R

c1f69ce5-7e61-4152-9c2d-e15cfbf7bb2e 30 6 5 auto

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

R

R 1241169677563715100000000000000000000000006183351688410011713415116618219921623324625325425425425425425425425425425425425425525512411799806243246000000000000000000000000000513294561779110712213915516918419921723224525125425425525425425425425425425425412411910484694934142000000000000000000000000000029213449657993108122138153166181195210225237247252254254255254254254254124121107897456422480000000000000000000000000000001310223449637789103116130144158171184198211225236246250254254254124122110947965483417500000000000000000000000000000000139162841546780911041161291421551671801912052172292401241231139984725643301430000000000000000000000000000000000114101728395163758698109120132144156166179124124116105897866514027134000000000000000000000000000000000000001271320314051617383931041141241241191099784746249392815510000000000000000000000000000000000000000022511162232405012412412111310391827261504131199200000000000000000000000000000000000000000000002231241241241161099988807263524436261683100000000000000000000000000000000000000000000001241241241211141079989827567585043352719115200000000000000000000000000000000000000000000124124124124119113108100928680746759524540332619127421000000000000000000000000000000000000000124124124124123119115109105989286817771666054484338332721161175321000000000000000000000000000000000124124124124124124121118114110106102979288838076716863585450464137332924201714118543211000000000000000000000001241241241241241241241241221211181161131101071041019793918885827976737068646057545249454239363331272422201816141211987554432211000124124124124124124124124124124124124123122121120119117116115113112110108106104103101999794939190888684828079777674727068666562605755535250494745444241393837124124124124124124124124124124124124124124124124124124124124124124123123123123122122122121121121121121120120120119119119119118117117115115114113112112112111110109108108107106106105105104103102124124124124124124124124124124124124124124124123123123122122122121120119118117116115114113112111110109108107106105104103103102100999796949392908987868684848281807978777675124124124124124124124124124123123121120117116114111109106104102999693918987858279767472706866625957555250484543413937353230272523212018171614131110101241241241241241241241221191161131091051029793908682797672696561575451474339363329242119161412975443211000000000000000124124124124124122118114110105100948984797571666055514641363227211713964321000000000000000000000000000001241241241241211161111069891858075696256494338322519148531000000000000000000000000000000000000012412412412311711010394878074675851443730221484200000000000000000000000000000000000000000012412412411911210493857769605143352617941000000000000000000000000000000000000000000000124124123115106958576685646382817820000000000000000000000000000000000000000000000001241241201111008778685544352312300000000000000000000000000000000000000000000124914191241241181079381715745342091000000000000000000000000000000000000000124101421324151617282124124115102877562473520810000000000000000000000000000000000001391424344657688089101112123135146124123111978269523924910000000000000000000000000000000001391728405365788810111212513715016117318519720912412210992776145301320000000000000000000000000000000161326385265789010411613014415616918219520822223324324925312412010687725338194000000000000000000000000000000614284257718599111127142155169182197211225238246251254254255254254124118101826546291000000000000000000000000000003112439557185100114130146160175190206222235246251254254255254254254254254254124117987959402030000000000000000000000000051631486581961111281451601761912082252402492542542542542542542542542542542542542543364 mat :

G

G 000000052543648410412414316418320322224525425425425425425425425425425425425425425525425425425425425425425425425425425425425425124222620919317716114312711195786145271700000001133151698910612614416418220122023925225425425425425425425425425425425425425425425425425425425425425425425425525425425425425425124323021419918316915213612210591750000000032037567291107125141161177196213231247254254254254254254254254254254254254254254254254254254254254254254254254254255254254254254254253247239226210197181168153138000000000825405873911061231391551721882052212372502542542542542542542542542542542542542542542542542552542542542542542542542542542542542542542542542542532482402292152020000000001122741587288103117133148163178193209224238250254254254254254254254254254254254254254254254254254255254254254254254254254254254254254255254254254254254253252000000000011327405568829711012413715116517919320822123524725325425425425425425425425425425425425425425425425425425425525425425425425425425425425425425425425525425400000000000111243649627488101113125138150163176189201214228239249253254254254254254254254254254254254254254254254254254254254254255254254254254254254254254254254000000000000171930415365768810011012213414415716817919120321422723624625025425425425425425425425425425425425425425425425425425425425425425425525425425425425400000000000000311223241526373839310411412413514415616517618619620621722823624524925225425425425425425425425425425425425425425425425425425425425425425425400000000000000013111928364756657383921021101201271371461561641741831932012102192292352432482502532542542542542542542542542542542542542542542542542540000000000000000002513202835445260687584919910711512313013814615516216917818619420120821722523223724324724925225425425425425425425425425425400000000000000000000024815202734404854606874818894100108114121127133140146155161167173179188195201207213219227231236241244246249251000000000000000000000000013581317222733384450556165717683889499103109115121126132136141146154160164170174179185193198000000000000000000000000000000012346913172023262934394348535760646871768287919499102106109115121000000000000000000000000000000000000000000124456689121418212325273031333638410000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011334456677991100000000000000000000000000000000000013445791216182124272932353944495256586265687175800000000000000000000000000000134610151822263136404751566064697480869094991031071131201241281331371411461531580000000000000000000000024612162229354047535965717784909610110711312012613113614314915716216717317818619419820420921422022623100000000000000000001381521293643505765728087931011081151231301361441521601661721801891962032092162242302352412442472502522542542542542540000000000000000028162533415058677584921011091181261341431521601681771851952022102192282342402462492522542542542542542542542542542542542542542540000000000000003112130394960697888991071181261371461561651761851952042142242332402472502532542542542542542542542542542542542542542542542542542542542540000000000000192131425364748697107118129140150161173184194205216228236246250253254254254254254254254254254254254254254254254254254254254254254254254255254000000000000316283852647588101112124136148160172184196209221233244250254254254254254254254254254254254254254254254254254254254254254255254254254254254254254254000000000005193145597185991111251381511641771922052182312442502542542542542542542542542542542542542542542542542542542542552542542542542542542542542542542542542540000000000520334863779210612113615016417819320922323724925425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425400000000031933506581971121291431601751912072222382502542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532502422340000000011430486582991151321491671832002172352492542542542542542542542542542542542542542542542552542542542542542542542542542542542542542542542542532482392272121991851720000000072643628099116134152171188208225244253254254254254254254254254254254254254254254255254254254254254254254254254255254254254254254249241227211198182168153137123107000000021937587697114134153174193211232249254254254254254254254254254254254254254255254254254254254254254254254255254254254254254247236219203188172156139124108937659443364 mat :

