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257d5d22-3673-45af-b7c6-9cb573e8d918 56 4 5 decimal

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

Digitizing an implicit contour

Step_1 => Create the image to be digitized [Gray]

x y XY x y / - :

a 816 π * sqrt * :

t0 1 time :

Electron path(s) from unrecorded source. x y f1 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * (0.0025 - : x y f2 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * (0.001 - : x y f3 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * (0.0001 - : 31 sys

f2 1 1 sys

1 time t0 - 26 s *

Explain . . .

Some implicit functions have NO Maple expansion.

Alternately, here, we plot X_Y and collect as image.

The XY digitized is MicMac in the center region,

cleaned manually in the collapsed area [subject to

human typos ... re-check].

]]> Gray

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255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255255130144 mat :

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 Gray

Convert existing gray pixels to black N i 1 Gray rows range j 1 Gray cols range N i j el 0 Gray i j el 85 ≤ 255 cases : for for N 21 line :

<= Min valued gray 85

N N :

Extract black pixels r N rows : c N cols : k 1 : i 1 c range j 1 r range N j i el 1 ≤ X k el i : Y k el r j - : k k 1 + : 31 line No pixel if for for 41 line

XY X Y augment :

iVBORw0KGgoAAAANSUhEUgAAAJAAAACCCAIAAAAmOtZ/AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAANDSURBVHhe7ZPRduMgDAX7/z+dZYtP2joc22AhXeGZlzRpDNJM+/WCVBAsGQRLBsGSQbBkECwZBEsGwZJBsGQQLBkESwbBkvFV2H4EebZaNEvBFuv9hmyy/K7zJxLNBNlF2ReimRSfORp5aCZCM0S7Tfkq2QI58H9UhWYhHGs/SUIzZ06Fn/egmRtXVF+KUQ4i22wuGu7IQLNJfP87XHXb14Bm5vQq7Q5AM0MGZI7Yp5kJYxoH1ZfLyDbMHXu3pNNsgJvS7hqnWRf3dRnoptlFTETZuKbZKVaKzESXgcjWxNaMsWKa7TAXYu+XZm9mqJgil2aFSRJmmX14s3nrT9T62GZTF5/rtIz+tGyz9/Ww+ZBm33+c0zd1Url8M7cF/Twu3MxzNVeJSzZzXsrb4GLN/NcJ0LdMs5BFYtwt0CxqhTBxqZsFDh9pLWmz2LGDlaVrFj5wvK9EzRRGlZCVopnIkCqmxJvpjCekSbaZ1GBajgSbqY2EoCMU/4C2VxkIdozcQAURTYK1CoozFcJladYqEKwNwboJVCZbq0CwBgQbJESccq0CwfYQbByCfUKwPQQbh2CfEGwPwcYh2CcE20OwQQLFKTcjWAOCdROuTLYZwdoQrAMRWZrN5GaS0iTYjGBHEOwERUFiI/HnfI7WP/32Go1srYrOeBJziNeqiAwZP0SKWhWFUYMnSFSrEj5w5PXpalVixw67O2mtSuDwMRenrlWJWiHg1gVqVUIW8b5ymVoV/3Vc71usVsV5Kb/LlqxV8VzN6aaFa1XcFvS4ZvlalbKmw6ZzL/DZQYrZ+048/Wmp3kxdfNbRj61Vmbf+lHMfXqsySYL9odR6M0OF8YnU2lGE2DoxO8t8spUwNGNzEKlOsVJkcAq1LmIi6u4R1Orivq5bz1NrgJvSBh8ut1JrmDv2Rh4jlQljGrufoZYhAzL7HqCWOb1KO75NrUkUsdfdXvpe14kwxkXD518ilRtXVJ98g1rOnAo/+jW1QjjW3v5deYZagRz4b3xKKhGaIfYfUUuKzxx/3lNLkF2U7U35lFqy/K7z/4VUKaiZftKBPtTKB8GSQbBkECwZBEsGwZJBsGQQLBkESwbBkkGwZBAsFa/XP4//z/4nob1IAAAAAElFTkSuQmCC N

Raw extraction to be cleaned

Step_2 => clean/collect the branches

raw XY ... NewXY after manual refactory

NewXY 11171122116213311531441154145114515611361671127178111818911191810110101911109112012108122113107132214107142215106152316105162417104172518103182619102192720102202721101212822100222923992330249824312597253226972632279627332895283429942935309330363192313732913238339133383490343935893540368836413787374238863843398539444084404541834146428242474381434844804449457945504678465147774752487648534975495550735056517251585270525953685361926892619370935994729458957395569675965597769753987798529978995110079100501018010149102811024810382103471048310446105841054510685106441078610743108871084210988109411108911040111901113911290112391139111338114921143711593115361169411635117951173411896118331199711933120971203212198121311229912230123100123291241011242812510212527126102126271271031272612810412825129105129241301061302313110613123132107132221331081332113410913420135110135191361111361813711113718138112138171391131391614011414015141115141141421151421414311614313144117144122122 mat :

XY 11 mat 11171122116213311531441154145114515611361671127178111818911191810110101911109112012108122113107132214107142215106152316105162417104172518103182619102192720102202721101212822100222923992330249824312597253226972632279627332895283429942935309330363192313732913238339133383490343935893540368836413787374238863843398539444084404541834146428242474381434844804449457945504678465147774752487648534975497449554954507350565172517151585157527052695260525953685367536653655364536353625361926892679266926592649263926292619370936993609359947294719458945795739556967596749655965497769753987798529978995110079100501018010149102811024810382103471048310446105841054510685106441078610743108871084210988109411108911040111901113911290112391139111338114921143711593115361169411635117951173411896118331199711933120971203212198121311229912230123100123291241011242812510212527126102126271271031272612810412825129105129241301061302313110613123132107132221331081332113410913420135110135191361111361813711113718138112138171391131391614011414015141115141141421151421414311614313144117144122362 mat 11 mat

Strip paired 0's from alternate [E1,e2] data Strip2 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 pairs are 0's if 11 line for R 51 line :

i 1 NewXY rows 3 range j 1 NewXY cols range E1 i j el NewXY i j el : for for

i 2 NewXY rows 4 range j 1 NewXY cols range E2 i j el NewXY i j el : for for

data Unest v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

red E1 Strip2 Unest : blue E2 Strip2 Unest : C1 red 1 col red 2 col augment : C2 blue 1 col blue 2 col augment : 41 line

The cleaned branches

C1 C2 2 1 sys

Step_3 => Export the collected branches

sub_1 C1 153 range 12 range el : sub_2 C2 531 range 12 range el : blueC sub_1 sub_2 stack : 31 line

C1 rows 106

sub_3 C1 10654 range 12 range el : sub_4 C2 54106 range 12 range el : redC sub_3 sub_4 stack : 31 line

blueC redC 72.5 64.5 + 100 green 15 mat 31 sys

Electron Parabolic Path

blueC redC 72.5 64.5 + 100 green 1 5 mat 6 0.812 x * + 4 1 sys

Once bueC, redC in hand .... =>

you can scale each direction as you wish.

]]> blueC redC 6 0.812 x * + 72.5 64.5 1 2 mat 4 1 sys

1 time t0 - 50 s *

x y f 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ 1 / * (:

u v q 1 u v 1 - 3 / u 2^v 2^+ sqrt * exp 2 v 2^* - u 2^+ 1 / * 31 mat * :

E u v q 2 - 22 - 22020 CreateMesh :