Contour utilities

5b647064-11a8-4140-b43b-e264b0846a45 25 6 5 decimal

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

f L H N level sol X 0 : dx H L - N / : 12 mat i 1 N range X i el L dx - (dx i * + : for j 1 X rows range Sol j el y X j el f level - y roots eval : j j 1 + : 21 line for X Sol augment 41 line :

collapse in utilities at top of work sheet.

Explore an hypersurface

The governing hypersurface parameter 1 ≤ 'c' c 1 :

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 :

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

Iso f 1.5 - 1.5 99 0.125 sol :

Iso

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

Iso f 1.5 - 1.5 49 0.125 sol :

Iso

Dual solver AlgoStyle . . .

1. They don't solve by themselves, you have to help from trial/error.

2. Depending upon the mathematical difficulty they reply red error.

3. This demo example flies in the blue otherwise than demanded .

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

Iso f 0.025 1.75 25 0.125 sol :

Iso

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

Iso f 1.5 - 1.5 990 sol :

Iso

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

Iso f 1 - 11990 sol :

Iso 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 :

A robust construct of the Scale function Mat Low High Scale min Mat Min : max Mat Max : maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 Mat rows range j 1 Mat cols range N i j el Mat i j el min - maxmin / : for for HighLow N * Low + 61 line :

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

λ 1.414214 :

L λ - : H λ : N 99 : 13 mat U L H N xd : ----- V U : 13 mat M x y f U V Sym : 31 line

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level 1 : ε 0.05 : 12 mat Q M ε level CONTR : XY Q Strip2 : (Export the project ≡ 31 line

re-center the system XY rows 100 : Xlevel XY 1 col XY rows 2 / - : Ylevel XY 2 col XY rows 2 / - : XYlevel Xlevel Ylevel augment : Next extract/digitize ≡ 51 line

XYlevel

1 time t0 - min 4.8

Engineering suite . . .

Up to this point of the isocurve project, we just have a view of the particular

level = 1. Useless as is whereas each lobe is not pairwise exportable.

The next operation will be a manual best fit Bézier-Bernstein through each

of the lobe, thus a smoth pairwise data set for each isocurve lobe.

Visit => Contour Solve Isocurve AlgoStyle Lobe Suite

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Polygon Lobe Cntrl data Lobe - 71 sys

Suite . . .

1. XYlevel is passed to ... Lobe Suite

2. IsoLobe & IsoScale returned here.

3. IsoScale is valued back to the

CONTR(M,ε,level) creator.

