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febb5a3d-420d-43e1-aaad-e4a16119559c 75 6 6 decimal

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

M F:\SmathExchange\Image Venturi50.bmp READRGB :

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G

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B

B 25525425425425425425425425425425425425425425425425425425425424322520418416414512510585675032153000000000000000000000000000000255254254254254254254254254254254254254254254254254254254254254249231214194176156138119100826649331750000000000000000000000000000255254254254254254254254254254254254254254254254254254254254254254253241225207189171154136119101846852372392000000000000000000000000025525525425425425425425425425425425425425425425425425425425425425425425425023822220518917215614012410791756147331982000000000000000000000025525525425425425425425425425425425425425425425425425425425425425425425425425424923922420819417816314813311710288736047342110500000000000000000002552552542542542542542542542542542542542542542542542542542542542542542542542542542542522432312162031891741601471331191059277665342301994100000000000000255255254254254254254254254254254254254254254254254254254254254254254254254254254254254254253249241230216204191178166153140128115102917767564433231484000000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425325124423522521220119017816715614313212210998887566564536271811731000255255254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254252251244237229218208199188176166158146135126116104968675675848393224162552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522512452392332262152061981891781691621531421331251171069789822552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522502492432372322272212102031961891801711641572552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512492482442382342302552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522512502552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512492452392342302262182092031972552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512472402352302212112031961881771691621541431351281212552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522482412352262152061971881771671591481381301201091009183726456472552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532512442372262152051941821711621501381281181069687746656453729201395225525525425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425324623822621420319017716615414113011810594837060494030201273000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425425425324623622320919618317015714313011710391766654433121116100000000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425124122721319818316915413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mat :

Functions/parameters ........ to construct 45° rot, λ background

gray R G + B + 3 / :

