Contour utilities

60949cc5-42d1-44d8-a89b-76aa988e393e 24 3 5 auto

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

Contour utilities

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 :

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

t0 1 time :

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

Generate the symmetric square [U,V] 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 :

The contour extractor , pair wise in X direction M ε level CONTR count 1 : i 1 M rows range j 1 M cols range M i j el level - abs ε ≤ u count el i : v count el j : 21 line count count 1 + : if for for u v augment 31 line :

data Strip2 nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ 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 n Mround i 1 M rows range j 1 M cols range m i j el M i j el n round : for for m 21 line :

~ 9 min

Explore an hypersurface

c 1 :

λ 1.414214 :

f 2 c * y * 3 x 2^* y 2^* y 4^- c 2^x 2^y 2^+ (* - 4 c 4^* + (* x cos * y sinh * 2 c * y * x 4^3 y 2^* x 2^* - c 2^x 2^y 2^+ (* - 4 c 4^* - (* x sin * y cosh * x y * x 2^y 2^+ (y 2^x 2^- 2 c 2^* + (* (* 2 c * sin * 31 mat :

x y f f 1 el f 2 el + f 3 el + :

L λ - : H λ : N 99 : 13 mat

U L H N xd :

V U :

M x y f U V Sym :

1 time t0 - min 1.4

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M

level_0 0 : level_1 1 : level_2 2 : 13 mat

y x f0 x y f level_0 + : y x f1 x y f level_1 + : y x f2 x y f level_2 + : 31 sys

i 1 M rows range :

Iso_0 i λ - λ Scale M 50 col augment :

f0 f1 f2 3 1 sys Iso_0

1 time t0 - min 4.7

0 & nth level contour [Tom G.]

level 1.05 : ε 0.001 : 12 mat

Bolean region x c level - ε + x ≤ (x level ε - ≤ (* :

N M c M * vectorize :

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1 time t0 - min 5.1

M

M 75.991 - 69.944 - 64.339 - 59.146 - 54.338 - 49.888 - 45.773 - 41.968 - 38.452 - 35.205 - 32.209 - 29.445 - 26.898 - 24.551 - 22.39 - 20.402 - 18.574 - 16.894 - 15.352 - 13.937 - 12.64 - 11.452 - 10.364 - 9.369 - 8.459 - 7.629 - 6.871 - 6.18 - 5.551 - 4.978 - 4.458 - 3.985 - 3.556 - 3.166 - 2.814 - 2.494 - 2.204 - 1.941 - 1.703 - 1.487 - 1.291 - 1.111 - 0.947 - 0.796 - 0.656 - 0.526 - 0.402 - 0.284 - 0.169 - 0.056 - 0.057 0.172 0.29 0.415 0.547 0.689 0.843 1.012 1.196 1.4 1.626 1.877 2.154 2.463 2.805 3.185 3.607 4.074 4.591 5.162 5.793 6.489 7.255 8.097 9.023 10.038 11.15 12.368 13.698 15.151 16.735 18.46 20.338 22.379 24.595 26.999 29.605 32.427 35.48 38.78 42.344 46.191 50.338 54.807 59.618 64.795 70.36 76.34 82.759 89.647 73.21 - 67.398 - 62.012 - 57.025 - 52.408 - 48.136 - 44.186 - 40.534 - 37.161 - 34.047 - 31.172 - 28.521 - 26.077 - 23.825 - 21.752 - 19.843 - 18.088 - 16.475 - 14.993 - 13.633 - 12.385 - 11.24 - 10.192 - 9.232 - 8.354 - 7.551 - 6.817 - 6.148 - 5.537 - 4.98 - 4.472 - 4.01 - 3.59 - 3.207 - 2.859 - 2.543 - 2.256 - 1.994 - 1.756 - 1.539 - 1.34 - 1.158 - 0.99 - 0.835 - 0.69 - 0.554 - 0.425 - 0.301 - 0.179 - 0.06 - 0.06 0.182 0.308 0.441 0.581 0.73 0.892 1.069 1.261 1.473 1.707 1.965 2.25 2.566 2.916 3.303 3.731 4.205 4.728 5.305 5.94 6.64 7.41 8.255 9.182 10.198 11.309 12.523 13.849 15.295 16.87 18.584 20.447 22.47 24.665 27.044 29.619 32.406 35.418 38.67 42.18 45.964 50.04 54.429 59.149 64.223 69.673 75.524 81.799 88.526 70.482 - 64.896 - 59.722 - 54.932 - 50.5 - 46.401 - 42.612 - 39.11 - 35.875 - 32.889 - 30.134 - 27.593 - 25.25 - 23.091 - 21.103 - 19.274 - 17.59 - 16.043 - 14.62 - 13.314 - 12.115 - 11.014 - 10.006 - 9.081 - 8.234 - 7.459 - 6.75 - 6.102 - 5.51 - 4.969 - 4.475 - 4.024 - 3.613 - 3.238 - 2.897 - 2.585 - 2.3 - 2.04 - 1.803 - 1.585 - 1.385 - 1.2 - 1.03 - 0.871 - 0.722 - 0.581 - 0.446 - 0.316 - 0.189 - 0.063 - 0.063 0.192 0.326 0.465 0.612 0.769 0.939 1.122 1.323 1.542 1.783 2.048 2.341 2.664 3.02 3.413 3.848 4.327 4.855 5.436 6.075 6.778 7.55 8.396 9.322 10.336 11.444 12.653 13.972 15.408 16.971 18.67 20.515 22.516 24.684 27.032 29.572 32.317 35.281 38.479 41.927 45.64 49.637 53.936 58.555 63.516 68.839 74.548 80.666 87.218 67.808 - 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level 1 : ε 0.05 : 12 mat Q M ε level CONTR : XY Q Strip2 : (Export the project ≡ 31 line

XY rows 100

re-center the system Xlevel XY 1 col XY rows 2 / - : Ylevel XY 2 col XY rows 2 / - : XYlevel Xlevel Ylevel augment : Next extract/digitize ≡ 41 line

XYlevel

1 time t0 - min 8.6

XYlevel 11 mat 49 - 846 - 745 - 740 - 639 - 638 - 637 - 636 - 635 - 634 - 633 - 632 - 631 - 630 - 629 - 628 - 627 - 626 - 625 - 620 - 719 - 718 - 717 - 714 - 813 - 812 - 811 - 32 - 11 - 25 - 10 - 34 - 10 - 22 - 10 - 99 - 20 - 9 - 98 - 19 - 7 - 18 - 7 - 106 - 17 - 6 - 105 - 16 - 4 - 15 - 4 - 113 - 14 - 3 - 112 - 41 - 2 - 121 - 13 - 1 - 12042 - 012 - 013112 - 113143211 - 214311 - 342410 - 415510 - 51661779 - 71889 - 819920108 - 1021118 - 1123113512261233137 - 147 - 157 - 186 - 196 - 206 - 216 - 265 - 275 - 285 - 295 - 305 - 315 - 325 - 335 - 345 - 355 - 365 - 375 - 385 - 395 - 405 - 415 - 466 - 476 - 507 - 1002 mat 11 mat

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Column explorer

i 1 M rows range :

c 20 :

C_0 i λ - λ Scale M 50 c - col augment :

C_1 i λ - λ Scale M 50 c + col augment :

C_0 C_1 2 1 sys