О спи­ра­лях

Пре­жде все­го, посмот­рим на ис­точ­ник вдох­но­ве­ния, ко­то­рый я слу­чай­но на­шёл в Ин­тер­не­те:

An infinity of Mega Pixels

Ри­су­нок 1. Фо­то­гра­фия «An infinity of Mega Pixels». Ис­точ­ник

Ка­ким пре­об­ра­зо­ва­ни­ям под­верг­ся этот сни­мок? Что нуж­но сде­лать с обыч­ной фо­то­гра­фи­ей, что­бы по­лу­чить это? Ка­кое долж­но быть ис­ход­ное фо­то? — Эти во­про­сы я за­да­вал се­бе в те­че­ние ча­са. По­ка, на­ко­нец, ме­ня не оза­ри­ло: на фо­то­гра­фии от­сут­ству­ет объ­ек­тив фо­то­ап­па­ра­та! А что вме­сто не­го? Вме­сто не­го... эээ... вся осталь­ная фо­то­гра­фия.

Т.е. ис­ход­ное изоб­ра­же­ние мож­но пред­ста­вить в ви­де коль­ца с вы­ре­зан­ной в се­ре­ди­не дыр­кой. Фор­ма дыр­ки мо­жет быть лю­бой. Кро­ме то­го, лю­бой мо­жет быть фор­ма внеш­ней гра­ни­цы. На­при­мер, это мо­жет быть всё остав­шее­ся изоб­ра­же­ние. В ка­че­стве при­ме­ра возь­мём коль­цо, изоб­ра­жён­ное на ри­сун­ке 2:

Коль­цо с крас­ной точ­кой

Ри­су­нок 2. Коль­цо. От­сут­ствую­щая об­ласть по­ка­за­на «шах­мат­ной до­с­кой»

Те­перь, ко­гда мы зна­ем, как вы­гля­дел ис­ход­ный сни­мок (это бы­ла обыч­ная фо­то­гра­фия с вы­ре­зан­ным объ­ек­ти­вом), мы мо­жем по­нять, что нуж­но сде­лать с фо­то­гра­фи­ей, что­бы она вы­гля­де­ла так, как на ри­сун­ке 1: нуж­но раз­ре­зать коль­цо в ка­ком-ни­будь ме­сте, и на­мо­тать его внутрь в спи­раль, бес­ко­неч­но по­вто­ряя. Но де­лать это нуж­но с умом. Пре­жде все­го, нуж­но по­до­брать та­кое пре­об­ра­зо­ва­ние ко­ор­ди­нат, что­бы ра­ди­у­сы оста­лись пер­пен­ди­ку­ляр­ны­ми пе­ри­метру. Ес­ли это­го не сде­лать, то бу­дут силь­ные гео­мет­ри­че­ские ис­ка­же­ния. Не­мно­го по­упраж­няв­шись с компле́ксными чис­ла­ми, мож­но прий­ти к вы­во­ду, что пе­ри­мет­ры и ра­ди­у­сы долж­ны пре­вра­тить­ся в два вза­им­но-ор­то­го­наль­ных се­мей­ства ло­га­риф­ми­че­ских спи­ра­лей. Ино­го не да­но!

Так мо­жет вы­гля­деть один ви­ток спи­ра­ли по­сле раз­ре­за­ния коль­ца:

Коль­цо за­кру­чен­ное в спи­раль
Коль­цо за­кру­чен­ное в спи­раль

Ри­су­нок 3. Коль­цо, за­кру­чен­ное в один ви­ток спи­ра­ли.
Изоб­ра­же­ния раз­ли­ча­ют­ся ско­ро­стью убы­ва­ния ра­ди­у­са спи­ра­ли

На са­мом де­ле, на ри­сун­ке 3 изоб­ра­жён один ви­ток ре­зуль­ти­рую­щей спи­ра­ли. В этот ви­ток по­па­ло чуть боль­ше од­но­го вит­ка ис­ход­но­го коль­ца: это вид­но по крас­ной точ­ке. Имен­но при та­кой ско­ро­сти «про­дви­же­ния вдоль коль­ца» мы по­лу­ча­ем кон­форм­ное отоб­ра­же­ние, со­хра­няю­щее уг­лы.

