Table 2 Initial conditions for the special cases of GCS
From: A rational cubic trigonometric approximation scheme of the generalized Cornu spirals
Initial conditions | Circular arc | Cornu spiral | Logarithmic spiral | Non-inflecting GCS | Normalized GCS |
|---|---|---|---|---|---|
S | 1.5707 | 4.0 | 8.0 | 3.0 | 1 |
r | 0.0 | 0.0 | −0.75 | 0.4 | 0.1 |
k(0) | 1.0 | 0.1 | 0.1 | 0.1 | 0.36 |
k(S) | 1.0 | 0.5 | 0.4 | 0.5 | 2.7 |
r(0) | (0, 0) | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
r(S) | (1, 1) | (3.362, 1.680) | (6.199, 3.959) | (2.670, 1.076) | (0.7499, 0.4915) |
θ(0) | 0 | 0 | 0 | 0 | 0 |
θ(S) | 1.5707 | 1.2 | 1.497 | 0.967 | 1.5672 |