Rooted uncrossed knight's paths of length <= 3

Hugo Pfoertner, 2019-01-06

OEIS A323131

Each knight move is represented by a straight line segment of scaled length 1,
which needs to be rotated and rescaled by Sqrt(5) to fit on a chessboard.
To enable the use of Markus Sigg's Snake Viewer program, the true
direction changes of the knight's path are rounded to the nearest integer
multiples of 9 degrees. The direction changes of the path are coded by letters and 0:
0 (continuation of previous direction), d, D, f, F, j, J (right angle turn), n, N, p, P.
See the examples for lenght = 2.
The diameter of the enclosing circle of the path calculated by the drawing program
usually deviates from the indicated exact diameter due to the said mapping of the angles.
Isomorphisms by reflection and path reversal are indicated by (same as ...)

Turning angle code, diameter of enclosing circle (symmetry)

Length = 2 (7 paths):

p, 1.0540925534 (symmetric)
j, 1.4142135624 (symmetric)
f, 1.7888543820 (symmetric)
0, 2.0000000000 (symmetric)
D, 1.8973665961 (symmetric)
J, 1.4142135624 (symmetric) (same as j)
N, 1.1180339887 (symmetric)

Length = 3 (47 paths):

pj, 1.4142135624
pd, 1.8973665961
p0, 2.0000000000
pF, 1.8027756377
pJ, 1.6288220359
pP, 1.3416407865 (symmetric)
jp, 1.4142135624 (same as pj)
jj, 1.4142135624 (symmetric)
jf, 1.8027756377
j0, 2.2360679775
jD, 2.4083189158
jJ, 2.2360679775 (symmetric)
jN, 1.8439088915
fn, 1.7888543820
fj, 1.8027756377 (same as jf)
fd, 2.4083189158
f0, 2.7202941017
fF, 2.7202941017 (symmetric)
fJ, 2.4083189158
fP, 1.8027756377 (same as pF)
0p, 2.0000000000 (same as p0)
0j, 2.2360679775 (same as j0)
0f, 2.7202941017 (same as f0)
00, 3.0000000000 (symmetric)
0D, 2.8635642127
0J, 2.2360679775 (same as j0)
0N, 2.0000000000
Dn, 1.9436506316
Dj, 2.4083189158 (same as jD)
Dd, 2.8635642127 (symmetric)
D0, 2.8635642127 (same as 0D)
DF, 2.4083189158 (same as fd)
DJ, 1.9436506316
DP, 1.8973665961 (same as pd)
Jp, 1.6288220359 (same as pJ)
Jj, 2.2360679775 (symmetric) (same as jJ)
Jf, 2.4083189158 (same as fJ)
J0, 2.2360679775 (same as j0)
JD, 1.9436506316 (same as DJ)
JJ, 1.4142135624 (symmetric) (same as jj)
JN, 1.4142135624
Nn, 1.6124515497 (symmetric)
Nj, 1.8439088915 (same as jN)
Nd, 1.9436506316 (same as Dn)
N0, 2.0000000000 (same as 0N)
NF, 1.7888543820 (same as fn)
NJ, 1.4142135624 (same as JN)

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