1b0c1e6d-b960-4999-8721-e14dd036036d 46 15 12 decimal

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

3D Utilities

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

1. Sr(X,Y,Z,u,v) creates the 3 sequential vectors required for 2D unicolor plot & 3D grid points. 2. Sym(f(x,y),U,V) a matrix creator. Both algorithms are paired with [U,V] => xd(L,H,N)

Sequential triplet : U, V, Z x y X x y Y x y Z u v Sr count 1 : i 1 u rows range j 1 v rows range U count el u i el v j el X eval : V count el u i el v j el Y eval : Z count el u i el v j el Z eval : count count 1 + : 41 line for for U V Z augment 31 line :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 41 line :

L 1 - : H 1 : N 40 : 13 mat U 1 - 1 N xd : V U : 12 mat 21 line

x y X x : x y Y y : x y Z 1 x 2^y 2^+ (- 0.1 / exp * : 31 sys

G x y X x y Y x y Z U V Sr : P1 G 1 col G 3 col augment : P2 G 2 col G 3 col augment : 31 sys

P2 rows 1681

select a trace n 18 :

Export the 'n' trace sub P2 n 1 - n + (N * + (n 1 N + (* (range 12 range el :

trace sub o 5 black plot :

P1 P2 trace 3 1 sys

Plot points, rotate

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

θ π - 2 / :

θ 1.5708 -

Stem plot

P1 θ rot *

Zone plot

P2 θ rot *

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 41 line :

u v f 1 u 2^v 2^+ (- 0.1 / exp * :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

U 0 :

V 0 :

L 1 - :

H 1 :

N 6 :

U L H N xd :

V U :

data x y f U V Sym :

data max 1

x y M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x linterp 51 line :

New x/y U stack V transpose data stack augment :

New x/y 1 - 0.667 - 0.333 - 0 0.333 0.667 11 - 0000000 0.667 - 00 0.004 0.012 0.004 00 0.333 - 0 0.004 0.108 0.329 0.108 0.004 000 0.012 0.329 1 0.329 0.012 0 0.333 0 0.004 0.108 0.329 0.108 0.004 0 0.667 00 0.004 0.012 0.004 001000000088 mat

Command line interpolation

sanity
sanity
user 1 - 0 New Spline 0.6667 - 0 New Spline 0.5 - 0 New Spline 31 mat 0 0.0117 0.1705 31 mat

<= Introduce the 3D surface plot u v q u v u v New Spline 31 mat :

M u v q 1 - 11 - 12121 CreateMesh :

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

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

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

α π 3 / :

β 0.0 - (π * :

φ 0.0 - (π * :

θ 0.25 π * :

<= Rotate around Y

γ α Ω1 β Ω2 * φ Ω3 * eval :

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

X 0 :

m 2 :

XY X m - X X X X X X m + 00 m 0 m - 0027 mat transpose :

plot M f :

plot XY 2 1 sys

α β φ θ 41 mat ° 60004541 mat

| | Orientation |

<= Rotate around Y

3D Utilities

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data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Sequential triplet : U, V, Z x y X x y Y x y Z u v Sr count 1 : i 1 u rows range j 1 v rows range U count el u i el v j el X eval : V count el u i el v j el Y eval : Z count el u i el v j el Z eval : count count 1 + : 41 line for for U V Z augment 31 line :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 41 line :

816 π * sqrt * 351.6702

a 1 : x y Φ 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - : 21 line

L 10 - : H 10 : N 50 : 13 mat U L H N xd : V U : 12 mat 21 line

x y X x : x y Y y : x y Z x y Φ : 31 sys

E x y X x y Y x y Z U V Sr : P1 E 1 col E 3 col augment : P2 E 2 col E 3 col augment : 31 sys

select a trace n 25 :

Export the 'n' trace sub P2 n 1 - n + (N * + (n 1 N + (* (range 12 range el :

Resume/collect project trace sub o 5 black plot : x Electron sub 1 col sub 2 col x cinterp : x c 110 - x ≤ (x 10 ≤ (& cases : 31 sys

x Electron x c * P2 trace 3 1 sys