Mollier

836aa01e-ee6e-45f6-b5ca-dd54862f1fe6 36 4 5 decimal

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

Mollier

Mollier 358.93 2 363.82 4.8 368.75 10.35 373.68 20.44 378.58 37.47 383.39 64.49 388.09 105.18 391.74 150.45 395.26 209.65 398.64 285.42 401.85 380.59 404.87 498.11 407.67 641.09 410.21 812.77 412.46 1016.5 414.37 1255.7 415.87 1534.1 416.87 1855.5 417.24 2175.3 417.14 2427.4 416.65 2700.8 415.69 2996.7 414.09 3316.8 411.6 3662.7 407.72 4036.8 401.33 4441.6 387.46 4882 366.59 4990282 mat :

Hermite . . . reverse interpolation, discrete, clean

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1. For best use/suite, revisit 'Interpolate HERMITE reverse direction'. 2. Wisely sparsed from the original over populated mid-region. 3. Alternately to Hermite, two Thiele segments will fit ... Exceptional for navigating independently over the two regions. NO need to spline pecewise like Hermite, however superior global view.

Xo Mollier 1 col : Yo Mollier 2 col : 12 mat

Global definition
fetched from below
collapsed area ... support Mollier . 14 black plot :

0.01 over populate demo t 01 0.1 range :

t rows 11

truncate t rows 2 - : 9

Hermite Interpolation modules

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

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

data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

subspaces is '1' for interpolation sub 1 :

H Xo sub subspace Yo sub subspace augment : Hermite Xo 1 el Yo 1 el 12 mat H stack : 21 line

isolate Hermite Hermite :

X Hermite 1 col : Y Hermite 2 col : 21 line

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

interpolate 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat *

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

polyline 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat *

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

collect the project xy U Unwrap V Unwrap augment : contour xy Strip : 21 sys

Ω contour :

Ω rows 290

Mollier 1 row Mollier Mollier rows row 21 sys 358.93 212 mat 366.59 499012 mat 21 sys

Ω Ω t rows Ω rows truncate - (range 12 range el :

Ω Ω eval :

Hermite produces discrete export interpolated values. At this point for convenience you can interpolate cinterp/ainterp from piecewise each branch adapted from 'All values project'

support Ω X 21 el Y 21 el + 200 green 1 5 mat 3 1 sys

Hermite interpolation 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat *

XY Mollier Mollier rows Mollier rows 9 - (range 12 range el :

XY XY eval :

Thiele modules

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

X XY 1 col : Y XY 2 col : 12 mat

length Thiele j XY rows : 10

Thiele on length of support points 'j' K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

recast the Cf on the system  [K,X,x] x Cf K X x Cfr :

Thiele K's coefficients @ support points X X Y 0 Thiele 366.59 4990 387.46 0.193241 - 401.33 106.780344 407.72 0.226563 411.6 1275.995874 414.09 0.008585 - 415.69 4883.760915 416.65 0.000445 - 417.14 10758.973754 - 417.24 8.717732 107 -^* 102 mat

Thiele K's coefficients. K X Y 0 Thiele 2 col :

K K 9 round vectorize eval :

x λ 1 X 1 el x ≤ (x X 10 el ≤ (& cases :

... slow plot x D x Cf x diff x λ * :

support XY . 12 black plot :

support x Cf x λ * 2 1 sys

366.59 499012 mat

417.24 2175.3 12 mat

XY Mollier 119 range 12 range el :

XY XY eval :

K Clear 1

Thiele modules

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

X XY 1 col : Y XY 2 col : 12 mat

length Thiele j XY rows : 19

Thiele on length of support points 'j' K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

recast the Cf on the system  [K,X,x] x Cf K X x Cfr :

Thiele K's coefficients @ support points X X Y 0 Thiele 358.93 2 363.82 1.746429 368.75 8.64335 - 373.68 2.779706 - 378.58 33.200059 383.39 0.995193 388.09 56.965423 391.74 0.154641 395.26 223.663608 - 398.64 0.033453 - 401.85 191.222458 - 404.87 1.118492 - 407.67 1.849286 410.21 1.140538 412.46 130.027091 414.37 0.014293 415.87 172.592315 - 416.87 0.058089 417.24 14.959475 - 192 mat

Thiele K's coefficients. K X Y 0 Thiele 2 col :

K K 9 round vectorize eval :

x λ 1 X 1 el x ≤ (x X 19 el ≤ (& cases :

... slow plot x D x Cf x diff x λ * :

support XY . 12 black plot :

u 385.5 :

track 32615364001536 u u Cf 32 mat :

track x Cf x λ * X 1 el 1000 X 1 el 500 - 2 2 mat support 4 1 sys

XY 358.93 2 363.82 4.8 368.75 10.35 373.68 20.44 378.58 37.47 383.39 64.49 388.09 105.18 391.74 150.45 395.26 209.65 398.64 285.42 401.85 380.59 404.87 498.11 407.67 641.09 410.21 812.77 412.46 1016.5 414.37 1255.7 415.87 1534.1 416.87 1855.5 417.24 2175.3 192 mat

417.24 2175.3 12 mat

u u Cf 12 mat 385.5 80.68 12 mat

358.93 212 mat

jmG: 20230223