gray Min 86

gray Max 167

iVBORw0KGgoAAAANSUhEUgAAAEAAAAAhCAIAAADmozp2AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAACGFJREFUWEed2OWSXDkSBWCPHYYnNDOOmZmZmZntVzSG93OcjtPqas/Oxt4fHVXVuqk8ICmVf506dernz59fv3799u1b/n758sUvCxcuXLBgQf9OfPWvRYsW/fr1q281Qj6Mj2Fz586dP3++tzz5MH4df5k3b96cOXO+f/8uwr/+/fHjxxwAjh8/fvDgwd27d2/dunXDhg0rV65csmTJsmXL1qxZs2nTpu3bt+/bt+/IkSNGXrhw4fr163fv3n38+PGrV68+fPjw+fPnt2/fvnjx4uHDh7dv375y5cq5c+dOnDhx6NChPXv2bNu2TQRxli9fvnTpUjFXr15tChPt2rVr//79wp48efL8+fNevHnz5r1790R++fLlu3fvPn78KH6C+9GkBly+fFl8rxw+fNjrO3fu/A3AfL6bT67mW7t2rZkWL168YsWKdevWbdmyZceOHZnMYJNdu3ZNro8ePXr+/LkJPn36ZLLXr18/ffr0/v37ppmAIezmzZuFQg0YHpHNYi4IEVckkvPujRs3pIuRZ8+eCfv+/XtI/H3z5o1fzOu/xgTMbwAASQ7NAEl3/fr1EcGzatUqX//++2//miDs1q1b0pU0KUQHwzQ+B4b/SgVa8QUPW4jfuHEjQQCIICYKkmgiB1RyxJkzZ6h99erVyBKyRjBR5smTJ1MAjh49euDAAWSgxByCEp0IpikGOnSCs2fPXrp0iZ3u3LlTqgAIDDOhyu/+a4yRxkuLr0ITRjILAGB4TMddyKIVxSJLwJw+fRqYKCPggwcPcMRmBDHXbwCeY8eOWQZcJEsisKlwMZK/weB3oY0xEmBvUZCOI4yqwVQlKYIw3sWLFyGJY+WHcnzJWPDIMoJhuSgD8N69ezOpdytO8EwBAFRQ9CSoNwWVdzDQYdRaRCPRCXZgRA0LQ64WHHFDTwQpEuSZMvblLtRGloDBTrgDxnQ0iTKA+UU+xYPE6COBKQCQwRcRYlajcVAdrAeBqjKQsazpvWgVoTaurdAMGiRWSLYUH7iLm4EsGN7wIl4FSQ6xmSmCh9PMa/aA8YBXSFMAvAxNlI2RgqHiAlAp8jLpo+/IB0GCRFrRJEuwru3+CAxlWNlqgYd0BgOPgjgt+7uULE4WMhGJsngwCxWDADMFIKNLgDUUDLIMB0YjoDCiht+FwxO2iiSakJRDuEs2AWMZZHOUrqSlDgA8lIk4PpOLaNDCDBK/2YUsHpZDSlHZ1iIU7qYBRITxfwVNisLIDphNlkeLxABoMYSngjGNgKgRnEmKR04ykx99RkgMVlSB5CtU9gaYeXIEhhRyTQPIiRYMWViEI0VhRI2YKvIViQ8xqN/JYgxlRjziIIwZRBbfLCCRCKlWc1SCioUIBRj6A4wa1gy5YIMEngILthkAgiFeYj78FYYly1SsgmOZyQ8YXiyYFAt9soFYbSAZY6TxlOQ3zhRHNDF5IMDMZUbzRi6ZRLERHsrpFoSRjiCTAHIwRwrhokaQxHO4DBhWkUrwyAwkxAeS5SH17BvZDQOs22J2EtiykAIvokEoJoTiFyQvSCA4o2Gh/gFAjjYwggQlBYOk4gkkoYuK2QIsQklFQoEX72X3gDC6wdAn+2MA5+mOaWSgevKuIIEt5j8CCIw+xRNIeQArNqyAV4SoQhiQwVmoQRsZPcFc2JBHVeBH/FEYCyEiXOT5XwFM4Pmnr8H5Xx74x6dclI6QEl7yoGZ8QlPJ+j8BjCk2oQll/pjExPQxZOSarRh/xqJ5Il3Vi4D/DqAroYshrNQt48SdMtNMOGTCHhPGiCW6SGL6LIDZqyUrZMZJPOH4cfmOa3di4da+kotrm1az6aY0rtQUnn/cl7JYuzsJ2N0pW3A2KOygaVKBcQ9N3gjuBhpGu8l09wxtOd3GfXPcOnsm9KTLsdBNMwnRcDwZcuphE785+Ho4qC8mT2LZ5xRLQTFxGIfj7InjEZZtvsVFzq9s8OORPPvw6qmc/HJyqXkU5zIbD+YeW6oJNYV6qWfzDAV6BqcAHOuI5h0/SDoZh+OxIgqvSTeMIiK5jkWRRFE4UT44WZtiagflkNphrIv8mBo2pdE0gJy+qajNmhsGfcdKrgWp1H1OmZCrxkQZ15q0BXbTTY2tEEiuuRwm0Zal6hwFnCqoBZy3Upnm/sBLHMUyM8ppJIX73o9SfGN9di2dK1/yzuUmtWf8MBbSY8bUR22qaLecP1bRvRjwkjislftWSsxcV3Ldkd6MG5kRY/YpodMLcZvJpay3mdwBcltN3ihRe5kVT0qu0KycnH0va91vQBo+Xkm6gghVKserWajMbbO1xjSAND9yleldTsa5xKRrIIQdLanPvhY3b9bkDR7I/Sv3ySTNEi6T4Th9lxCcm1fYjW9Ttzfd2ZdjI6cvNLlc5+aW7g3um32IJ4jQXmuPYGxMyKkNDw5O3rkEtxuFadtLbsC5Lo69iV7nczi0a5RLX3otZS23cBeJKQV6ox+7aOE+2Ysy0Q9sM2JsDaXDJXV8W4LpoqVXlyZXGlDpArYHkbvRRHdo7BuM7Y8JnacbWyEj7dE2I5J9e4DsLlY6TWkwhvX0SdvV8kt8YoyRxrfvFILas0nedrOac3Z/Lm3TNhvjzO5X061FxmCPNDHlnZYWJLhHRvpZafpZbWlfphGLdS3eNOTGvmK7sHSf6Je10Zt+2WjL9uGS9OymYrQ1tU3CVjHV3G0zWbqSzsmKmHSSmS/Zs53tXGh31nRese5J2xXraYmODeo2jOsT67I9Y6ylQYYXhp5QtQ2lJj22ddPSndFet0ZREvr9NY1faBrnJHsp2vtwQMcQTwR8WAmmZ3Rx/9hbty6zltKRthKsB3yPeYeUHhEi27X+2CqWldzw+x/EmK0upT741gAAAABJRU5ErkJggg== gray

m n q m n m n - 22 mat :

