以自然法則為基礎的水墨擴散之研究

(1)

ͽҋ൒ڱ݋ࠎૄᖂ۞ͪግᕖ೸̝ࡁտ

ͳ؟ᅛ ͳ̥౰ Ղܷኰ

઼ϲ̚Ꮈ̂ጯྤੈࡊጯࡁտٙ

ၡ! ࢋ

Kunii അགྷ೩΍кჯޘᕖ೸ሀݭֽሀᑢͪግᕖ೸ன෪Ăҭߏ΁۞ࡁտ̪ѣ αี৿εĂώ͛ፂѩ೩΍Լซ̝྽ĄࢵАĂԧࣇΐˢ˞৽ૺ۞পّĄԧࣇॲፂ

઼̚३ڱ৵ՄĶކ৽ķ۞ۏநপኳĂ൴ण΍׍ѣ৳ྮᄃӛّͪ۞৽ૺඕၹĂ֭

ሀᑢ΍ͪግᕖ೸д࠹ள۞৽ૺপّ˯۞ᕖ೸ன෪Ą׎ѨĂԧࣇ҂ᇋࢦ˧Я৵Ă ឰͪግᕖ೸ਕЯᑕࢦ˧ٙயϠ۞ᇆᜩĂৌ၁гͅᑕ΍൪छд̙Т้୆ޘ۞൪ڕ

˯ү൪ॡ۞ଐဩĄГ۰Ăԧࣇଯጱ΍Ԇፋăϒቁ۞ᇴࣃՐྋ͞ڱĄԧࣇՐ΍ᇴ ࣃՐྋܑϯ̳ёĂ˵൴னࢦࢋ۞ᙝࠧࣃࢨט୧Іćܲᙋ˞ᇴࣃՐྋ۞ќᑦّᄃ ϒቁّĄ౵ޢĂԧࣇणϯͪግᕖ೸д઼̚३ڱᄃ׍ѣͪግࢲॾ۞ᇆည఍ந۞ᑕ ϡ၁ּĂរᙋ˞ٙ೩͞ڱ۞࿀ৌሀᑢඕڍᄃ၁ϡᆊࣃĄ

ᙯᔣෟĈͪግᕖ೸ă઼̚३ڱăͪግࢲॾ۞ᇆည఍நăҋ൒ڱ݋ăܧᑢৌࢍზ

፟ဦጯĄ

A STUDY OF PHYSICALLY-BASED INK DIFFUSION

Chung-Ming Wang Ren-Jie Wang Jiunn-Shyan Lee

Institute of Computer Science National Chung Hsing University

Taichung Taiwan 402, R.O.C.

Key Words: ink diffusion, Chinese calligraphy, Chinese ink painting image processing, physically-based approach, non-photorealistic computer graphics.

ABSTRACT

Kunii proposed a “Multidimensional diffusion model” to simulate ink diffusion phenomena with some success. However, his research also shows four defects. In this paper, we present four approaches to strengthen his work. First, we consider ink diffusion with the influence of two types of paper that are commonly utilized in the Chinese calligraphy. This allows the simulation to reflect handwritten examples. Second, we consider ink diffusion under the gravity factor, allowing ink diffusion to be synthesized realistically. Third, we derive mathematical expressions and the boundary conditions when solving the “Multidimensional diffusion model”. This makes it feasible to secure the correctness and convergence of the numerical computing. Finally, we present ink diffusion applications both in Chinese calligraphy and in processing images subject to such phenomena.

In conclusion, the proposed approaches enhance Kunii’s work, resulting in more visually plausible simulation as well as feasible applications.

(2)

˘ă݈! ֏

ͪግᕖ೸(ink diffusion)ன෪۞ሀᑢߏܧᑢৌࢍზ፟ဦ ጯ(non-photorealistic computer graphics)۞ࢦࢋࡁտ͹ᗟ̝

˘[1-6]Ąొ̶ጯ۰ֹϡ෭ဦڱ(texture mapping)ֽயϠপؠ

۞ͪግड़ڍ[1,3,4,11-17]ć൒҃ĂϤٺግҒ۞፧୶ăͪณ۞

кဿඈЯ৵ౌົᇆᜩͪግᕖ೸ன෪ĂЯѩĂKnuii ᄮࠎྏဦ ಏ৷гͽ෭ဦڱֽሀᑢኑᗔ۞˯ࢗன෪̙֭ዋЪĄ࠹ͅ

۞Ă΁ᄮࠎᑕྍͽҋ൒ڱ݋(physically-based)ࠎֶᕩĂଂ࠹

ᙯጯந඾͘Ă֭౅࿅ۏநጯ˯۞ྋᛖĂ͞ਕ၆ͪግᕖ೸۞

ሀᑢҹႽ׎ΑĄKnuii Яѩ೩΍˘࣎Ķкჯޘᕖ೸ሀݭķ (multidimensional diffusion model)[7]ֽሀᑢግϗ̚۞ͪ׶

჆۞ᕖ೸ன෪Ąѩሀݭଂቱវ௕̄۞ሤ˧ጯྻજ۞֎ޘΝ ሀᑢግϗᕖ೸۞જүĂֹ֭ϡ׌࣎ᇴጯ͞඀ёֽೡࢗͪ׶

჆дᕖ೸ซҖ̚۞Ϲ̢үϡĄдᕖ೸࿅඀̚Ăͪă჆۞ณ གྷ࿅ࢍზͽޢĂ፧ޘజෛᛇ̼јግ႑Ă̙Т۞ግณĂົѣ

̙Т඀ޘ۞ᕖ೸Ă̙υגຍΝ఍நĂ྿ј˞׎΁Тጓࡁտ ጯ۰ٙ൑ڱ྿ז۞ሀᑢड़ڍĄ

ԧࣇᄮࠎ Knuii ٙ೩΍۞ሀݭᔵ൒ͽЪͼҋ൒ڱ݋۞

পֽّྋᛖᕖ೸۞જүĂҭ׎ࡁտҌ̪͌ѣα࣎ϏႽநຐ

̝఍Ăࣃ଀ԧࣇஎˢࡁտ֭Լซ׎৿εĄࢵАĂ΁۞ሀݭ ၆ಫ̬ۏኳ۞҂ᇋͣ৿׹ؼĄKunii ่҂ᇋநຐېڶ˭̙ӣ Їңಫ̬ۏኳ۞ᕖ೸ன෪Ă΁֭Ϗ҂ᇋᕖ೸ॡѣ৽ૺхд

۞Я৵Ąధк৽ૺᔵ൒ܑࢬ˯࠻ֽໂࠎᙷҬĂҭ൪छд̙

Т৽ૺү൪ޢݒព΍मளᅲ̂۞മߖপّĄּтĂέ៉ކ

৽׶̂ౙ۞Ϝۍކ৽̝γ៍࠰ࠎϨҒĂҭߏ׌۰̰ӣۏ࠹

ளĂٙӔன۞ግ႑̙֭Ⴝ൒࠹ТĄЯѩĂԧࣇᄮࠎдሀᑢ

ͪግᕖ೸ॡĂѣυࢋ૟৽ૺ̝Я৵ৼˢ҂ᇋĄ׎ѨĂKunii

۞ࡁտ֭Ϗ҂ᇋࢦ˧၆ᕖ೸ன෪۞ᇆᜩĄᔵ൒ Kunii ̝ሀ ݭ̚ѣ׌࣎ᄃࢦ˧ѣᙯ۞ણᇴĄ൒҃Ă΁д၁னॡ֭Ϗ҂

ᇋѩ˟࣎ણᇴĂ҃ߏ૟̝నࠎ࿬ĂԆБଵੵࢦ˧၆ᕖ೸۞

ᇆᜩĂ൑ଂរᙋ׎ሀݭдѩ׌Я৵ᇆᜩ˭̝ϒቁّĄԧࣇ ᄮࠎ൪छдү൪ॡĂ่͌ᇴົдԆБͪπ۞൪ڕ˯౹үĂ

̂кᇴӮົᖣӄ൪ߛٕឪϲٺॸࢬ۞̍үπέĄ൑ኢ൪ߛ

ٕ̍үπέĂૄώ˯Ӯົர຋้୆ĄЯѩĂࢦ˧၆ͪግᕖ

೸ன෪̝ሀᑢ၁дࣃ଀ࢦෛĂ̙टنෛĄѩγĂࡶਕ૟ѩ Я৵ৼˢ҂ᇋĂឰֹϡ۰ΞͽᖣϤણᇴ۞አፋĂሀᑢ΍׍

ѣ̙Тࢦ˧ᇆᜩ඀ޘ۞ᕖ೸ड़ڍĂ݋૟ՀΞͽᒺൺሀᑢඕ ڍᄃৌ၁͵ࠧͪግᕖ೸̝෼ᗓĂणனሀᑢ۞ԆፋّĄௐˬĂ Kunii ֭Ϗଯጱ׎ሀݭ۞ᇴጯՐྋ͞ڱĂ˵֭Ϗ೩΍ᙝࠧࣃ ࢨט୧ІĄ΁૟ࢦ͕ٸдྋᛖ΁۞ᕖ೸ሀݭĂ၆ٺтңͽ ᇴࣃڱՐྋ۞࠹ᙯ௟༼Ă඾ግ̙кĄགྷ࿅ଯጱޢĂԧࣇ൴ ன ͽ ᇴ ࣃ Ր ྋ ॡ Ă ొ ̶ ણ ᇴ ۞ ᙝ ࠧ ࣃ ୧ І (boundary condition)υืଠט଀༊Ăӎ݋૟ົౄјᇴࣃՐྋ׍ѣ൴೸

