Euler system

c75e59f3-e3aa-43b8-ba49-e0cfa59f5a78 13 4 5 decimal

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

Example 12 . . . Interpolate 2D matrix

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data 000000 0.7 0.65 0.6 0.45 0.3 0.15 1.4 1.35 1.2 0.8 0.55 0.25 2.15 2.1 1.75 1.25 0.85 0.4 2.95 2.75 2.35 1.7 1.15 0.6 3.8 3.5 2.95 2.15 1.5 0.75 4.8 4.3 3.65 2.65 1.85 1 5.95 5.2 4.3 3.1 2.2 1.25 7.05 6.05 5.1 3.65 2.55 1.5 8.35 7 5.85 4.2 3 1.8 9.6 7.95 6.65 4.85 3.4 2.1 10.95 8.9 7.45 5.4 3.9 2.45 12.55 9.85 8.2 6 4.4 2.8 14.15 10.85 9.05 6.65 4.9 3.2 15.75 11.85 9.8 7.25 5.35 3.6 156 mat :

end 15.75 11.85 9.8 7.25 5.35 3.6 16 mat transpose :

j x λ idx 014 range : idx data j col x ainterp 21 line :

x j c 10 x ≤ (x end j el ≤ (& cases :

plot 1 x λ x 1 c * 2 x λ x 2 c * 3 x λ x 3 c * 4 x λ x 4 c * 5 x λ x 5 c * 6 x λ x 6 c * 61 sys :

plot

114 λ 15.75

M x y 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 s j el B C 1 C rows j j submatrix y linterp : for A transpose s x linterp 51 line :

Metric the system for data table interpolation

Lo 0 : Hi 1 : 12 mat

rangeX i 1 data cols range mx i el i Hi Lo - data cols / * : for mx 21 line :

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

New rangeY rangeX transpose data stack augment : 0 0.1667 0.3333 0.5 0.6667 0.8333 1 0.0667 000000 0.1333 0.7 0.65 0.6 0.45 0.3 0.15 0.2 1.4 1.35 1.2 0.8 0.55 0.25 0.2667 2.15 2.1 1.75 1.25 0.85 0.4 0.3333 2.95 2.75 2.35 1.7 1.15 0.6 0.4 3.8 3.5 2.95 2.15 1.5 0.75 0.4667 4.8 4.3 3.65 2.65 1.85 1 0.5333 5.95 5.2 4.3 3.1 2.2 1.25 0.6 7.05 6.05 5.1 3.65 2.55 1.5 0.6667 8.35 7 5.85 4.2 3 1.8 0.7333 9.6 7.95 6.65 4.85 3.4 2.1 0.8 10.95 8.9 7.45 5.4 3.9 2.45 0.8667 12.55 9.85 8.2 6 4.4 2.8 0.9333 14.15 10.85 9.05 6.65 4.9 3.2 1 15.75 11.85 9.8 7.25 5.35 3.6 167 mat

New 11 el x/y :

New x/y 0.167 0.333 0.5 0.667 0.833 1 0.067 000000 0.133 0.7 0.65 0.6 0.45 0.3 0.15 0.2 1.4 1.35 1.2 0.8 0.55 0.25 0.267 2.15 2.1 1.75 1.25 0.85 0.4 0.333 2.95 2.75 2.35 1.7 1.15 0.6 0.4 3.8 3.5 2.95 2.15 1.5 0.75 0.467 4.8 4.3 3.65 2.65 1.85 1 0.533 5.95 5.2 4.3 3.1 2.2 1.25 0.6 7.05 6.05 5.1 3.65 2.55 1.5 0.667 8.35 7 5.85 4.2 3 1.8 0.733 9.6 7.95 6.65 4.85 3.4 2.1 0.8 10.95 8.9 7.45 5.4 3.9 2.45 0.867 12.55 9.85 8.2 6 4.4 2.8 0.933 14.15 10.85 9.05 6.65 4.9 3.2 1 15.75 11.85 9.8 7.25 5.35 3.6 167 mat

