cc045380-9115-4a8b-80c0-f7a363e881c3 7 4 5 decimal

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

θ rot θ cos θ sin - θ sin θ cos 22 mat :

Fourier . . . star

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add/delete extreme'0'

Global points specs algo data spec pts i 1 data rows range p i el char size clr spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

Y svg 000100017 mat * transpose :

svg 0.75 :

Fourier "ifft" from padded created vector [Numeric] v ifft N v length : n 0 N range I n 1 + el 1 N sqrt / v k 1 + el e i 2 π * n * N / (* k * -^* (k 0 N 1 - sum eval * : for I 31 line :

r 0.125 : x f1 r x 2^- sqrt ± : 21 sys

U Y ifft mat2sys sys2mat : a U Re mat2sys sys2mat : b U Im mat2sys sys2mat : 31 line

ab a b augment : char size clr spec . 14 red 13 mat : pts ab char size clr spec pts : 31 line

ab pts 2 1 sys ab x f1 2 1 sys

ab 0.2835 0 0.2554 - 0.123 - 0.1767 0.2216 0.0631 - 0.2764 - 0.0631 - 0.2764 0.1767 0.2216 - 0.2554 - 0.123 0.2835 8.6932 1015 -^* - 82 mat

θ π - 2 / : ° 90 -

Rot ab θ rot * :

Rot x f1 2 1 sys

Y 0 :

U 0 :

a 0 :

b 0 :

Fourier . . . circle/ellipse

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svg 1.5 : pad 12 : sx 0.6255 2 / - : sy 0 : 41 line

Circle pad system Y n 2 pad * 1 - (: i 1 n range Y i el 1 : for i 2 n 1 - (range Y i el 0 : for svg Y * 41 line :

The population of the '0' padding sets the angular population of the coplanar. Circles have "2*pad" points. Here, we shift the native svg circle by ½ . Exercise your own project ...

U Y ifft mat2sys sys2mat : a U Re mat2sys sys2mat sx + : b U Im mat2sys sys2mat sy + : 31 line

π pad / ° 15

Y transpose 1.5 000000000000000000000 1.5 123 mat

ø 1 :

circ ø a * ø b * augment : char size clr spec . 12 red 13 mat : circle circ char size clr spec pts : 31 line

Single coplanar circle

circ circle circle 1 1 el 0.5 circle 1 1 el 0.5 - 2 2 mat 3 1 sys

ø 0.5 :

oblate/prolate ellipse(s) ell 1 a * ø b * augment : char size clr spec . 9 black 13 mat : ellipse ell char size clr spec pts : 31 line

Single coplanar ellipse

circle ellipse circle 1 1 el 0.5 circle 1 1 el 0.5 - 2 2 mat 3 1 sys