ड़ᑕĂ൑ڱՐྋĄЯѩĂԧࣇᄮࠎࡁտ Kunii ሀݭ۞ᇴጯ ՐྋଯጱĂ၆ٺࣧؕሀݭ۞Ԇፋّѣϒࢬ۞੒ᚥĂࢫҲ˞

ޢˠ͔ϡྍሀݭ۞ӧᙱޘĄ౵ޢĂKunii ֭Ϗणன΍ͪግᕖ

೸࠹ᙯ۞ᑕϡ၁ּĄ࠹ͅ۞Ă΁่णϯ˘ႍግ႑۞д̙҂

ᇋ৽ૺ۞ଐڶ˭۞ͪግᕖ೸ன෪ĄԧࣇᄮࠎтਕᖣϤ˘ֱ

၁ᅫ۞ᑕϡ၁ּणϯᕖ೸۞ඕڍĂ่̙Հਕᖳಱሀᑢ۞ඕ ڍĂ˵Հਕणனͪግᕖ೸дৌ၁͵ࠧ۞ᑕϡቑᘞĄ

ώኢ͛ૄٺ˯̝ࢗજ፟Ă૟ͽՀ׹ؼăԆፋ۞֎ޘֽ

ࡁտͪግᕖ೸۞યᗟĂ֭೩΍αีԫμֽԼซ Kunii ၆ͪ

ግᕖ೸ࡁտ̝৿εĄௐ˟༼ԧࣇࢵАଣ੅ግϗ׶ކ৽۞ۏ நপّĂ֭аᜪă̶ژͪግሀᑢᅳા̚۞ࢦࢋ࠹ᙯࡁտĄ ௐˬ༼ԧࣇࢵАୃࢗ Kunii ۞Ķкჯޘᕖ೸ሀݭķĂͽүࠎ ࡁտͪግᕖ೸۞ጯநॲፂĄତ඾ྎ௟ᄲځтңॲፂѩሀ ݭĂଯጱ΍׎ᇴࣃڱ۞Րྋ͞ڱĄԧࣇ˵૟ୃࢗдՐྋ࿅

඀̚Ăٙ൴ன۞ᙝࠧࣃࢨטĂѩࢨט֖ͽᇆᜩᇴࣃՐྋ̝

ќᑦᄃ൴೸Ąତ඾ԧࣇᄲځтң૟৽ૺăࢦ˧׌࣎Я৵ጱ ˢሀݭ̚Ą˯ࢗ఺ֱౌߏ Kunii ࡁտٙϏഅ೩΍۞Ąௐα

༼णϯԧࣇֶፂ৽ૺăࢦ˧ăᙝࠧᇴࣃٙሀᑢ΍۞ͪግᕖ

೸ඕڍĄѩγĂԧࣇ˵૟ѩඕڍᕖ̈́ሀᑢ઼̚३ڱă׍ѣ

ͪግࢲॾ۞ᇆည఍நඈᑕϡĄௐ̣༼ԧࣇᓁඕώࡁտĂ֭

ᄲځϏֽΞਕ۞ࡁտ͞ШĄ

˟ăࡦഀۢᙊᄃ࠹ᙯࡁտ 1. ࡦഀۢᙊ

ĶግϗķĂ͹ࢋј̶ߏϤͪă჆ΐ˯͌ณቱኳ஄Ъ҃

јĂ׎ۏநّኳତܕቱវ໘୵۞পّĄቱវ໘୵఼૱׍к

̶೸ّ(poly dispersed nature)ůӈቱវ௕̄໘୵̝̚ቱវ

௕श̂̈Ӯ̙˘Ąٙѣቱវ௕शٙҫ௢ΐ۞Ѻ̶ͧဦӔઐ

୆ ې (skew) ̶ Ҷ Ă ఼ ૱ Ξ ͽ ϡ ұ ֶ ڗ ໄ ர ̶ Ҷ (poisson distribution)ֽೡࢗĄಶ຋៍҃֏Ăቱវ௕̄д୵វ̝̚ྻ

જҖࠎĂࠎο६ྻજܑ̝னćλ៍҃֏Ă׎ྻજҖࠎĂࠎ ᕖ೸ன෪̈́Ⴃژڧજன෪(osmosis) [8]Ą˵ಶߏᄲĂଂሤ˧

ጯྻજ۞៍ᕇֽ࠻Ă჆௕̄дͪ̚ͽο६ྻજ۞͞ёдொ

જĄ፧ޘດ੼Ă࠹̢༥ᇠ۞፟ົດ̂Ăொજ۞ిޘດၙć

፧ޘດҲĂ࠹̢༥ᇠ۞፟ົດ̈Ăொજ۞ిޘດԣć፧ޘ Ҳז჆௕̄Ξͽ̙צٲՁĂҋϤொજ۞ॡ࣏Ăொજిޘ౵

ԣĂ૟ז྿ؠిĄ

Ҍٺͪд৽˯۞ᕖ೸Ă͹ࢋߏצזͨ௟үϡ۞ᇆᜩĄ ԧࣇͽ઼̚३ڱᘱ൪౵૱ֹϡ۞৽ૺůކ৽(xuan paper, shium paper)ࠎ၆෪Ăֽᄲځ৽۞࠹ᙯপّĄކ৽͹ࢋՄफ़ ߏᑪϩٕอϩĂࠎ˞ᆧΐግҒ̈́ግᙶĂ૱дልफ़̚ΐˢк ณ̝ѻል(bamboo pulp)Ąކ৽۞ૄࢦ(basis weight)ăݓޘ (thickness)ă૜ޘ(density)ăπ໣ޘ(smoothness)ăӛͪޘ (water absorption)ăߘహޘ(softness)ăϨޘ(brightness)̈́৽

˧ඈপّᄃү൪ॡ̝ྻඊ̈́ግҒѣ૜̷۞ᙯܼĄ׎̚Ăކ

৽۞૜ޘ่̙ᇆᜩ৽˧ϺᇆᜩӛግّĂ҃ӛͪޘᄃӛግّ

ѣ૜̷ᙯܼĂӛግّ˫ᄃግҒѣᙯĄ

έ៉ކ৽̝૜ޘπӮ̂ࡗд 0.45g/cm³νΠĂ͟ώކ

৽ࡗ 0.4 g/cm³Ă҃̂ౙ۞ϜۍކπӮҲٺ 0.4 g/cm³Ą૜ޘ

̈Ă΃ܑ৽ᆸ̚۞͋ᅩкĂѣӀٺӛّͪĞЯࠎͨ௟үϡ

ͧྵځពğĂ҃჆௕̄ົдͪ̚ᕖ೸Ăӛّͪޘ̂۰Ăӛќ

(3)

ဦǬ ̙Тކ৽ӛግّ̝ͧྵĄ૜ޘ౵̈۞ϜۍކĂ׎ӛ ግّ౵рĂግ႑ᕖ೸౵̂ĂግҒ౵โ[9]

۞ግณϺкĂܑன΍ֽ۞ግҒྵஎĂግᙶត̼ྵ̂Ąဦ 1 ߏˬ჌ކ৽۞ӛግّ̝ͧྵĂΞͽ࠻΍έ៉ކ৽۞ӛግّ

౵मĂ͟ώކ৽Ѩ̝ĂϜۍކ৽౵ָĄ҃ӛግ౵р(ግ႑ᕖ

೸౵̂)۞Ϝۍކ৽Ă׎ግҒͧӛግّྵम۞έ៉ކஎ˘

ֱĄˬ჌ކ৽̚πӮ૜ޘ౵̈۞ߏϜۍކĂ׎ញჯྵ௟Ă

͋ᅩྵк[9]Ą

Ҍٺކ৽ញჯ۞ܜޘ̈́ᆵޘĂॲፂ઼̂̚ౙጯ۰۞ࡁ տĂᑪϩញჯ۞πӮܜޘቑಛд 2.825 Ҍ 2.952 ୮Ѽ(10^-3 Ѽ)̝มćᆵޘд 7.68 Ҍ 8.2 ຋Ѽ(10^-6Ѽ)̝ม[10]Ąᔵ൒ѩ ᇴፂΪߏ၁រඕڍ̝˘Ă֭ܧ໤ቁࣃĂҭ˵Ә෦ԧࣇĂކ

