f3cd8c03-2fde-4cb7-8e25-34087fc620a5 45 3 5 decimal

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

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

i 030 range :

j 018 range :

radius 20 :

p π - i π * 15 / + :

q π - j π * 9 / + :

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

i 1 u rows range R i el 5 u i el * 625 i - / + : for

i 1 u rows range r i el 1.5 u i el * 425 i - / + : for

The 3 vectors [u,R,r] ... The 3 matrices [X,Y,Z] do sanity check Mathcad 11.

X 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 : for for mx 21 line :

Y i 131 range j 119 range my i j el r t el q j el u t el / sin * eval : for for my 21 line :

Z i 131 range j 119 range 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 : for for mz 21 line :

t x X Unwrap : t y Y Unwrap : t z Z Unwrap : t xyz t x t y t z augment eval : 41 line

Thanks Ber7 for speeding the Torus. I have not found the same Mathcad orientation. Interesting about plotting and rotate the "scatter vectors" system. Scatter is the (x,y,z)in augmented form ||| from matrices.

step1 120 range :

Extract a specific "roll" 20 xyz 0.257 - 0.354 - 8.157 0.591 - 0.354 - 8.072 0.9 - 0.354 - 7.923 1.174 - 0.354 - 7.716 1.402 - 0.354 - 7.458 1.574 - 0.354 - 7.16 1.683 - 0.354 - 6.834 1.726 - 0.354 - 6.493 1.7 - 0.354 - 6.15 1.607 - 0.354 - 5.819 1.45 - 0.354 - 5.513 1.236 - 0.354 - 5.244 0.973 - 0.354 - 5.023 0.671 - 0.354 - 4.859 0.342 - 0.354 - 4.758 0 0.354 - 4.723 0.342 0.354 - 4.758 0.671 0.354 - 4.859 0.973 0.354 - 5.023 1.236 0.354 - 5.244 1.45 0.354 - 5.513 1.607 0.354 - 5.819 1.7 0.354 - 6.15 233 mat

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

Torus t xyz γ * eval :

@ Frame rate [1], rolling is visible

Torus

angle Ω1 1000 angle cos angle sin - 0 angle sin angle cos 33 mat :

Матрица преобразования для поворота вокруг оси y angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Матрица преобразования для поворота вокруг оси z angle Ω3 angle cos angle sin - 0 angle sin angle cos 000133 mat :

α 180 ° * :

β 135 ° * :

φ 270 ° * :

γ α Ω1 β Ω2 * φ Ω3 * eval : 1.2989 1016 -^* 0.7071 - 0.7071 1 1.8369 1016 -^* 0 1.2989 1016 -^* - 0.7071 0.7071 33 mat

R 1 : r 0.5 : 12 mat

u v f R r u cos * + (v cos * (R r u cos * + (v sin * r u sin * 31 mat :

Torus equation

x,y mesh = even, practical limit 30 x 30 ... 40 x 40 M u v f π - π π - π 3030 CreateMesh :