B

B 25525425425425425425425425425425425425425425425425425425425424322520418416414512510585675032153000000000000000000000000000000255254254254254254254254254254254254254254254254254254254254254249231214194176156138119100826649331750000000000000000000000000000255254254254254254254254254254254254254254254254254254254254254254253241225207189171154136119101846852372392000000000000000000000000025525525425425425425425425425425425425425425425425425425425425425425425425023822220518917215614012410791756147331982000000000000000000000025525525425425425425425425425425425425425425425425425425425425425425425425425424923922420819417816314813311710288736047342110500000000000000000002552552542542542542542542542542542542542542542542542542542542542542542542542542542542522432312162031891741601471331191059277665342301994100000000000000255255254254254254254254254254254254254254254254254254254254254254254254254254254254254254253249241230216204191178166153140128115102917767564433231484000000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425325124423522521220119017816715614313212210998887566564536271811731000255255254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254254252251244237229218208199188176166158146135126116104968675675848393224162552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522512452392332262152061981891781691621531421331251171069789822552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522502492432372322272212102031961891801711641572552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512492482442382342302552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542522512502552552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512492452392342302262182092031972552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522512472402352302212112031961881771691621541431351281212552552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532522482412352262152061971881771671591481381301201091009183726456472552552542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532512442372262152051941821711621501381281181069687746656453729201395225525525425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425324623822621420319017716615414113011810594837060494030201273000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425425425324623622320919618317015714313011710391766654433121116100000000000025525525425425425425425425425425425425425425425425425425425425425425425425425425425124122721319818316915413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mat :

30 deg * sin 0.5

gray R G + B + 3 / :

gray Min 86

gray Max 167

m n q m n m n - 22 mat :

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

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 gray

16786 - 81

deg2rad π 180 / ≡ 0.017453292519943 ≡

gray rows gray cols 12 mat 336412 mat

magnitude vector vect mag vect vect * sqrt :

v Abs j 1 v rows range a j el v j el abs : for a 21 line :

deg 30 :

λ 235 :

Explain "sanity"

"sanity" is done vs Mathcad 11, Paul W. [McGill University, Montréal]. Paul W. shared unpricable collaboration to the Mathsoft Collaboratory. Paul's last visit was "now I have to take care of my own garden". This "Aurevoir" was clear to us: life is short but not the heritage.

On-line sanity [open suite]
on the "UserDegree" 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 bilin mc nc uc vc 22 mat : 161 line

Piecewise sanity is complete

A 0.866025 0.5 - 0.5 0.866025 22 mat

m n q A * specific order for this application ≡

m n q A * 60.579 38.926 3.421 - 71.926 - 22 mat

uv1 61

uv2 72

m n 12 mat u v 12 mat stack 3364617222 mat

N 17 32.5 31 36.5 22 mat

bilin 17 32.5 31 36.5 22 mat

sanity suite on "user deg" ... sanity up to matching canevas  [i,j]
.................... sanity [i,j] => successful .................... 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 : p 12 range q 12 range i s 1 p el : j s 2 q el : 31 line for for 51 line for for i j 12 mat 211 line :

speeds up calcul
...  210/47  ... A x y 21 mat uc vc 21 mat - (* eval

A x y 21 mat uc vc 21 mat - (*

Input string NOT
in correct format
i.e: NOT commutative x y 21 mat uc vc 21 mat - (A *

w 0.769 0.231 0.756 0.244 22 mat ≡

p 12 range q 12 range i s 1 p el : j s 2 q el : 31 line for for

i j 12 mat 267912 mat ≡

t0 1 time :

rotated image was sharpened IrfanView.

Photo R G B deg λ rotate :

Photo 267912 mat

[i,j] matching canevas indices

1 time t0 - 47 sec *

gray rows gray cols 12 mat 336412 mat

The original directions are [33 64] ... after the bilinear "s0" the new image cancas directions elongate/stretche. Though, I don't understand [i,j] in the final steps, I accept. "Why should I refuse my meal if I don't understand the process of digestion" [Lord Kelvin]. "The result is too beautiful not to be true" [Paul Dirac].

Read next: attempt the final rotation step "input string was not in correct format" Rotate Image.sm remToDo