৽ញჯܧ૱௟̈Ăܧ҇ீٙٽ֍Ą 2. ࠹ᙯࡁտ

็௚дܧᑢৌࢍზ፟ဦጯ˯Ăѣᙯͪግ۞ࡁտĂ̙ኢ ߏሀᑢඊהሀ௡(brush model)ΝயϠତܕৌ၁ͨඊඊᛈ۞

ड़ڍ[2-4,11-13]ćٕ۰ߏֹϡҋؠ۞ဦᇹ(pattern)Ă૟ˬჯ

۞ሀݭٕ˟ჯ۞ᇆညĂͽግͪඊ(pen-and-ink)઼ٕͪ̚ግ൪ (Chinese ink painting)۞ࢲॾΝܑன[1,14-17]Ă఺ֱࡁտ̂

кֹϡܧҋ൒ڱ݋͞ڱֽயϠͪግड़ڍĄ΁ࣇ඾ீٺயϠ পड़۞ႊზڱĂ҃ܧଣտ఺ֱड़ڍ۞јЯĂЯѩдᒅ৽ă

̙ఢ݋Ҁ̼ඈᕖ೸ன෪۞ሀᑢ˯Ăຏᛇ̪̙ૉৌ၁Ąࠎ˞

੠ՐՀৌ၁۞ड़ڍĂSmall[18]׶ Curtis ඈˠ[19]дͪ૾

(watercolor)۞ሀᑢ̚೩΍˞ͪăᗞफ़௕̄ă৽ૺញჯ۞ໄ هĂͽྵЪٺҋ൒ڱ݋۞͞ڱֽሀᑢͪ૾۞Ч჌ன෪ĂЯ

҃଀זՀৌ၁۞ඕڍĄҭߏĂ઼ͪ̚ግֹϡ۞৵Մ̙Тٺ

ͪ૾Ă̙ਕԆБइϡͪ૾۞நኢĄѣొ̶ጯ۰т Kunii ඈ ˠĂဘྏ˞ྋͪግᕖ೸۞јЯĂԼଳϡЪͼጯந۞͞ڱֽ

ሀ ᑢ ͪ ግ ᕖ ೸ ۞ ซ Җ Ą Kunii ඈ ˠ ѝ ഇ ۞ ࡁ տ ͽ ௕ ̄ (particle)ᕖ೸ሀݭֽྋᛖͪግ۞ᕖ೸ன෪[20]Ą΁ᄮࠎግϗ Шγᕖ೸۞ిޘߏॡม۞בᇴĂΞͽϡ˘࣎ܕҬבᇴֽܑ

ϯĂግϗߏ˘჌ቱវ໘୵Ă჆௕̄۞̂̈ߏӔ૱ၗ̶ҶĂ

҃ግϗ۞፧ޘ׶჆۞ᔺ௕πӮ̂̈ѣᙯĂΞͽϡ˘࣎૱ၗ

̶Ҷבᇴ p(s)ֽܑϯĄ఺࣎௕̄ᕖ೸ሀݭᔵ൒ᖎಏҭෛᛇ

ड़ڍݒ̙֭௑Ъ၁ᅫ۞ҋ൒ࠧᕖ೸ன෪ĄࢵАĂ௕̄ᕖ೸

ሀݭ̚۞ᕖ೸ిޘܼᖎಏгϡ˘̳࣎ёֽܑϯĂтڍߏ๪

ԛግ႑إΞϤ๪͕ШγࢍზĂҭߏ၆ٺ̙ఢ݋ԛې۞ግ႑

૟൑ڱሀᑢĄ׎ѨĂᕖ೸۞ඕڍΪ̶јα࣎ҒลĂ̪൒൑

ڱޝჟቁ۞Ъͼ၁ᅫ۞ன෪ĄЯࠎግϗд৽˯۞ᕖ೸Ă̙

ኢٕͪ჆Ăᑕྍߏ˘჌ాᜈ۞̶ҶĂ߇ግ႑۞ᗞҒ̙ᑕྍ

Ϊϡѣࢨ۞ҒลֽܑϯĄ౵ޢĂቱវ໘୵۞௕̶̄̂̈Ҷ

֭ܧ૱ၗ̶੨Ă҃ߏӔұֶڗໄர̶ҶĂ̈௕̄ҫ̂кᇴĂ

̂௕̄ҫ͌ᇴ[8]Ą

౵ܕ Yu ඈˠ[5]׶ Huang ඈˠ[6]˵ଳϡ˞ତܕҋ൒ڱ

݋۞͞ڱֽሀᑢͪግᕖ೸ன෪Ą΁ࣇֹϡ˞ᇴጯܑϯёֽ

ሀᑢͪă჆ă৽ૺඈᕖ೸Я৵ĂΞଓ၆ͪግᕖ೸۞ࡁտ̪

̙ૉԆፋĂЯࠎ΁ࣇ֭Ϗ҂ᇋࢦ˧၆ͪግᕖ೸۞ᇆᜩĄ

ˬăͽҋ൒ڱ݋ࠎૄᖂ۞ͪግሀᑢԫμ

ѣᝥٺ௕̄ᕖ೸ሀݭ̙֭ਕྋᛖ၁ᅫ۞ᕖ೸ன෪ĂЯ ѩ Kunii ඈˠ˜Г೩΍າ۞Ķкჯޘᕖ೸ሀݭķ[7]Ą఺࣎

ሀݭଂሤ˧ጯྻજ(thermal motion)۞֎ޘΝࡁտĂҬͼͧ

ྵӚЪግϗ఺჌ቱវ໘୵۞ۏநপّĄϤٺԧࣇ۞ࡁտͽ ѩሀݭࠎૄᖂĂЯѩĂԧࣇ૟АᖎࢋᄲځྍሀݭĂ൒ޢГ

ֶѨୃࢗԧࣇԼซ఺࣎ሀݭֹٙϡ۞͞ڱĄ 1. кჯޘᕖ೸ሀݭ

Kunii ៍၅ግϗᕖ೸ޢ۞ဦԛĂ൴னግ႑ົӔனˬ჌

ግҒડાĈግϗۡତႍд৽˯۞੓ؕડ(initial zone)ăᗞҒ

౵எ۞โҒᙝࠧડ(black border)׶ᗞҒྵ୺۞ѷҒᕖ೸ડ (gray zone)Ą఺࣎͞ڱ૟ͪግᕖ೸ෛࠎͨ௟үϡ׶ቱវ໘

୵পّ۞ტЪүϡඕڍĂ΁૟ግϗᕖ೸̶јĶͪķ׶Ķ჆ķ

׌࣎ჯޘֽଣ੅Ą઄న৽ૺߏ˘࣎˟ჯ۞πࢬĂ၆৽ૺܑ

ࢬ˯Їຍ˘ᕇ(x,y)Ăдॡม t ۞ॡ࣏Ăͪ۞ܑࢬ૜ޘϡ g(x,y,t)

ֽܑϯĂ჆۞ܑࢬ૜ޘϡf(x,y,t)ֽܑϯĄ༊ᕖ೸ฟؕซҖĂ

˵ಶߏግϗࣣࣣႍ˯৽ૺ۞֤˘ᒠม(Ϻӈ t=0 ۞ॡ࣏)Ăͪ

׶჆۞ܑࢬ૜ޘт˭Ĉ

g(x,y,0)=C1 f(x,y,0)=C2 (x,y) ∈D0

g(x,y,0)=0 f(x,y,0)=0 (x,y) ∉D0

D0ܑϯ੓ؕડĄ˯ࢗ˟ёనؠ˞ܐؕ۞ᙝࠧ୧ІĄ

༊ᕖ೸ฟؕซҖĂͪ׶჆۞ܑࢬ૜ޘត̼ᄃॡม۞ᙯ

ܼĂΞͽϡ˭ࢬ۞͞඀ёֽܑϯĄܑࢬ૜ޘԼត͹ࢋߏϤ ᕖ೸׶઀ᒌ׌࣎Я৵ՙؠĄ̳ё(1)ă(2)̶Ҿᄲځͪă჆۞

ត̼ଐԛĄ

) 1 ( ²

y q g x p g g g t a

g

∂ + ∂

−

∇

∂ =

∂

τ (1)

) ) (

( f

f Z g t

f = ∇ ∇

∂

∂ (2)

׎̚Ăણᇴa ՙؠͪд৽˯۞ᕖ೸(Kunii дѩ઄నࠎ

૱ᇴ)Ăтڍ৽ૺ̙ߏᄦઇ଀ޝӮ̹Ă҃ߏѣֱ͞Шّ۞ញ ჯĂ݋a ົᐌ඾৽˯۞ळᇾ(x,y)Լត̙҃ТĄણᇴ_τ¹΃ܑ

(4)