]]> IsocurveLobe

IsoLobe 49 - 7 48.135 - 6.783 47.243 - 6.581 46.324 - 6.395 45.381 - 6.224 44.415 - 6.068 43.428 - 5.927 42.423 - 5.802 41.4 - 5.692 40.361 - 5.597 39.308 - 5.517 38.242 - 5.452 37.164 - 5.401 36.077 - 5.366 34.981 - 5.345 33.878 - 5.339 32.769 - 5.348 31.655 - 5.371 30.537 - 5.409 29.417 - 5.461 28.296 - 5.527 27.175 - 5.607 26.055 - 5.702 24.936 - 5.81 23.821 - 5.932 22.709 - 6.068 21.603 - 6.218 20.502 - 6.382 19.407 - 6.558 18.32 - 6.749 17.242 - 6.952 16.172 - 7.169 15.112 - 7.398 14.063 - 7.641 13.025 - 7.896 12 - 8.164 10.986 - 8.444 9.987 - 8.737 9.001 - 9.041 8.03 - 9.358 7.074 - 9.687 6.134 - 10.028 5.211 - 10.38 4.305 - 10.743 3.416 - 11.118 2.545 - 11.504 1.694 - 11.901 0.861 - 12.308 0.048 - 12.727 0.744 13.155 1.516 13.594 2.266 14.042 2.994 14.501 3.7 14.969 4.383 15.447 5.042 15.933 5.678 16.429 6.289 16.933 6.875 17.446 7.436 17.968 7.97 18.497 8.478 19.034 8.959 19.579 9.412 20.131 9.837 20.69 10.233 21.256 10.599 21.829 10.936 22.408 11.242 22.993 11.516 23.583 11.759 24.179 11.969 24.781 12.146 25.387 12.289 25.998 12.397 26.613 12.469 27.232 12.506 27.855 12.505 28.482 12.466 29.111 12.389 29.743 12.272 30.377 12.115 31.014 11.916 31.652 11.675 32.291 11.391 32.932 11.062 33.573 10.688 34.214 10.267 34.856 9.799 35.496 9.282 36.136 8.715 36.775 8.097 37.412 7.426 38.047 6.701 38.679 5.921 39.308 5.084 39.935 4.19 40.557 3.236 41.175 2.22 41.789 1.142 42.397 1.152 1011 -^* 43497 - 48.135 6.783 - 47.243 6.581 - 46.324 6.395 - 45.381 6.224 - 44.415 6.068 - 43.428 5.927 - 42.423 5.802 - 41.4 5.692 - 40.361 5.597 - 39.308 5.517 - 38.242 5.452 - 37.164 5.401 - 36.077 5.366 - 34.981 5.345 - 33.878 5.339 - 32.769 5.348 - 31.655 5.371 - 30.537 5.409 - 29.417 5.461 - 28.296 5.527 - 27.175 5.607 - 26.055 5.702 - 24.936 5.81 - 23.821 5.932 - 22.709 6.068 - 21.603 6.218 - 20.502 6.382 - 19.407 6.558 - 18.32 6.749 - 17.242 6.952 - 16.172 7.169 - 15.112 7.398 - 14.063 7.641 - 13.025 7.896 - 12 8.164 - 10.986 8.444 - 9.987 8.737 - 9.001 9.041 - 8.03 9.358 - 7.074 9.687 - 6.134 10.028 - 5.211 10.38 - 4.305 10.743 - 3.416 11.118 - 2.545 11.504 - 1.694 11.901 - 0.861 12.308 - 0.048 12.727 - 0.744 - 13.155 - 1.516 - 13.594 - 2.266 - 14.042 - 2.994 - 14.501 - 3.7 - 14.969 - 4.383 - 15.447 - 5.042 - 15.933 - 5.678 - 16.429 - 6.289 - 16.933 - 6.875 - 17.446 - 7.436 - 17.968 - 7.97 - 18.497 - 8.478 - 19.034 - 8.959 - 19.579 - 9.412 - 20.131 - 9.837 - 20.69 - 10.233 - 21.256 - 10.599 - 21.829 - 10.936 - 22.408 - 11.242 - 22.993 - 11.516 - 23.583 - 11.759 - 24.179 - 11.969 - 24.781 - 12.146 - 25.387 - 12.289 - 25.998 - 12.397 - 26.613 - 12.469 - 27.232 - 12.506 - 27.855 - 12.505 - 28.482 - 12.466 - 29.111 - 12.389 - 29.743 - 12.272 - 30.377 - 12.115 - 31.014 - 11.916 - 31.652 - 11.675 - 32.291 - 11.391 - 32.932 - 11.062 - 33.573 - 10.688 - 34.214 - 10.267 - 34.856 - 9.799 - 35.496 - 9.282 - 36.136 - 8.715 - 36.775 - 8.097 - 37.412 - 7.426 - 38.047 - 6.701 - 38.679 - 5.921 - 39.308 - 5.084 - 39.935 - 4.19 - 40.557 - 3.236 - 41.175 - 2.22 - 41.789 - 1.142 - 42.397 - 1.152 1011 -^* - 43 - 2022 mat :