Оста­лось сде­лать со­всем ма­лое: бес­ко­неч­но про­длить изоб­ра­же­ние спи­ра­ли в обе сто­ро­ны. При этом счи­тая, что бо­лее мел­кие вит­ки ви­зу­аль­но на­хо­дят­ся, на­при­мер, за бо­лее круп­ны­ми. По­до­брав ско­рость убы­ва­ния ра­ди­у­са так, что­бы внеш­няя часть вит­ка со­сты­ко­ва­лась с внут­рен­ней ча­стью преды­ду­ще­го вит­ка, по­лу­чим:

Коль­цо за­кру­чен­ное в бес­ко­неч­ную спи­раль

Ри­су­нок 4. Коль­цо, за­кру­чен­ное в бес­ко­неч­ную спи­раль

Уже луч­ше. От­сю­да вид­но, кста­ти, что «ра­ди­у­сы» — не пря­мые ли­нии, а то­же ло­га­риф­ми­че­ские спи­ра­ли, в каж­дой точ­ке пер­пен­ди­ку­ляр­ные «диа­мет­рам».

Те­перь нуж­но сде­лать то же, но с на­сто­я­щей фо­то­гра­фи­ей. Нуж­но лишь най­ти коль­цо! Огля­нув­шись во­круг се­бя, я уви­дел мно­го ко­лец. Но од­но из них мне по­нра­ви­лось боль­ше все­го — это же­на Али­на:

Же­на с кар­ти­ной в ру­ках

Ри­су­нок 5. Фо­то­гра­фия для об­ра­бот­ки: же­на с кар­ти­ной в ру­ках.
Обои на сте­не по­ели кро­ли­ки

Чем не коль­цо? Оста­лось лишь вы­ре­зать дыр­ку (изоб­ра­же­ние спе­ци­аль­но рас­ши­ре­но, что­бы бы­ло вид­но коль­цо, об­ра­зо­ван­ное не­про­зрач­ной об­ла­стью):

Вы­ре­зан­ная кар­ти­на

Ри­су­нок 6. Фо­то­гра­фия с вы­ре­зан­ной дыр­кой

Важ­ное за­ме­ча­ние: дыр­ку луч­ше все­го вы­ре­зать с по­мо­щью ин­стру­мен­та Extract в про­грам­ме Adobe Photoshop. Дру­гой спо­соб не поз­во­лит по­лу­чить ка­че­ствен­ное изоб­ра­же­ние! Как бы тща­тель­но вы не сде­ла­ли вы­де­ле­ние вдоль края дыр­ки, по­сле уда­ле­ния внут­рен­но­сти у вас оста­нет­ся ста­рый пе­ре­ход цве­тов в быв­ший цвет дыр­ки по кра­ям. В от­ли­чие от про­сто­го вы­де­ле­ния, ин­стру­мент Extract кро­ме уда­ле­ния лиш­них пик­се­лов (плав­но­го ухо­да в про­зрач­ность), поз­во­ля­ет пе­ре­счи­тать цвет изоб­ра­же­ния на гра­ни­це, убрав плав­ный пе­ре­ход в цвет фо­на. «По­сле та­ко­го пе­ре­счё­та изоб­ра­же­ние мо­жет быть на­ло­же­но на фон дру­го­го цве­та» — так на­пи­са­но в справ­ке Adobe Photoshop. И это аб­со­лют­но вер­но! «Фо­ном дру­го­го цве­та» в на­шем слу­чае бу­дет яв­лять­ся са­мо изоб­ра­же­ние.

Раз­ре­зая коль­цо и бес­ко­неч­но его на­ма­ты­вая, мож­но по­лу­чить же­лае­мый ре­зуль­тат:

Фо­то­гра­фия, за­кру­чен­ная в спи­раль

Ри­су­нок 7. Фо­то­гра­фия, за­кру­чен­ная в спи­раль

Изоб­ра­же­ние, по­ка­зан­ное на ри­сун­ке 7, на­мо­та­но от наблю­да­те­ля. На­мот­ка на наблю­да­те­ля то­же мо­жет дать ин­те­рес­ные ре­зуль­та­ты:

Спи­раль на­мо­тан­ная на наблю­да­те­ля

Ри­су­нок 8. Спи­раль, на­мо­тан­ная на наблю­да­те­ля. Ори­ги­наль­ное изоб­ра­же­ние

Про­грам­ма

Ну а те­перь са­мое глав­ное — моя про­грам­ма.