ͪ۞઀ᒌిޘĄpăq ՙؠͪ߹۞͞ШĂ఺׌࣎ણᇴ׶ࢦ˧

۞үϡѣᙯ(Kunii дѩ઄న păq ࠎ 0)ĄבᇴZ(^g_f)ՙؠ˞

჆̶̄д̙Т፧ޘ˭۞ᕖ೸ిதĂ఺ߏ˘࣎ܧ૱ࢦࢋ۞ב ᇴĂົۡତᇆᜩ౵ޢ۞ᕖ೸јဦ۞ඕڍĄKunii ඈˠགྷ࿅၁ រĂԱז˞Z(^g_f)בᇴ۞ϯຍဦĄ

2. ᇴࣃՐྋ۞ଯጱᄃԫμ

Kunii ૞ڦٺ̬௜ሀݭ۞ໄهĂ֭ϏᄲځᇴࣃՐྋ۞

௟༼Ąԧࣇд၁ү఺࣎кჯޘᕖ೸ሀݭ۞Րྋ࿅඀ॡĂ૟

ົࢬᓜ׌̂߄ጼĄࢵАĂԧࣇυื૟఺׌࣎ઐ຋̶͞඀ё ᖼјᇴࣃ۞͞ёĂ̖ਕӀϡ࿪ཝ۞ࢍზՐྋĄѩγĂ၆ٺ

) (^g_f

Z בᇴ Kunii ࣧؕኢ͛ΪѣϯຍѡቢĂ֭՟ѣЇң࠹ᙯ

۞ᇴፂΞֻણ҂ĄϤٺѩѡቢ΃ܑ۞ߏ჆௕̄д̙Т፧ޘ

˭۞ྻજిޘĂߏ˘࣎ܧ૱ࢦࢋ۞בᇴĂ̙Ր΍Z(^g_f)̝ ᇴࣃĂᕖ೸ሀݭ૟൑ڱϒቁгྻүĄͽ˭ߏԧࣇྋՙ఺׌

࣎ӧᙱ۞͞ڱĄ

ࢵАĂ̳ё(1)Ξͽϡᇴࣃڱܑϯт˭Ĉ

΄

x G t G q

x t p

t G x q x r p

G G G r G

G

x t y

x y G g

nj n i

j i

nj i nj n i

j n i

j i

j n n i

j i

1 , ,

1

, 1 , 1 , , 1 , 1 ,1

,

] 1 )

( 4 1 [

) (

, ) , , (

+ +

+

− + + −

∆ + ∆

∆ ∆

∆ + +

−

− +

+ + +

=

∆

=

∆

=

τ

׎̚ 4

, 1 ) ( ²

2 <

∆

= ∆ r

x t r a

ТநĂ̳ё(2)

nj n i

j n i

j i

n j n i

j i

F r F

F F F s F

x y t

y x f F

, 1

, 1 , , 1 , 1 1 , ,

] 4 1 [ ) (

, ) , , (

− + + + +

=

∆

=

∆

=

+

− + + −

΄

׎̚ s

x t s Z ^f

g

4

≒1 , ) (

) (

∆ 2

= ∆ (3)

ԧࣇކӘ׌࣎˟ჯੱЕ g(x,y)ăf(x,y)̶ֽҾܑϯдळ ᇾ(x,y)˯۞ͪ׶჆۞ณĂ݋˯ࢗ׌࣎ᇴࣃܑϯёӈᄲځ˞

тңፆүϫ݈ g(x,y)ăf(x,y)׌࣎ੱЕֽՐ଀˭˘࣎ॡมᕇ

۞g’(x,y)ăf’(x,y)ࣃĄࣃ଀ڦຍ۞ߏĂё̄̚۞ r ׶ s ౌѣ ᙝࠧ୧І۞ࢨטĂϺӈ Kunii ሀݭ̚۞ણᇴ a ׶Z(^g_f)בᇴ ࣃౌѣ˯ࢨĄԧࣇᄮࠎ఺࣎ࢨטдՐྋ۞࿅඀̚ܧ૱ࢦ

ࢋĄѩ˜ЯࠎĂࡶֶ̙ೈѩࢨט୧ІĂ݋ᇴࣃՐྋѣΞਕ

ົ൴೸̙҃ົќᑦĄ൴೸۞ᇴࣃՐྋ૟ౄјٙՐ̝ᇴࣃྋ

׍ѣ࠹༊಼ޘ۞˯˭ዩજĂᇆᜩᇴࣃྋ۞ϒቁّĂጱ࡭౵

ޢ۞ሀᑢ۞࿅඀˵ົѣٙઐᅲăᄱमĄ఺ֱᙝࠧࣃ۞ࢨט ୧ІߏԧࣇགྷϤଯጱ࿅඀ٙ̚൴ன۞Ăд Kunii ۞ࣧؕኢ

֭͛̚Ϗഅ೩̈́Ą

ܑ˘! ჆дͪ̚۞ᕖ೸בᇴࣃ(Z(^g_f))

1 2 3 4 5 6 7 8 9

0 0.001 0.002 0.004 0.009 0.0244 0.0605 0.1018 0.1539 10 11 12 13 14 15 16 17 18 0.2009 0.231 0.2401 0.2421 0.2436 0.2445 0.2447 0.2466 0.2468

0.3 0.25 0.2 0.15 0.1 0.05

01 2 3 4 5 6 7 8 9 10 g/f Z(g/f)

11 12 13 14 15 16 17 18

ဦ 2 Z(^g_f)בᇴ̝ѡቢဦ

ҌٺZ(^g_f)בᇴࣃĂдᇴࣃڱ̚˵Яࠎᙝࠧࣃ۞ࢨ טĂ҃ѣ࠹၆۞ࢨט୧І(ણ֍̳ё(3))ĂЯѩԧࣇυืд ι۞˯˭ࢨ̝มԱವЪዋ̝ᇴࣃֽ႕֖ѩבᇴဦԛĄ

2 2

) ( 25 .

≒0 ) (

4

≒ 1 , ) (

) (

x t Z

x s t s Z

f g f g

∆

×

⇒

∆

= ∆

ࠎ͞ܮࢍზĂԧࣇА׽ؠ∆t=1Ă∆x=1ĂΞפ଀

25 . 0 ) (^g_f ≤

Z Ă֭дቢԛ˯פ଀ 18 ࣎ࣃтܑ˘̈́ဦ 2Ąב ᇴѡቢ˯۞׎΁ࣃĂΞͽֹϡ̰೧ڱՐ଀Ą

3. ΐˢ৽ૺ۞পّ

д Kunii ۞ࣧؕኢ֭͛̚Ϗഅ҂ᇋͪግᕖ೸д৽ૺ۞

ሀᑢĄԧࣇ૟৽ૺ۞ሀᑢ̶ј׌̙࣎Т۞ᆸѨֽ఍நĈ˘

ᆸߏγ៍Ξෛ۞৳ྮĂϡֽՙؠᙝቡ۞Ҁ̼ԛېćΩ˘ᆸ ߏགྷϤ৳ྮ̈́৽ૺ૜ޘࢍზ҃଀۞ӛّͪĂϡֽՙؠግ႑ ᕖ೸۞඀ޘĄ

ࢵАĂௐ˘ՎߏயϠٙᅮ۞৳ྮĄԧࣇᄮࠎކ৽۞ញ ჯܧ૱௟̈ĞπӮܜޘቑಛд 2.825 Ҍ 2.952 mm ̝มćᆵ ޘд 7.68 Ҍ 8.2µm ̝ม[10]ğĂᄃ׎யϠ௟̈ᙱ֍۞ញჯĂ

̙тயϠෛᛇ˯Ξ֍۞৳ྮֽ଀ЪநĄ

ԧࣇ઄న఺ֱ௟̈ញჯдౄ৽۞࿅඀̚ົϹᖐјྵ

ܜྵ௖۞ញჯՁĂ҃ញჯՁ۞ଵЕ૟ၹј৳ྮĄញჯՁྵ

૜۞г͞ĂϤٺ۩ᅩྵ̈Ăͨ௟үϡྵ̙ځពĞᕖ೸જү

ྵ̈Ăග˘࣎̈۞a ࣃğćញჯՁྵழ۞г͞ĂϤٺ۩ᅩྵ

̂Ăͨ௟үϡྵځពĞᕖ೸જүྵ̂Ăග̂۞a ࣃğĄ҃۩

ᅩ˵ԛј˞ᙷҬटጡ۞үϡĂ჆௕̄υื૟۩ᅩ๱႕̖ਕ ᚶᜈᕖ೸Ąԧࣇֹϡ Small[18]۞͞ڱֽயϠ৽ૺញჯĂ఺

˵ߏጯ۰ࣇ૱ϡ۞͞ڱĄдෛᛇ˯ĂញჯՁᇴϫ෸к۞г

͞ග̟ྵஎ۞ᗞҒĂ৽ૺ۞৳ྮಶົ΍னĄ૟θ ࢋՐд 0^o

(5)

