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1cfd1a09-c5a8-4e8e-8163-bb7ca05f2695 25 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Formule approximative de la clothoïde

b 2 sqrt :

convenient 'N' N 10 :

x f 1 b / 1 - (n^x 4 n * 3 +^* 2 n * 1 + (! (4 n * 3 + (* b 4 n * 2 +^* / (n 0 N sum * :

x g 1 b / 1 - (n^x 4 n * 1 +^* 2 n * (! (4 n * 1 + (* b 4 n *^* / (n 0 N sum * :

Clothoid t 0 π sqrt 0.01 range : i 1 t rows range U i el t i el f eval : V i el t i el g eval : 21 line for U V augment 31 line :

Clothoid Clothoid :

Clothoid 1 0.5475 0.9774 . 4 black 1 5 mat 0.5475 1.25 0.5475 0.25 - 2 2 mat 4 1 sys

π sqrt 1.7725

Clothoid Clothoid rows row 0.5475 0.9774 12 mat

x FS π 2 / t 2^* sin t 0 x int :

x FC π 2 / t 2^* cos t 0 x int :

π 2 / x 2 ^ * cos π 2 / x 2 ^ * sin 2 1 sys

Project notes:

This ws is in option ∫ accuracy 50.
Increasing accuracy has no impact,

Cornu s π : x s - s 0.99 s * - range : i 1 x rows range U i el x i el FS eval : V i el x i el FC eval : 21 line for U V augment 41 line :

box 0.714 - 0.78 0.714 0.78 0.714 0.78 - 0.714 - 0.78 - 0.714 - 0.78 52 mat :

x y axes x y / - :

Cornu Cornu :

Cornu box 0.5 0.5 + 100 red 1 5 mat axes 4 1 sys

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

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value table col lookup k 1 : j k table rows range table j col el value ≡ index k el j : k k 1 + : 21 line continue if for k 1 ≡ index NO match : index if 31 line :

ROW Cornu 2 col Max Cornu 2 lookup : 13311 mat

ROW Cornu ROW row augment 133 0.4436 0.7798 13 mat

Cornu Cornu 2 col Max 2 findrows 0.4436 0.7798 12 mat

x FS π 2 / t 2^* sin t 0 x int :

x FC π 2 / t 2^* cos t 0 x int :

1 FS 0.4383

1 FC 0.7799

t x' π 2 / t 2^* sin :

t y' π 2 / t 2^* cos :

t0 1 time :

curvature x 1 - 1 0.95 - range : i 1 x rows range U i el x x' (2^sqrt u 0 x int vectorize eval : V i el x y' (2^sqrt u 0 x int vectorize eval : 21 line for U 1 el V 1 el augment 31 line :

curvature curvature :

curv curvature . 3 black plot :

curvature curv 0.4 - 0.512 - + 40 red 1 5 mat 3 1 sys

1 - 0 0.9389 - 0.1449 - 0.8602 - 0.2646 - 0.7705 - 0.3589 - 0.6755 - 0.4287 - 0.5798 - 0.4758 - 0.4871 - 0.5027 - 0.4004 - 0.512 - 0.3215 - 0.5066 - 0.2516 - 0.4891 - 0.1913 - 0.4619 - 0.1407 - 0.4274 - 0.0995 - 0.3874 - 0.0669 - 0.3435 - 0.0423 - 0.297 - 0.0245 - 0.2488 - 0.0126 - 0.1996 - 0.0053 - 0.1499 - 0.0016 - 0.1 - 0.0002 - 0.05 - 00212 mat

1 time t0 - min 0.2

0.4 - 0.512 i * - arg ° 128 -