Её мож­но ска­чать от­сю­да: Spiral.zip (167 Кбайт, ска­ча­но 990 раз). Впол­не мо­жет глю­чить. Най­дё­те ошиб­ку — пиши́те.

Про­грам­ма до­ста­точ­но мощ­ная. Она мо­жет за­кру­чи­вать изоб­ра­же­ния в две сто­ро­ны (по- и про­тив ча­со­вой стрел­ки), а так­же к наблю­да­те­лю и от наблю­да­те­ля. Про­грам­ма спо­соб­на ра­бо­тать с 16-ти бит­ным цве­том (внут­рен­нее пред­став­ле­ние цве­та — все­гда 32 би­та на ка­нал, HDR, учи­ты­ва­ет­ся ди­на­ми­че­ский диа­па­зон ис­ход­ной фо­то­гра­фии при сме­ше­нии цве­тов) и 16-бит­ной про­зрач­но­стью. Име­ет­ся хо­ро­шая ин­тер­по­ля­ция (на уров­не би­ку­би­че­ской), а так­же адап­тив­ный ан­тиа­ли­а­синг. Про­грам­ма впол­не мо­жет об­ра­бо­тать бес­ко­неч­ное чис­ло вит­ков за ко­неч­ное вре­мя бла­го­да­ря спе­ци­аль­ным ал­го­рит­мам упро­ще­ния и от­се­че­ния. Кро­ме то­го, под­дер­жи­ва­ет­ся ра­бо­та на мно­го­ядер­ных про­цес­со­рах.

Ис­ход­ное изоб­ра­же­ние — обя­за­тель­но PNG с про­зрач­но­стью (аль­фа-ка­нал) с глу­би­ной цве­та 8 или 16 бит на ка­нал. PNG мо­жет быть как Interlaced, так и сплош­ной. Я це­лый день по­тра­тил на до­бав­ле­ние под­держ­ки 16-бит­ных PNG в биб­лио­те­ку, в ко­то­рой из­на­чаль­но та­кой под­держ­ки не бы­ло.

Под­го­тав­ли­ва­е­те ис­ход­ное изоб­ра­же­ние, как опи­са­но вы­ше, пе­ре­тас­ки­ва­е­те мыш­кой на зна­чёк про­грам­мы. Про­грам­ма за­пус­ка­ет­ся и спра­ши­ва­ет у вас не­сколь­ко па­ра­мет­ров:

  • xc — ко­ор­ди­на­та x цен­тра бу­ду­щей спи­ра­ли в ис­ход­ном изоб­ра­же­нии. Вы долж­ны ука­зать точ­ку, на­хо­дя­щу­ю­ся в пре­де­лах дыр­ки. К этой точ­ке бу­дет «стре­мить­ся» изоб­ра­же­ние. На­при­мер, ес­ли точ­ка на­хо­дит­ся вы­ше цен­тра дыр­ки, то каж­дый ви­ток бу­дет ши­ре вни­зу и у́же ввер­ху. Ес­ли же, на­при­мер, сни­зу каж­до­го вит­ка у вас по­яви­лась не­же­ла­тель­ная «пу­стая» об­ласть, то центр спи­ра­ли нуж­но сме­стить вниз.
  • yc — ко­ор­ди­на­та y цен­тра спи­ра­ли в ис­ход­ном изоб­ра­же­нии.
  • kRho — во сколь­ко раз сле­дую­щий ви­ток мень­ше преды­ду­ще­го. В при­ме­рах вы­ше я ис­поль­зо­вал kRho, не силь­но от­ли­чаю­щий­ся от 0.5. Ес­ли это чис­ло от­ри­ца­тель­ное, то на­мот­ка бу­дет ве­стись к наблю­да­те­лю. В этом слу­чае дыр­ка в изоб­ра­же­нии не обя­за­тель­на (см. ри­су­нок 8).
  • kPhi — во сколь­ко раз ви­ток спи­ра­ли бу­дет длин­нее, чем ви­ток оп­ти­маль­ной дли­ны. При оп­ти­маль­ной дли­не ис­ка­же­ния ми­ни­маль­ны, од­на­ко изоб­ра­же­ние «раз­во­ра­чи­ва­ет­ся» при ухо­де вдаль. Что­бы это­го из­бе­жать, мож­но вве­сти kPhi чуть боль­ше еди­ни­цы (про­грам­ма под­ска­зы­ва­ет зна­че­ние kPhi, нуж­ное для по­лу­че­ния па­ра­л­лель­ных ли­ний).
  • Result image width — ши­ри­на ре­зуль­ти­рую­ще­го изоб­ра­же­ния (це­лое чис­ло пик­се­лов)
  • Result image height — вы­со­та ре­зуль­ти­рую­ще­го изоб­ра­же­ния (це­лое чис­ло пик­се­лов)
  • Color toning factor — ди­на­ми­че­ский диа­па­зон ис­ход­но­го изоб­ра­же­ния. Ес­ли изоб­ра­же­ние сня­то при яр­ком сле­пя­щем све­те, то этот ко­эф­фи­ци­ент мож­но сде­лать боль­ше еди­ни­цы, на­при­мер, 3.0. Для спо­кой­ных пас­мур­ных све­то­вых усло­вий по­дой­дёт зна­че­ние 1.0. Этот ко­эф­фи­ци­ент ис­поль­зу­ет­ся для пра­виль­но­го на­ло­же­ния те­ней (ес­ли вы ре­ши­те сде­лать ис­ход­ный файл с те­ня­ми, от­бра­сы­вае­мы­ми на про­зрач­ность), а так­же пра­виль­ной об­ра­бот­ки бли­ков и ан­тиа­ли­а­син­га.
  • High-quality processing: вво­ди­те «y» или «n» в за­ви­си­мо­сти от то­го, хо­ти­те ли вы, что­бы про­грам­ма ра­бо­та­ла очень дол­го, но про­из­ве­ла ка­че­ствен­ную кар­тин­ку, или же в два ра­за быст­рее, но кар­тин­ка бу­дет ме­нее ка­че­ствен­ной.
По­сле это­го про­грам­ма (очень дол­го) ана­ли­зи­ру­ет и об­ра­ба­ты­ва­ет ис­ход­ное изоб­ра­же­ние, и про­из­во­дит файл то­го же ти­па, что и ис­ход­ный, с име­нем, по­лу­чае­мым пу­тём до­бав­ле­ния «_spiral» к име­ни ис­ход­но­го фай­ла.

При­мер

Кар­тин­ки с круж­ка­ми, при­ве­дён­ные вы­ше — для де­мон­стра­ции. В них про­зрач­ность убра­на и по­ка­за­на при по­мо­щи шах­мат­ной дос­ки.

Про­грам­ме же нуж­на та­кая кар­тин­ка: с про­зрач­но­стью, с дыр­кой внут­ри (при на­мот­ке на наблю­да­те­ля дыр­ка внут­ри не нуж­на) и (воз­мож­но) по кра­ям:

Об­ра­зец ис­ход­но­го фай­ла

Ри­су­нок 9. Об­ра­зец ис­ход­но­го фай­ла

За­тем вво­дим па­ра­мет­ры в про­грам­му...

SAn Spiral 1.01 Beta. Copyright (C) 2008 Sukhinov Anton
E-mail: #########@GMail.com

Enter xc (spiral center in the source image): 232
Enter yc (spiral center in the source image): 232
Enter kRho (0.0<kRho<1.0): 0.4
Enter kPhi (...): 1.0
Enter result image width: 464
Enter result image height: 464
Enter color toning factor (default: 1.0): 1.0
Use high-quality processing? (y/n): y

Loading D:\ring.png...

Processing:
  Scanning image...
  Remapping using 2 processor kernels...
Done in 4 seconds.

Saving D:\ring_Spiral.png...

The program finished successfully. Press [Enter] to exit...

...и по­лу­ча­ем ре­зуль­тат (со спи­ра­ле­вид­ной дыр­кой):

Ре­зуль­тат об­ра­бот­ки фай­ла

Ри­су­нок 10. Ре­зуль­тат об­ра­бот­ки фай­ла с ри­сун­ка 9

Дру­гие про­грам­мы

Ко­неч­но же, моя про­грам­ма — не един­ствен­ная. Су­ще­ству­ют дру­гие про­грам­мы, поз­во­ляю­щие по­лу­чить по­хо­жие кар­тин­ки:

  • MathMap пла­гин для GIMP. Поз­во­ля­ет вруч­ную за­да­вать фор­му­лы пре­об­ра­зо­ва­ний; име­ет боль­шую биб­лио­те­ку го­то­вых пре­об­ра­зо­ва­ний. Ссыл­ка.
  • Фильтр Hyper Tiling™ из на­бо­ра KPT® Collection (ком­мер­че­ский про­дукт). Ссыл­ка.