ဦ 3 ̙Т৳ྮ۞৽ૺĄνဦࠎϒϹ৳ć̚ဦࠎ୆୧৳ć Πဦࠎ඙ې৳

ٕ 90^oΞͽயϠކ৽˯૱֍۞ݬۡ࠹Ϲ୧৳ć૟θ ࢋՐд 45^oಶѣ˞୆୧৳Ą૟ញჯՁ۞ቢ୧ϤۡቢԼјѡቢĂٕӔ ߙ჌Ԋొّ۞̶ҶĂΞͽઇ΍̙Т܅৳۞৽ૺ(ဦ 3)Ą

Ϊѣ৳ྮĂإ̙֖ͽܑன৽ૺ۞मளّĄּтĈέ៉

ކ׶Ϝۍކд৳ྮ˯՟ѣ̦ᆃ̙ТĂΞߏӛّͪݒѣम ҾĂܑன΍ֽ۞ግᙶ˵̙ТĄЯѩĂੵγ៍۞৳ྮ̝γĂ ӛّͪ۞ܑன̖ߏ౵ࢦࢋ۞Ą఺ߏԧࣇௐ˟Վࢋઇ۞̍үĄ

ௐ˟Վኬ̟ӛّͪĄ݈ࢬኘזކ৽۞ૄࢦăݓޘă૜

ޘăπ໣ޘăӛͪޘăߘహޘăϨޘ̈́৽˧ඈপّᄃү൪ ॡ̝ྻඊ̈́ግҒѣ૜̷۞ᙯܼĂ҃ྫྷግϗ۞ᕖ೸ᙯܼ౵̂

۞ᑕྍߏӛͪޘĂӛͪޘດ̂۰Ă׎ӛግّດૻĄͧྵέ

៉ކ৽ă͟ώކ৽ă̂ౙϜۍކ৽۞ӛͪ(ግ)ّ(֍ဦ 1)Ă Ξͽۢ྽Ăކ৽૜ޘྵ̈۰Ăӛّͪྵ̂ĄЯѩĂд၁ү

৽ૺ۞ॡ࣏Ă৽ૺ૜ޘྵ̂۰Ğтέ៉ކğĂග̟ྵ̈۞ӛ

ّͪć૜ޘྵ̈۰ĞтϜۍކğĂග̟ྵ̂۞ӛّͪĂтѩ

͞ਕ૟̙Тކ৽۞পّܑன΍ֽĄ҃఺࣎ӛّͪтңኬ̟

׸ĉԧࣇ۞͞ڱߏଂ̳ё(1)۞ણᇴ a ඾͘Ăa ࣃྵ̂ॡĂ ᕖ೸ன෪ྵځពĂԧࣇᄮࠎ఺࣎ણᇴ׶ӛّͪјϒͧĄд ӛّͪૻ۞г͞ග̟ྵ̂۞a ࣃćӛّͪ̈۞г͞ග̟ྵ

̈۞a ࣃĄކ৽˯۞̙ТҜཉѣ̙Т۞ a ࣃĂӛّͪྵ̂

۞ϜۍކĂ׎πӮa ࣃ˵ົͧྵ̂Ą

Яࠎέ៉ކ৽۞πӮ૜ޘࡗд 0.45g/cm³Ă҃Ϝۍކࡗ д 0.38g/cm³ĂЯѩĂ૜ޘd ᄃᕖ೸ܼᇴ a ̝ᙯܼт˭Ĉ

ai,j =0.50 ů ( di,j ů 0.38 ) × 5.0 + 0.3 (4)

׎̚di,jࠎކ৽˯ळᇾᕇ( i , j )̝ញჯ૜ޘĂώࡁտሀᑢ̝

Ϝۍކ৽۞di,jࣃࡗд 0.38 νΠĂέ៉ކ̝ di,jࣃົརд 0.45 ܢܕĄai,jࠎळᇾᕇ( i , j )̝ӛّͪĂॲፂሀᑢඕڍĂϜۍ ކ̝ai,jπӮࣃࠎ 0.8Ăέ៉ކࠎ 0.45 ۞ॡ࣏Ăдෛᛇ˯ົ

౵ତܕဦ 1 ̝ྏግ၁រ۞ඕڍĄ

Гֽ૟ᕖ೸ܼᇴa ᄃ৽ૺ৳ྮ Paper[xi][y_j].h ඕЪĄࠎ

˞ഴ͌ࢍზજүĂึܮ૟৽˯Տ˘ळᇾᕇᄃ a ࠹ᙯ۞ొ

̶Ă˘׀ࢍზĂхˢ৽ૺ۞ྤफ़ඕၹ̚Ĉ

Paper[xi][y_j].r = ( a_i,j × Paper[xi][y_j].h )² ×∆t / (∆x)² (5)

˯̳ࢗё(4)ă(5)Ξͽ૟৽ૺ˯Տ˘ᕇ۞ӛّͪᄃ৽۞

૜ޘă৳ྮඕЪĂГӀϡ̳ё(1)ă(2)ֽซҖᕖ೸જүĂಶ Ξͽ྿זԧࣇඕЪ৽ૺপّ۞ϫ۞˞Ą౵ޢĂдјဦล߱Ă

ဦ 4 ࢦ˧၆ͪግᕖ೸̝ᇆᜩĄ૟έ៉ކ৽ݬۡШ˭Ăϡ

ͨඊ๮˯୶ግĂᖣϤᇴҜ࠹፟ٙٮᛷז۞ͪግШ˭

ᕖ೸̝၁ᅫன෪

ࢋ૟ግ႑ពϯ΍ֽ۞ॡ࣏Ă҂ᇋဦ 1 ٙ࠻ז۞ன෪ůέ៉

ކ৽ͧϜۍކ৽۞ግҒࢋֽ଀Ϩ˘ֱĂԧࣇΐˢ˘࣎၆ͧ

ણᇴcontrastĂኬ̟έ៉ކ contrast=0.009ĂϜۍކ contrast=

0.006 ۞ࣃĂֽ྿זѩϫ۞Ą

఺࣎ፋЪ˞৽৳׶ӛّͪ۞৽ૺྤफ़ඕၹт˭Ĉ typedef struct {

double h; //ញჯՁᇴϫĂΞෛᛇ̼ј৳ྮ

float carbon; //঻ҝ۞჆௕̄ณ

float r; //Ϥӛّͪՙؠ a Гࢍზr=a²∆t/( x∆ )² } mesh_struct;

mesh_struct Paper[800][800]; //paper structure

৽ૺඕၹ̚۞ણᇴ h ϡֽхٸགྷ࿅ྍᕇ۞ញჯՁᇴ ϫĂ૟ֽෛᛇ̼۞ॡ࣏ĂΞͽឰ̂۞h ࣃ၆ߍזஎ۞ᗞҒĂ

̈h ࣃ၆ז୺۞ᗞҒĂܑன΍৽۞৳ྮĄણᇴ carbon ܑϯ

჆௕̄дѩᕇ۞ӛܢณĂѩࣃ۞̂̈׶h ѣᙯĄ 4. ࢦ˧Я৵۞҂ณ

д Kunii ۞ࣧؕኢ֭͛̚Ϗഅ҂ᇋࢦ˧၆ͪግᕖ೸̝

ᇆᜩĄԧࣇᄮࠎ൪छдү൪۞ॡ࣏Ă൪ڕ૱૱ߏ้୆۞Ă

఺၆ͪግᕖ೸ົ̙ົѣᇆᜩĉඍ९ߏۺؠ۞Ąဦ 4 ߏԧࣇ ၁ᅫઇ၁រĂ૟έ៉ކ৽ݬۡШ˭Ăϡͨඊ๮˯୶ግĂᖣ ϤᇴҜ࠹፟ٙٮᛷז۞ግ႑Ш˭ᕖ೸ன෪ĂΞͽځពг࠻

זࢦ˧၆ᕖ೸۞ᇆᜩĄግ႑۞˯͞Яࠎͨ௟үϡљੵࢦ˧

үϡĂΪѣֱ຋۞ᕖ೸൴ϠĂ҃˭͞ੵ˞ͨ௟үϡ̝γĂ ᔘΐ˯ࢦ˧۞үϡĂٙͽᕖ೸ͧྵ̂ĄϤٺͪ̂кـ˭͞

ᕖ೸Ăٙͽౄј˭͞ግ႑ᗞҒྵ୶۞ன෪Ą

дкჯޘᕖ೸̳ё㝯Ăણᇴ păq ᄃࢦ˧үϡѣᙯĂ Kunii ૟׎઄నࠎ 0Ăܑϯ΁֭Ϗ၁ү఺࣎ొ̶Ą p ΃ܑ X

͞ШĂq ΃ܑ Y ͞ШĂ༊৽ૺͪπٸཉ۞ॡ࣏Ăpăq ࠰ࠎ 0ć༊৽ૺԆБݬۡ۞ॡ࣏Ăp ٕ q ૟྿ז౵̂ࣃĄԧࣇϼ

໰ࢦ˧ΐిޘд୆ࢬ͞Ш˯̶ณ۞ࢍზ͞ڱĂֽ఍நpăq д৽ૺ้୆ॡ۞ଐڶĂ֍ဦ 5Ą

tp=p×sin(x_slope) ! 0ŷx_slopeŷ90°

tq=q×sin(y_slope) 0ŷy_slopeŷ90° (6)