θ f θ cos θ sin - θ sin θ cos 22 mat :

gray rows gray cols 12 mat 336412 mat

deg 30 :

λ 235 :

Absolute value of a vector v Abs j 1 v rows range a j el v j el abs : for a 21 line :

Round OFF a matrix/vector M n Round 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 :

v1 mwabs

v2 mwabs

This part is sanity checked

R G B deg λ rotate m R rows : n R cols : θ deg π * 180 / : A θ f : bounds m n q A * : v1 bounds 1 col : v2 bounds 2 col : uv1 v1 mwabs Max 0 round : uv2 v2 mwabs Max 0 round : u uv1 : v uv2 : N m n 12 mat u v 12 mat stack : N N 1 + 2 / : mc N 11 el : nc N 12 el : uc N 21 el : vc N 22 el : 41 line prepare pixel canvas wht 11113 mat transpose λ * : RGB u 3 v * el 0 : x 1 u range y 1 v range s0 A x y 21 mat uc vc 21 mat - (* eval mc nc 21 mat + : s s0 Floor s0 Floor 1 + augment : s s 2 col s 4 col augment : w s 2 col s0 - s0 s 1 col - augment : p 12 range q 12 range i s 1 p el : j s 2 q el : suite to code 31 line for for k 13 range # for 61 line for for # 211 line :

Up to [i,j] sanity is OK, next is to code the "on error", hoping the suite will follow.

k 13 range RGB x y v k 1 - (* + el sum k el 0 round : for

p 12 range q 12 range i s 1 p el : j s 2 q el : a gray : b a i j el 1 ≠ wht a if : sum sum w 1 p el w 2 q el * (b * + : 61 line for for

Attempt "on error" & suite failed ... RemToDo

R G B deg λ rotate m R rows : n R cols : θ deg π * 180 / : A θ f : bounds m n q A * : v1 bounds 1 col : v2 bounds 2 col : uv1 v1 Abs Max 0 round : uv2 v2 Abs Max 0 round : u uv1 : v uv2 : N m n 12 mat u v 12 mat stack : N N 1 + 2 / : mc N 11 el : nc N 12 el : uc N 21 el : vc N 22 el : 41 line prepare pixel canvas wht 11113 mat transpose λ * : RGB u 3 v * el 0 : x 1 u range y 1 v range s0 A x y 21 mat uc vc 21 mat - (* eval mc nc 21 mat + : s s0 Floor s0 Floor 1 + augment : s s 2 col s 4 col augment : w s 2 col s0 - s0 s 1 col - augment : sum 00013 mat transpose : p 12 range q 12 range i s 1 p el : j s 2 q el : a R G + B + 3 / : a i j el a wht : sum sum w 1 p el w 2 q el * (a * + : if k 13 range RGB x y v k 1 - (* + el sum 0 Round : for 61 line for for 61 line for for RGB 211 line :

w 0.769 0.231 0.756 0.244 22 mat ≡

i j 12 mat 267912 mat ≡

ii 1 i range jj 1 j range a ii jj el ¬ 1 ≡ for for b wht : b a : if

ii 1 i range jj 1 j range a ii jj el a m n el ¤ for for b wht : b a : if

b a i j el 1 ≠ wht a if :

Input string was not in correct format a wht : sum # : if

a i j el (a m n el (¤

RotatedImage R G B deg λ rotate :

RotatedImage #

A function that tests an arbitrary point 
for its membership in the critical region. Test a i j el (a m n el (* :

1 Test - b wht : Test b a : while 21 line while

sum 0012 mat transpose :

w 0.769 0.231 0.756 0.244 22 mat :

Ω p 12 range q 12 range Ω p q el w 1 p el w 2 q el * (gray p q el * : for for Ω 21 line :

Ω 0 Round 732322722 mat