202 отзыва на запись «О спи­ра­лях»

Ан­тон, у ме­ня воз­ник­ло не­сколь­ко во­про­сов при ра­бо­те с Ва­шей про­грам­мой Воз­ни­ка­ет ошиб­ка при ра­бо­те: Error: Source image must have RGBa format Не мог­ли бы вы объ­яс­нить, что мне нуж­но ис­пра­вить, для то­го что­бы про­грам­ма за­ра­бо­та­ла, и ещё: где ре­гу­ли­ро­вать глу­би­ну цве­та изоб­ра­же­ния в фор­ма­те .png. За­ра­нее спа­си­бо!
Доб­рый день! Эта ошиб­ка озна­ча­ет, что у те­бя ли­бо не цвет­ное изоб­ра­же­ние, ли­бо аль­фа-ка­на­ла (про­зрач­но­сти) нет. Ведь без аль­фа-ка­на­ла не­воз­мож­но сде­лать дыр­ку в изоб­ра­же­нии. В Фо­то­шо­пе про­ще все­го сде­лать так: От­кры­ва­ешь свою фо­то­гра­фию (ка­кой бы она ни бы­ла). Вы­де­ля­ешь её всю и ко­пи­ру­ешь в бу­фер об­ме­на. За­тем со­зда­ёшь но­вую: File→New. В ок­не вы­би­ра­ешь Preset: Clipboard (что­бы раз­ме­ры и глу­би­на цве­та взя­лись из бу­фе­ра об­ме­на), Color Mode: RGB, Background Contents: Transparent. На­жи­ма­ешь OK, — и у те­бя со­зда­ёт­ся изоб­ра­же­ние RGBa со сплош­ной дыр­кой. Встав­ля­ешь в изоб­ра­же­ние со­дер­жи­мое бу­фе­ра об­ме­на. Уда­ля­ешь лиш­нее во встав­лен­ном изоб­ра­же­нии с по­мо­щью «Eraser Tool», вы­де­ле­ния и кноп­ки Del, или, луч­ше все­го, ин­стру­мен­та Extract. По­том со­хра­ня­ешь: File→Save, там обя­затель­но вы­клю­ча­ешь гал­ку «As a Copy». Format ука­зы­ва­ешь PNG.
Толь­ко се­год­ня уви­дел в Се­ти «спи­раль­ные» кар­тин­ки, и уже по­про­бо­вал сде­лать та­кую-же. Всё от­лич­но по­лу­чи­лось. Огром­ное спа­си­бо ав­то­ру!!! Вот бла­го­да­ря та­ким та­лан­там и ста­но­вишь­ся горд за Рос­сию.
А при ка­кой ошиб­ке вы­во­дит­ся со­об­ще­ние
Error: Can not load file: C:ProgramsWhithout_installSpiral2.jpg
?
К со­жа­ле­нию, про­грам­ма по­ни­ма­ет толь­ко .png-фай­лы.
Спа­си­бо, по­сле про­чте­ния со­дер­жа­тель­ной ча­сти за­ме­ча­ние про фор­мат фай­ла не за­ме­тил По­бе­жал про­бо­вать
Hi People
How are you doing?
пи­шет:
Error: Floating point division by zero
в чем про­блем­ма?
Ин­те­рес­но. Ска­жи­те, ка­кие па­ра­мет­ры вы вво­ди­те про­грам­ме, и ка­кие раз­ме­ры ис­ход­но­го изоб­ра­же­ния?
Ни­как не мо­гу ска­чать са­му про­грам­ку! Со­хра­ня­ет в html и все!((((((
Под­ска­жи­те что не­пра­виль­но де­лаю!!!
Это ошиб­ка сай­та. Бу­ду ис­кать при­чи­ну…
Вро­де бы ис­пра­вил.
Спа­си­бо! Ска­ча­лась! Вот толь­ко те­перь на­до с RGB разо­брать­ся! Не все изоб­ра­же­ния хо­чет чи­тать!)
Обои на сте не по ели кро ли ки
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