(6)

Y-slope

Z X-slope

g

g×sin

ဦ 5 ৽ૺ้୆ޘθ ᄃࢦ˧ΐిޘg ̝ᙯܼ

ဦ 6 дέ៉ކ৽ă඙ې৳ྮăͪπٸཉ۞୧І̝˭Ă̙

Т፧ޘඊྫ̝ม۞Ϲ̢үϡଐԛĄΞͽ࠻ז̙ఢ݋

Ҁ̼۞ᙝቡ׶ᒅ৽۞മߖड़ڍ

x_slope ׶ y_slope ̶Ҿܑϯ৽ૺд X ͞Ш׶ Y ͞Ш˯۞้

୆ޘĄ̳ё(1)̚۞ păq ̶Ҿϡ tp, tq פ΃ĂӈΞͅᑕ৽ૺ

้୆ॡĂࢦ˧၆ᕖ೸۞ᇆᜩĄ

αăሀᑢඕڍ

ώ༼णனԧࣇ၆ٺͪግሀᑢ̝ඕڍĄԧࣇ૟̶јᕖ೸

ன෪۞ሀᑢă઼̚३ڱ۞Ъјă̈́׍ѣͪግࢲॾ۞ᇆည఍

நඈˬొ̶ֽᄲځԧࣇ۞ඕڍĄ 1. ᕖ೸ன෪۞ሀᑢ

ࢵАĂሀᑢ̙Т፧ޘ۞ግд৽˯۞Ϲ̢үϡଐԛĄဦ 6 ߏдέ៉ކ৽඙ې৳ྮăͪπٸཉ۞୧І̝˭Ăԧࣇֹ

ϡ࠹Тግณ(ink_quantity=0.040)۞፧ግ(water_rate=0.03)׶

୶ግ(water_rate=0.80)Ăдކ৽ထ˯׌ඊĄԧࣇΞͽ൴னι ࣇЧҋӔன˞̙Т඀ޘ۞ᕖ೸׶̙ఢ݋Ҁ̼۞ᙝቡĄ፧ግ

̶ͪ౵͌Ăೀͼ̙ົᕖ೸ć୶ግ̶ͪ౵кĂᕖ೸౵ᆖचĄ ࢦࢋߏĂд፧ግ׶୶ግ۞Ϲ˽఍ົ΍னമߖ۞ଐԛĂயϠ ᙷҬᒅ৽۞ड़ڍĞ఺ߏͪግ൪˯౵૱֍۞ԫμğĄ఺ֱࢦࢋ

ဦ 7 д඙ې৳ăግณ 0.10ăግҒ 0.40 ୧І̝˭Ă̙Т

۞ކ৽۞ᕖ೸ड़ڍĄνဦߏӛّͪૻ۞ϜۍކĂΠ ဦߏέ៉ކĄϜۍކӔன΍ྵ̂۞ᕖ೸ّ׶ྵโ۞

ግᙶܑன(ኛણ໰ဦ 1 ۞ྏግඕڍ)

ဦ 8 ৽ૺݬۡٺгࢬĂ፧ă̚ă୶ˬ჌̙Т፧ޘግϗᕖ

೸۞ሀᑢඕڍĄΞͽ࠻΍୶ግӣͪྵкĂצࢦ˧ᇆ ᜩྵ̂Ă҃ͷ˭͞ግҒྵ୶

۞႑ግன෪Ăд׎΁ր௚ΞਕυืপҾ఍நĂҭߏԧࣇ۞

͞ڱଂጯந΍൴Ă̙υ߇ઇĂܮਕயϠ෭ܕৌ၁ன෪۞ඕ ڍĄ

ဦ 7 णϯ̙Тކ৽۞ሀᑢड़ڍĄԧࣇϫ݈၁ү˞׌჌

̙Т۞ކ৽ůέ៉ކ৽(Tainwan xuan paper)׶Ϝۍކ৽

(jade-white xuan paper)Ă఺׌჌ކ৽۞γ៍՟ѣ̦ᆃ̙

ТĂӛّͪݒѣमளĄඕڍពϯд඙ې৳ྮăግณ 0.10ă ግҒ 0.40 ୧І̝˭ĂϜۍކ৽ͧέ៉ކ৽ѣྵ̂۞ᕖ೸ّ

׶ྵโ۞ግᙶܑன(Ξͽ׶ဦ 1 ۞၁ᅫྏግඕڍ࠹̢၆

໰)ĄΞ֍଀ੵ˞৽৳̝γĂӛّͪՀߏ၁ү৽ૺॡĂ̙Ξ

৿͌۞ࢦࢋপّĄ

ੵ˞Հр۞৽ૺඕၹ̝γĂਕҋજຏᑕࢦ˧۞ត̼Ă

˵ߏώࡁտ۞˘̂পҒĄဦ 8 ߏԧࣇሀᑢ৽ૺԆБШ˭ݬ

ۡгࢬॡĂࢦ˧၆Тᇹግณ 0.050 ۞፧(ግҒ 0.01)ă̚(ግ Ғ 0.40)ă୶(ግҒ 0.58)ˬ჌̙Т፧ޘግϗᕖ೸۞ᇆᜩଐ ԛĄԧࣇΞͽ࠻΍৽ૺ้୆ޘ၆୶ግ۞ᇆᜩ̂ٺ၆፧ግĂ

఺ߏЯࠎ୶ግ̚۞ͪณྵк۞ቡ߇Ą

ԧࣇ۞ր௚၆ٺЇຍX ׶ Y ͞Ш۞้୆ౌਕҋજͅᑕ дᕖ೸જү˯ĄॲፂགྷរĂ૟p ׶ q ۞ࣃనؠј_τ¹۞˘Η

۞ॡ࣏ĂΞͽ଀΍ତܕৌ၁ግ႑(ဦ 4)۞ඕڍĄ

(7)

2. ઼̚३ڱ۞Ъј

ຐࢋ˘ඊ˘ထгሀᑢ३ڱྻඊᆷф۞࿅඀Ăԧࣇᅮࢋ

А଀זඊထ(stroke)۞ྤੈĂ൒ޢдඊထ˯யϠግᕇĂĶᆷķ д৽˯ĂГඕЪԧࣇ۞ᕖ೸ሀ௡ĂӈΞЪјໂࠎৌ၁۞३ ڱфĄ

(˘) ϡፚ๪ֽᕜפඊထ

ͨඊྻඊᆷфٕү൪۞ॡ࣏ĂົЯࠎግϗ፧୶̙Тă ግณкဿ̙˘ăࠤҌྻඊిޘԣၙă৽ૺӛግّ̂̈

ඈЯ৵үϡĂౄјՏ˘ඊထѣ̙Т۞ግᙶត̼Ąຐ଀

ז఺჌ͪግ۞ड़ڍĂΪѣያΝሀᑢ఺˘ඊ˘ထ۞જ үĂд˘ඊ˘ထ̝มኬ̟̙Т۞ግҒăግณĂГඕЪ

˘ૺѣপّ۞৽׶ᕖ೸үϡĂಶΞͽሀᑢᆷфٕү൪

۞࿅඀˞ĄҭߏĂࢋтңሀᑢ˘ඊထ׸ĉWong ׶ IP[12]

ᄮࠎͨඊ׶৽ૺ࠹Ϲ۞̷ࢬΞͽϡ˘࣎ፚ๪ֽܑϯĂ Տ˘ඊထ(stroke)Ξͽϡ఺ֱ̙Т̂̈ă͞Ш۞ፚ๪ඊ

ྫ(footprint)ֽ௡ЪĄ఺ֱፚ๪่̙Ξͽ௡јඊထ۞γ ԛĂፚ๪۞யϠึԔಶߏඊึĂԧࣇΞͽдՏ˘ඊထ

۞ฟؕග̟ግҒግณඈણᇴĂඊထ۞পّಶΞͽన ؠĄયᗟߏĈтңᕜפඊထ׸ĉԧࣇ۞͞ڱߏ(ણ֍ဦ 9)Ĉ

(1) ૟ࢋᓜᇟ۞фᏮ΍ј BMP ᑫĄ

(2) ϡ໣ဂдඊထ˯ொજĂ΄ொજ͞Ш׶ x ค̝ӵ֎

ࠎɞĂ݋дொજ͞Шထ˘ݬۡቢĂᄃඊထᙝ̝ࠧ

Ϲᕇ̶Ҿࠎ(x1,y1)ᄃ(x2,y2)Ą

(3) ፚ๪๪͕ळᇾ )

