f22c036c-d889-41ea-b21d-4858058b8d6d 3 15 12 decimal

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

range/assign the system i 030 range : j 018 range : 12 mat radius 20 : p π - i π * 15 / + : q π - j π * 9 / + : 41 mat

k 0 radius range u k 1 + el 1 radius k - 1 k + / + : for

Rolling the Torus:

Original idea from Steven Finch [Mathcad/Mathsoft].

Adapted Smath in collaboration ... Jean Giraud/Ber7

... this last version Ber7 20170922

Steven is also a piano music composer.

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i 1 u rows range R i el 5 u i el * 625 i - / + : r i el 1.5 u i el * 425 i - / + : 21 line for

isolate the vectors u u : R R : r r : 13 mat

i 131 range j 119 range mx i j el R t el p i el u t el / sin * r t el 1 q j el u t el / cos - (* p i el u t el / sin * - eval : my i j el r t el q j el u t el / sin * eval : mz i j el R t el 1 p i el u t el / cos - (* r t el 1 q j el u t el / cos - (* p i el u t el / cos * + eval : 31 line for for t X mx : t Y my : t Z mz : 31 sys 21 line

γ 0 0.7071 - 0.7071 0.7071 - 0.5 0.5 0.7071 - 0.5 - 0.5 - 33 mat :

N 21 :

step1 12 N * 10 + 1 - (range :

PlotData t N > (t N 10 + ≤ (& t N : t N 10 + > t 2 N * 10 + t - : t t : if if i 1 t X cols range i 1 ≡ L1 t X i col t Y i col t Z i col augment γ * 11 mat eval : L1 L1 t X i col t Y i col t Z i col augment γ * 11 mat stack eval : if for L1 mat2sys.1 31 line :

The transformation of a plate into a torus(Jean Giraud)

PlotData