<p> Euler system </p>

65f369d8-18c2-46ca-ace4-1de4c7e4e00f 8 4 5 decimal

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

Matrix vx vy Spline2D Aa Matrix 112 Matrix cols submatrix : Bb Matrix 2 Matrix rows 11 submatrix : sub Matrix 2 Matrix rows 2 Matrix cols submatrix : j 1 Aa length 2 range spl j el Bb sub 1 sub rows j j submatrix vy linterp : for Aa transpose spl vx linterp 51 line :

data 482519548571589603 0.7377 0.7238 0.7143 0.7068 0.7003 0.6953 26 mat :

482 0.7377 519 0.7238 548 0.7143 571 0.7068 589 0.7003 603 0.6953 62 mat transpose 482519548571589603 0.7377 0.7238 0.7143 0.7068 0.7003 0.6953 26 mat

Prepare the data set ------------------------------------------------

data C j 1 data cols range C j el j : for C transpose 21 line :

data R i 1 data rows 1 + range R i el i 1 - : for R 21 line :

data R data C data stack augment

New data R data C data stack augment :

<= this position may be 
any alpha/numeric char. New 11 el x/y :

New x/y 12345614825195485715896032 0.7377 0.7238 0.7143 0.7068 0.7003 0.6953 37 mat

sanity
sanity
user New 31 Spline2D New 42 Spline2D New 3.5 1.5 Spline2D 31 mat 548 0.71 280.11 31 mat

Lo 0 : Hi 1 : 12 mat

User raw matrix raw surface : #

rangeX i 1 raw cols range vx i el i Hi Lo - raw cols / * : for vx 21 line :

rangeY i 1 raw rows range vy i 1 + el i Hi Lo - raw rows / * : for vy 21 line :

New rangeY rangeX transpose raw stack augment : #

New 11 el x/y :

Explain this Smath document:

1. A square/rectangular matrix is from user.

2. The matrix is metric in the domain [X & Y directions].

3. Can be used to interpolate within the [X, Y] domain.

4. The Spline(New,x,y) algo is passed in the vector function

q(u,v) that will produce the Smath style 3 vectors 3D

CreateMesh(q(u,v),L,H,L,H,N,N)

5. It is subjected to Euler pre-assigned rotation system.

6. f(M) extracts the 2D surface plot for the X_Y plot.

]]>

New x/y 11 mat

For this demo, the user raw matrix is 
auto-constructed in the metric domain.
copy/paste in 'New'
strictly interpolate within
the respective domains:
X [1/3 ... 1],,, Y[1/6..1] New x/y 0.3333 0.6667 1 0.1667 482599 - 812 - 0.3333 519574 - 793 - 0.5 548555 - 777 - 0.6667 571540 - 764 - 0.8333 589528 - 754 - 1603518 - 745 - 74 mat :

sanity
sanity
user New 0.6667 0.5 Spline2D New 11 Spline2D New 0.75 0.75 Spline2D 31 mat 555 - 745 - 590.23 - 31 mat

1. Construct the 3D plot

<= Introduce the 3D surface plot vu vy q vu vy New vu vy Spline2D 31 mat :

CreateMesh paramaters L 1 - : H 1 : N 21 : 31 sys

N mesh within the bounds [L, H] in each directions M3D vu vy q L H L H N N CreateMesh :

<p> Euler system </p>

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 π 4 / :

β 0.25 - (π * :

φ 0.0 - (π * :

<= Rotate around Y θ 0.125 π * :

2. Construct the 2D interpolated surface plot

Euler combined γ α Ω1 β Ω2 * φ Ω3 * eval :

M3D f B M3D θ Ω3 * γ * eval : B 1 col B 2 col augment 21 line :

plot the 2D surface plot plot M3D f :

plot 1 1 sys

rotate/zoom by mouse. 'γ' rotation added to calm down the mouse "rotate/zoom"

M3D γ * 0.1 *