once done isolate

Duro x/y 0.167 0.333 0.5 0.667 0.833 1 0.067 000000 0.133 0.7 0.65 0.6 0.45 0.3 0.15 0.2 1.4 1.35 1.2 0.8 0.55 0.25 0.267 2.15 2.1 1.75 1.25 0.85 0.4 0.333 2.95 2.75 2.35 1.7 1.15 0.6 0.4 3.8 3.5 2.95 2.15 1.5 0.75 0.467 4.8 4.3 3.65 2.65 1.85 1 0.533 5.95 5.2 4.3 3.1 2.2 1.25 0.6 7.05 6.05 5.1 3.65 2.55 1.5 0.667 8.35 7 5.85 4.2 3 1.8 0.733 9.6 7.95 6.65 4.85 3.4 2.1 0.8 10.95 8.9 7.45 5.4 3.9 2.45 0.867 12.55 9.85 8.2 6 4.4 2.8 0.933 14.15 10.85 9.05 6.65 4.9 3.2 1 15.75 11.85 9.8 7.25 5.35 3.6 167 mat :

# col[X] row[Y] Spline

sanity
user
user Duro 0.667 0.4 Spline 2.15 MPa @ = Duro 0.6 0.35 Spline 2.09 MPa @ = Duro 0.4 0.7 Spline 6.98 MPa @ = 31 mat

Metric/Interpolate otherwise simple example

°C vx 251015202516 mat :

мм vy 1.5 2.0 2.5 4.0 5.0 51 mat :

Вт/м else 49172535454101928395051120314254512233547606142638516656 mat :

native Smath from f(x) menu 
[vx, vy] in ascending order # # # # # InterpBilinear

vx vy else 7.5 3.0 InterpBilinear 16.1667

1. Construct the 3D plot

Introduce the 3D surface plot uu vv q uu vv Duro uu vv Spline 31 mat :

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

N mesh within the bounds [L, H] in each directions M3D uu vv q L H L H N# N# CreateMesh :

Euler system

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 0.0 - (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 :

x y axes x y / - :

plot the 2D surface plot plot M3D f :

plot axes 2 1 sys

3. Back to the very original Durometer

°C vx 01234516 mat :

мм vy 01234567891011121314151 mat :

data 000000 0.7 0.65 0.6 0.45 0.3 0.15 1.4 1.35 1.2 0.8 0.55 0.25 2.15 2.1 1.75 1.25 0.85 0.4 2.95 2.75 2.35 1.7 1.15 0.6 3.8 3.5 2.95 2.15 1.5 0.75 4.8 4.3 3.65 2.65 1.85 1 5.95 5.2 4.3 3.1 2.2 1.25 7.05 6.05 5.1 3.65 2.55 1.5 8.35 7 5.85 4.2 3 1.8 9.6 7.95 6.65 4.85 3.4 2.1 10.95 8.9 7.45 5.4 3.9 2.45 12.55 9.85 8.2 6 4.4 2.8 14.15 10.85 9.05 6.65 4.9 3.2 15.75 11.85 9.8 7.25 5.35 3.6 156 mat :

native Smath from f(x) menu 
[vx, vy] in ascending order
Metric both directions at will # # # # # InterpBilinear

copy MPa/paste ▼ in empty place holder MPa 1 :

vx vy data 2.5 4.5 InterpBilinear MPa 2.2875

Discretize for X_Y plot

15.75 11.85 9.8 7.25 5.35 3.6 16 mat transpose

λ1 t 0 15.75 0.1 range : i 1 t rows range λ1 i el 1 t i el λ eval : for t λ1 augment 31 line :

λ2 t 0 11.85 0.1 range : i 1 t rows range λ2 i el 2 t i el λ eval : for t λ2 augment 31 line :

λ3 t 0 9.8 0.1 range : i 1 t rows range λ3 i el 3 t i el λ eval : for t λ3 augment 31 line :

λ4 t 0 7.25 0.1 range : i 1 t rows range λ4 i el 4 t i el λ eval : for t λ4 augment 31 line :

λ5 t 0 5.35 0.1 range : i 1 t rows range λ5 i el 5 t i el λ eval : for t λ5 augment 31 line :

λ6 t 0 3.6 0.1 range : i 1 t rows range λ6 i el 6 t i el λ eval : for t λ6 augment 31 line :

Enveloppe 15.75 18.47 11.85 9.66 9.8 6.49 7.25 3.21 5.35 1.605 3.6 0.52 62 mat :

vx Enveloppe 1 col : vy Enveloppe 2 col : 12 mat x Env vx vy x ainterp : x c 10 x ≤ (x 16 ≤ (& cases : 31 mat

plot λ1 λ2 λ3 λ4 λ5 λ6 x Env Enveloppe 81 sys :

plot