relative curvature error (σ)/CPU time (s) | Circular arc | Cornu spiral | Logarithmic spiral | Non-inflecting GCS | Normalized GCS |
|---|---|---|---|---|---|---|
G 2-approximation (Theorem 1) | σ | 9.7977 × 10−8 | 5.911 × 10−4 | 7.8252 × 10−4 | 5.52 × 10−4 | 0.0012 |
CPU time | 21.6380 | 17.769 | 39.0940 | 14.9760 | 21.1380 | |
G 1-approximation (Theorem 2) | σ | 5.62 × 10−5 | 8.94 × 10−4 | 3.60 × 10−3 | 4.10 × 10−3 | 0.0010 |
CPU time | 34.0870 | 20.230 | 45.0670 | 25.9800 | 26.9880 |