2 2 , 1 2

2 ( 1 ) ,

( x x y y ye

xe = + + Ą

(4) ፚ๪̝ܜश

2

) 1 2 ( ) 1 2

(x x ² y y ²

ea − + −

= Ăൺश

eb=ொજ෼ᗓ

(5) ૟ xeăyeăɞăeaăeb ᆷˢඊྫᑫĄ (6) ࢦኑՎូ 2 ҌՎូ 5 ۡזඊထᕜפԆјĄ (˟) дፚ๪˯פᇹώ

ѣ˞ፚ๪۞ඊྫĂ੨Ъפᇹώ۞͞ڱĂΞͽ଀זፚ๪

˯Տ˘ᕇ۞ҜཉĂ఺ֱᕇ۞ҜཉΞͽ΃ܑግႍ۞Ҝ ཉĂЯࠎඊͨߏତܕӮ̹гཆдඊ୛˯Ăٙͽᇹώ۞

פڱᑕྍͽӮ̶̹Ҷࠎࣧ݋Ą઄నፚ๪۞ܜशࠎ aĂ ൺशࠎbĂ݋ፚ๪˯Ӯ̶̹Ҷ۞ᇹώ(uniformed sample) פڱΞͽ౅࿅т˭ࢍზ଀זĄ

∫ ∫

∫ ∫ = = +

=^{θ θ} ^θ ^θ ^θ θ

θ θ θ

θ θ

0 0 2 2 2 2

2 2 2

0 0 sin cos

1 2

) 2

( d

b a

b d a rdrd r

A ^r

∫ ₊ ₊

= ^θ θ

θ

0 2 2 2 2

2 2

cos ) (

1

2 d

a b a b a

t dt t d

Let ₂

1 tan 1

= +

⇒

= θ θ

Y

Y (x2,y2)

(x1,y1) (xe,ye)

ea

eb

Mouse move

Mouse move ဦ 9 ϡፚ๪ᕜפඊထ۞͞ڱĄ׎̚ĂMouse move ΃ܑ

໣ဂொજ۞͞Ш y

x ( cos sin )

∫ +

=

∫ × +

− + +

=

⇒

) tan(

0 2 2 2

2 2

) tan(

0 2

2 2 2 2 2

2

1 2

1 1

1 ) 1 (

1 ) 2

(

θ

θ θ

t dt a b b

a

t dt a t

b a b

A a

bdt d a b

Lettanα=at⇒1+tan²α α=

×

=

⇒ ( ) 2

2 2b Aθ a

α α α

θ d

a b a a b b

b a

) tan 1 ( tan )

(

1 ₂

)) tan(

( tan

0 2 2 2

1 × +

∫ + ×

−

) tan ( 2 tan

1 θ

b a ab ₋

=

) tan ( 2tan 4

) tan ( 2 tan )

( ¹ ₁

1 j

j j

b a abb

a ab A

Let A θ

π π θ θ

ε ⁻

−

=

2 )) tan(

(

tan ¹ πε₁

θ a

b

j = −

⇒

j j

j a b

b r a

r

And _j

θ θ

ε ε

θ ₂ ₂ ₂² ₂

2 2

2 = sin + cos

=

] 1 , 0 [ ,

cos sin

2 )) tan(

( tan

2 1

2 2 2 2

1 1

u

b a

b r a

r

a b

j j

j

ε ε θ θ

ε ε

πε θ

 θ













= +

=

⇒

−

(7)

(8)

ဦ 10 ፚ๪Ӯ̹פᇹ۞ඕڍ

˯ࢬ̳ёдᑕϡ۞ॡ࣏ĂࢵАд 0~1 ̝มயϠ˘࣎ใ ᇴࣃ΄׎ࠎε₁Ăགྷ࿅ࢍზΞͽՐ଀˘࣎θࣃĄТᇹ۞Ă д 0~1 ̝มயϠௐ˟࣎ใᇴࣃ΄׎ࠎε₂Ăགྷ࿅aăb

׶θ۞ࢍზĂΞͽ଀ז˘࣎r ࣃĂѣ˞θ׶rĂፚ๪˯

۞˘࣎ᇹώಶΞͽՐזߏ(rsinθ,rcosθ)ĂຐՐк͌࣎

ᇹώĂಶࢦኑ˯ࢗࢍზк͌ѨĄ

Ϥٺԧࣇ۞͞ڱ่ዋϡдα̶̝˘࣎ፚ๪˯Ăтڍࢋ

д˘࣎Ԇፋ۞ፚ๪˯פᇹώĂ݋υื૟ᇹώᓁᇴϫπ Ӯ̶੨זα࣎α̶̝˘۞ፚ๪ĂГӀϡ˯ࢗ͞ڱՐ΍

ᇹώĄဦ 10 ߏдፚ๪˯πӮפᇹ۞ඕڍĄ (ˬ) ૟ፚ๪ඊྫᖼೱјግྫ

༊ԧࣇࢋдކ৽˯ሀᑢ३ڱٕᘱ൪۞ॡ࣏ĂΞͽА૟

ކ৽Ķઇķ΍ֽĂ൒ޢϡ໣ဂд৽˯ᕇ΍˭ඊ۞Ҝཉ (xm,ym)ĂಶΞͽֶԔԯඊྫᑫ̰۞ፚ๪˘˘Ķᆷķז

৽˯Ąࣧඊྫᑫ̰ௐi ࣎ፚ๪̝ፚ๪͕ࠎ(xe_i,ye_i)Ă୊

ᖼ֎ޘɞ_iĂܜൺश̶Ҿࠎ eaiăebiĂٸזކ৽˯۞າ

๪͕ࠎ(xe’,ye’)Ă݋ळᇾᖼೱт˭Ĉ













− + −











=













m m i

i

y ye

x xe ye xe ye xe

1 1

' '

(8)

д৽˯Ăͽ఺࣎(xe’,ye’)ࠎፚ๪๪͕Ăܜशࠎ eaiĂൺ शࠎ eb_i۞ፚ๪˯Ӯ̹פᇹĂͽՙؠͨඊඊͨĞϺӈ ግႍğ۞ҜཉĂດତܕ๪͕۞Ҝཉග̟ྵк۞ግณĂ ግณ੃ᐂдੱЕ brush_ink[x_i][y_j]̚ĂГ૟ѩፚ๪୊ᖼ

֎ޘɞ_iĄ၁ᅫोͨඊᆷфĂ఼૱ౌߏАڭግĂ൒ޢ̖

˘ඊ˘ထгᆷĂٙͽĂԧࣇ۞ግณдĶᆷķՏ˘ඊထ

۞ௐ˘࣎ፚ๪ඊྫ݈ಶග̟ߙ˘ؠࣃĂ׎ޢᐌ඾ඊה Ķᆷķд৽˯Ăд৽˯۞Ї˘ᕇĂഴ͌۞ግณϤ৽˯

ྍᕇ۞ӛّͪՙؠĂ̙ߏ˘࣎૱ᇴࣃĄ

পҾࢋ೩΍ᄲځ۞ߏĂፋ࣎Ķᆷфķ۞࿅඀ߏͽજ൪ дሀᑢĂՏ˘ထ˭Ν۞ॡ࣏Ăր௚ҋજॲፂግณăግ Ғ׶৽ૺপّࢍზͪ׶჆۞ᕖ೸ࣃĂ֭ͷϲӈдᏈ၌

˯ពϯјဦඕڍĄဦ 11 ߏԧࣇሀᑢдӛّͪྵ̂۞Ϝ ۍކ৽˯Ă̶Ҿͽ͌ณ۞፧ግ(ግณ 0.025 ግҒ 0.030)

