Radial Construction

7de51a1a-f428-4bd2-b40a-9d59aad37e5f 12 15 12 decimal

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

Radial Construction

tt rkf D A rkf 1 el rkf 2 el 21 mat * :

A 022 - 022 mat :

tt rkf D 022 - 022 mat rkf 1 el rkf 2 el 21 mat *

span 1 n π * / : α π : (overlap ≡ 21 line

circles n setCs U 00013 mat : p circles W p span 21 mat : Urk W 0 α n tt rkf D rkfixed : U U Urk stack : 31 line for B U 3 col U 2 col augment : 31 line :

Rename: Y => .. else variable name t u RK u 2 el u 3 el 1 u 1 el (2^- (* u 2 el * (u 1 el - 031 mat :

Either 'rkfixed' or 'Rkadapt' Y0 t0 t1 N sradial Y0 t0 t1 N t u RK Rkadapt :

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem Nvy vy length : i 1 Nvy range q i el 3 : q Nvy el 2 : 21 line for 11 line i 1 Nvy range v i el i : for i 1 Nvy range Ω 3 i * el vy i el : for u q v replicate : V u Ω augment : V V 3 V rows 12 submatrix : 71 line :

1. specify the radial grid system

radii & number of grid circles
'n' ... populate circles circles 0.375 0.75 113 mat : n 200 : 21 mat

Circles system

--------
radius radial
-------- Y0 0 1.25 031 mat :

t0 0 : t1 2 π * : N 12 : 31 line

Radial system

2. collect the radial grid system

stacked circles
Xradial stem
Yradial stem radcirc circles n setCs : Xradial Y0 t0 t1 N sradial 3 col : Yradial Y0 t0 t1 N sradial 2 col : 31 sys

pairwise radial radial Xradial stem 2 col Yradial stem 2 col augment :

Lissajous

u 0 : v 2 π * : pop 41 : 13 mat u v pop var u v u v u - pop / + (range : t u v pop var : 31 sys

Lissajous t fX 1 t sin * : t fY 12 t * sin * : 21 sys

i 1 t rows range X i el t i el fX eval : for

i 1 t rows range Y i el t i el fY eval : for

Lissajous X Y augment :

circles number, radii ≡ n populate circles ≡ t0 t1 12 mat radial disposition ≡ N N radial ≡ Y0 1 el radius radial ≡ 51 line

radial radcirc 2 1 sys radial radcirc Lissajous 3 1 sys

radcirc rows 604

radial 1.25 00000 1.08 0.63 0000 0.63 1.08 00000 1.25 0000122 mat

radcirc 00 0.002 0.375 0.01 - 0.375 0.022 - 0.374 0.034 - 0.373 0.045 - 0.372 0.057 - 0.371 0.069 - 0.369 0.08 - 0.366 0.092 - 0.364 0.103 - 0.361 0.114 - 0.357 122 mat

L H N xd U 0 : dx H L - N / : 12 mat i 1 N range U i el L dx - (dx i * + eval : for U 31 line :

L 2 π * - : H 0 : N 100 : 13 mat x L H N xd : 21 mat

t0 1 time :

x R1 0.25 x cos * : x R2 0.5 x cos * : x R3 0.75 x cos * : x R4 x cos : 41 sys

x I1 0.25 x sin * : x I2 0.5 x sin * : x I3 0.75 x sin * : x I4 x sin : 41 sys

C1 x R1 vectorize x I1 vectorize augment : C2 x R2 vectorize x I2 vectorize augment : C3 x R3 vectorize x I3 vectorize augment : C4 x R4 vectorize x I4 vectorize augment : 41 sys

collection slows the plot,
sometimes  useful whereas it
allows manipulating the plot
vg: Maths Tangent/Normal plot C1 C2 C3 C4 41 sys :

Quite demanding x y axes x y / - :

x r c r 2^x 2^- sqrt ± :

C1 C2 C3 C4 4 1 sys C1 C2 C3 C4 radial Lissajous 6 1 sys x 1 c x 0.5 c 2 1 sys

1 time t0 - 0.9 s *