IsoScale

IsoScale 1.414 - 0.202 1.389 - 0.196 1.364 - 0.19 1.337 - 0.185 1.31 - 0.18 1.282 - 0.175 1.253 - 0.171 1.224 - 0.167 1.195 - 0.164 1.165 - 0.162 1.134 - 0.159 1.104 - 0.157 1.073 - 0.156 1.041 - 0.155 1.01 - 0.154 0.978 - 0.154 0.946 - 0.154 0.914 - 0.155 0.881 - 0.156 0.849 - 0.158 0.817 - 0.16 0.784 - 0.162 0.752 - 0.165 0.72 - 0.168 0.688 - 0.171 0.655 - 0.175 0.623 - 0.179 0.592 - 0.184 0.56 - 0.189 0.529 - 0.195 0.498 - 0.201 0.467 - 0.207 0.436 - 0.214 0.406 - 0.221 0.376 - 0.228 0.346 - 0.236 0.317 - 0.244 0.288 - 0.252 0.26 - 0.261 0.232 - 0.27 0.204 - 0.28 0.177 - 0.289 0.15 - 0.3 0.124 - 0.31 0.099 - 0.321 0.073 - 0.332 0.049 - 0.343 0.025 - 0.355 0.001 - 0.367 0.021 0.38 0.044 0.392 0.065 0.405 0.086 0.419 0.107 0.432 0.126 0.446 0.146 0.46 0.164 0.474 0.182 0.489 0.198 0.504 0.215 0.519 0.23 0.534 0.245 0.549 0.259 0.565 0.272 0.581 0.284 0.597 0.295 0.613 0.306 0.63 0.316 0.647 0.324 0.664 0.332 0.681 0.339 0.698 0.345 0.715 0.351 0.733 0.355 0.75 0.358 0.768 0.36 0.786 0.361 0.804 0.361 0.822 0.36 0.84 0.358 0.858 0.354 0.877 0.35 0.895 0.344 0.914 0.337 0.932 0.329 0.95 0.319 0.969 0.308 0.987 0.296 1.006 0.283 1.024 0.268 1.043 0.252 1.061 0.234 1.08 0.214 1.098 0.193 1.116 0.171 1.134 0.147 1.153 0.121 1.171 0.093 1.188 0.064 1.206 0.033 1.224 3.173 1013 -^* 1.241 1.414 0.202 - 1.389 0.196 - 1.364 0.19 - 1.337 0.185 - 1.31 0.18 - 1.282 0.175 - 1.253 0.171 - 1.224 0.167 - 1.195 0.164 - 1.165 0.162 - 1.134 0.159 - 1.104 0.157 - 1.073 0.156 - 1.041 0.155 - 1.01 0.154 - 0.978 0.154 - 0.946 0.154 - 0.914 0.155 - 0.881 0.156 - 0.849 0.158 - 0.817 0.16 - 0.784 0.162 - 0.752 0.165 - 0.72 0.168 - 0.688 0.171 - 0.655 0.175 - 0.623 0.179 - 0.592 0.184 - 0.56 0.189 - 0.529 0.195 - 0.498 0.201 - 0.467 0.207 - 0.436 0.214 - 0.406 0.221 - 0.376 0.228 - 0.346 0.236 - 0.317 0.244 - 0.288 0.252 - 0.26 0.261 - 0.232 0.27 - 0.204 0.28 - 0.177 0.289 - 0.15 0.3 - 0.124 0.31 - 0.099 0.321 - 0.073 0.332 - 0.049 0.343 - 0.025 0.355 - 0.001 0.367 - 0.021 - 0.38 - 0.044 - 0.392 - 0.065 - 0.405 - 0.086 - 0.419 - 0.107 - 0.432 - 0.126 - 0.446 - 0.146 - 0.46 - 0.164 - 0.474 - 0.182 - 0.489 - 0.198 - 0.504 - 0.215 - 0.519 - 0.23 - 0.534 - 0.245 - 0.549 - 0.259 - 0.565 - 0.272 - 0.581 - 0.284 - 0.597 - 0.295 - 0.613 - 0.306 - 0.63 - 0.316 - 0.647 - 0.324 - 0.664 - 0.332 - 0.681 - 0.339 - 0.698 - 0.345 - 0.715 - 0.351 - 0.733 - 0.355 - 0.75 - 0.358 - 0.768 - 0.36 - 0.786 - 0.361 - 0.804 - 0.361 - 0.822 - 0.36 - 0.84 - 0.358 - 0.858 - 0.354 - 0.877 - 0.35 - 0.895 - 0.344 - 0.914 - 0.337 - 0.932 - 0.329 - 0.95 - 0.319 - 0.969 - 0.308 - 0.987 - 0.296 - 1.006 - 0.283 - 1.024 - 0.268 - 1.043 - 0.252 - 1.061 - 0.234 - 1.08 - 0.214 - 1.098 - 0.193 - 1.116 - 0.171 - 1.134 - 0.147 - 1.153 - 0.121 - 1.171 - 0.093 - 1.188 - 0.064 - 1.206 - 0.033 - 1.224 - 3.491 1013 -^* - 1.241 - 2022 mat :

IsoLobe IsoScale

jmGiraud: 2018-10-26