׶кณ۞̚ግ(ግณ 0.050 ግҒ 0.400)ᆷ΍Ķϖķф۞

ඕڍĂΞͽ୻຾г࠻זግณ͌۞ॡ࣏̖ѣ۞Ķ઀הķ ड़ڍ(non-inking effect)Ăͽ̈́ͪк۞ॡ࣏Шγᕖ೸ٙ

ౄј۞ĶҀ̼ķड़ڍ(effects of fibers)Ą

ဦ 11 ̙ТግҒăግณ̝˭۞३ڱሀᑢඕڍĄ˯ဦግณ͌

ٙౄј۞Ķ઀הķड़ڍć˭ဦࠎͪณкٙౄј۞ᙝ ቡ̙ఢ݋ĶҀ̼ķड़ڍ

3. ׍ѣͪግࢲॾ۞ᇆည఍ந

ԧࣇ۞ր௚׍ѣ೼ّ࿆ĂΪࢋѣဦ৵۞ྤੈĂಶΞͽ ซҖͪግ఍நĂΞͽۡତ၆ᇆညઇ఍நĂ˵ޝटٽᄃ׎΁

ˬჯƝ˟ჯјဦր௚ඕЪĄΪࢋ఺ֱјဦր௚૟׎˟ჯ۞

јဦඕڍĂ˵ಶߏᏮ΍זᏈЍ၌˯۞ဦ৵ྤफ़Ăਖ਼ගᕖ೸

ሀ௡༊ᏮˢĂТॡ੨Ъග̟৽ૺăᕖ೸඀ޘඈણᇴనؠĂ

˘ૺ׍ѣͪግമߖࢲॾ۞ᇆညಶயϠ˞ĄтңซҖ׸ĉࢵ

АĂግϗ۞፧୶׶ᇆညྤफ़ѣᙯĂԧࣇࢋ૟ဦ৵ᗞҒ RGB

ྤफ़ᖼೱјโϨ۞ lumaĂд NTSC ពϯր௚㝯ĂΞͽ౅࿅

˭ࢬ̳ёᖼೱĈ

[

⁰^.²⁹⁹ ⁰^.⁵⁸⁷ ⁰^.¹¹⁴

]

^, ⁰≤ ≤¹













= ⋅ luma

B G R luma

ତ඾Ăॲፂ luma ࣃĂԱ΍׎࠹၆ᑕ̝ͪ wateră჆ carbon

۞ࣃ༊үᕖ೸ࢍზ۞ܐࣃĂր௚ಶਕฟؕซҖᕖ೸જү˞Ą

20 _ rate water water luma×

= (9)

water_rate ܑϯ౵̂ӣͪณĂ׎ࣃϤ 0 ז 0.80Ăߏϡ

ֽՙؠമߖ඀ޘ۞ણᇴĂΞͽϤֹϡ۰ֽአፋĄԧࣇឰ water ۞ࣃд 0 ז 0.04 ̝มĄ

(9)

ဦ 12 ̙Т water_rate ࣃĂயϠ̙Т۞ͪግड़ڍĄϤ˯҃

˭ֶԔߏࣧؕ۞ણ҂ᇆညăwater_rate ̶Ҿඈٺ 0ă 0.4 ă 0.8 ඈ ୧ І ˭ Ă ٙ ய Ϡ ۞ ͪ ግ ఍ ந ड़ ڍ Ą water_rate ࣃດ̂Ă୶Ғొ̶ٙ଀ז۞മߖड़ڍດ̂

50 )

].

][

[ max

06 _ . 1 (

) (

h luma j i Paper d

contrast water

carbon

− −

−

× +

=

(10)

contrast ߏ ݈ ࢬ ೩ ࿅ ۞ ৽ ૺ ۞ ၆ ͧ ણ ᇴ ( Ϝ ۍ ކ 0.006ăέ៉ކ 0.009)ĂPaper[i][j].h ߏ৽˯(i , j)ळᇾ˯ྍᕇ

̝ញჯՁᇴϫĂd_max ߏ৽ૺ۞౵̂ញჯՁᇴϫĂώր௚

࿰నࣃࠎ 4Ą̳ё(10)Ξͽֹᇆည۞ࢦࢋ዇၏ొ̶ĂӈᗞҒ

౵โ(luma=0)Ăϡ౵፧۞ግҒܑϯĂ˵ಶߏѩ఍۞ͪณ water=0ć҃౵Ϩ۞ొ̶Ğluma=1ğĂࢋϡ౵୶۞ግҒĂ water_rate ົՙؠѩ఍۞ͪณ water ࣃĄଂဦ 12 Ξͽ࠻΍Ă water_rate ࣃດ̂Ă୶Ғొ̶ٙ଀ז۞മߖड़ڍດ̂Ă water_rate ඈٺ౵̂ࣃ 0.80 ॡĂโҒొ̶ֶᖞ̙͉മߖĄ ဦ 13 ߏԧࣇ૟ࣧؕ۞โϨ઼൪ᇆညᑫ[21]Ăдέ៉ކ

৽ă඙ې৳ăwater_rate=0.40 ۞୧І˭Ă఍நјമߖड़ڍ Հૻধ۞ͪግ൪үĄ૾Ғᇆည׶ˬჯሀ௡јဦ(3D model render)˵Ξͽ఍நјᙷҬ۞ͪግࢲॾĄ

̣ăඕኢ̈́Ϗֽ̍ү

ώ͛ࡁտͽҋ൒ڱ݋ࠎૄᖂ۞ͪግᕖ೸Ąԧࣇ̶ژ Kunii ۞Ķкჯޘᕖ೸ሀݭķ̝৿εĂ֭׍វ೩΍Լซ۞α

࣎͞ڱĄԧࣇ҂ᇋ৽ૺᄃࢦ˧Я৵Ă˵ଯጱ΍ѩሀݭдᇴ ࣃՐྋ࿅඀̚۞ࢦࢋᙝࠧ୧ІĂЯ҃଀ͽሀᑢ΍Հৌ၁۞

ͪግᕖ೸ன෪Ą౵ޢĂԧࣇͽͪግᕖ೸д઼̚३ڱᄃ׍ѣ

ͪግࢲॾ۞ᇆည఍ந׌ีᑕϡ၁ּĂणன˞ٙ೩͞ڱ۞࿀

ৌሀᑢඕڍᄃ၁ϡᆊࣃĄ

ώࡁտѣαี׍វ̝੒ᚥĄ1. ጱˢ৽ૺЯ৵Ăֹͪግ ᕖ೸ሀᑢՀ̷Ъ၁ᅫć2.҂ᇋࢦ˧ᇆᜩĂֹሀᑢՀඡ၁ă Ԇፋć3.ଯጱ Kunii ሀݭԆፋϒቁ۞ᇴࣃՐྋ͞ڱĂܲᙋ˞

ᇴࣃՐྋ۞ќᑦّᄃϒቁّć4.೩΍˞ͪግᕖ೸д઼̚३ ڱᄃ׍ѣͪግࢲॾᇆည఍ந׌ีᑕϡ၁ּĂणϯ˞࿀ৌ۞

ሀᑢඕڍ֭ᕖ̂ሀᑢ۞ᑕϡቑᘞĄԧࣇͽநኢࠎॲፂĂଂ

ဦ 13 ˯ဦࠎࣧؕᇆည[21]Ą˭ဦߏдέ៉ކ৽ă඙ې৳ă water rate=0.40 ۞୧І˭۞ͪግ఍நඕڍĄѩॡ୶ Ғొ̶۞ڑཧͪግᕖ೸ड़ڍځពĂপҾߏဦ˯͞۞

ѻཧ΍ன˞ࣧဦٙ՟ѣ۞ግᙶड़ڍ

ҋ൒ڱ݋ࠎֶᕩֽሀᑢͪግᕖ೸ன෪ߏ˘࣎Ъநăѣड़ă

׹ؼ۞͞ڱĄᓁඕώ͛Ăԧࣇٙ೩۞͞ڱԼซ Kunii ͞ڱ

̝৿εĂ೩̿кჯޘͪግᕖ೸ሀݭ۞׹ؼᄃԆፋّĄឰͪ

ግᕖ೸่̙Ъͼҋ൒ڱ݋Ăඕڍ࿀ৌĂ˵ՀࠎԆ౯ΞҖĄ ϏֽĂԧࣇ૟၆ͪግᕖ೸۞ณઇซ˘Վ۞̶ژĂԓ୕

ਕ૟ሀᑢड़ڍઇ଀Հჟ໤ă௟ቜĄ

௑ཱི৶͔

a ᕖ೸ܼᇴ

di,j ކ৽˯ळᇾᕇ(i,j)̝ញჯ૜ޘ g ࢦ˧

g(x,y) ͪд৽˯ळᇾ(x,y)ܑ̝ࢬ૜ޘ(ܑࢬ፧ޘ) f(x,y) ჆д৽˯ळᇾ(x,y)ܑ̝ࢬ૜ޘ(ܑࢬ፧ޘ)

τ

1 ઀ᒌܼᇴ

pĂq XĂY ͞Ш۞ࢦ˧̶ณ )

(^g_f

Z ჆۞ᕖ೸בᇴ θ ୊ᖼ֎ޘ

(10)

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2002 ѐ 10 ͡ 21 ͟! ќቇ 2003 ѐ 02 ͡ 11 ͟! ܐᆶ 2003 ѐ 08 ͡ 14 ͟! ኑᆶ 2003 ѐ 08 ͡ 26 ͟! ତצ