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クリエイティブコーディングのための数学+JavaScript入門 三角関数と行列

F7e037740c16b5f67925bf11c080ed85?s=47 feb19
January 07, 2016
Programming
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クリエイティブコーディングのための数学+JavaScript入門 三角関数と行列

F7e037740c16b5f67925bf11c080ed85?s=128

feb19

January 07, 2016
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Transcript

  1. ΫϦΤΠςΟϒ ίʔσΟϯάͷͨΊͷ ਺ֶʴ+BWB4DSJQUೖ໳ ࡾ֯ؔ਺ͱߦྻ ৽य़εϖγϟϧ ͔ͨ͸͠ͷͿͻΖ ୈҰճΫϦΤΠςΟϒίʔσΟϯάษڧձʮϕΫτϧʯ੒Ռ෺ ୈೋճΫϦΤΠςΟϒίʔσΟϯάษڧձʮྗʯ੒Ռ෺ άϧʔϓలʮ3FqFDUJPOʯग़ల࡞඼ԋग़ άϧʔϓలʮVOGSBNFʯग़ల࡞඼ʰ3FOEBOʱ

  2. ΫϦΤΠςΟϒίʔσΟϯάͰ਺ֶʁ w ύʔςΟΫϧΛࣗ༝ʹඈ͹͍ͨ͠
 ˠ଎౓ͷܭࢉɺϕΫτϧɺҠಈྔܭࢉ w ৭Λࣗ༝ʹมԽ͍ͤͨ͞
 ˠपظ֯౓ͷܭࢉɺೱ୶ͷ࿈ଓతมԽ w େྔͷΦϒδΣΫτʹμϯεͯ͠΋Β͍͍ͨ
 ˠ੍࣌ؒޚʢλΠϜϥϓεʣɺߴ౓ͳมܗܭࢉ

    w δΣωϨΠςΟϒΞʔτΛ࡞Γ͍ͨ
 ˠ਺ֶΞϧΰϦζϜͷཧղ

  3. ໨ඪ ᶃ ࡾ֯ؔ਺ͱߦྻͰදݱʹ׆༻Ͱ͖Δ෦෼Λ஌Δ w શ෦͸஌ΒΜͰ΋Կͱ͔ͳΔΘΑ ᶄ ਺ֶࣜˠ+BWB4DSJQU΁Ҡ২Ͱ͖ΔΑ͏ʹͳΔ w ը૾ɺԻ੠ॲཧͷXJLJQFEJB΍࿦จ͕׆༻Ͱ͖ ΔΑ͏ʹͳΓ·ͧ͢

    Ұ෦ҙ༁͕͋Γ·͢ਖ਼֬ੑ͸ଞͷจݙΛࢀߟʹͯ͠Ͷ

  4. ΞδΣϯμ ᶃ ؔ਺ͱ͸ N  ᶄ ࡾ֯ؔ਺ͱ͸ N  ᶅ

    ࡾ֯ؔ਺Λ࢖ͬͨίʔσΟϯάମݧ N  ᶆ ߦྻͱ͸ N  ᶇ ߦྻΛ࣮૷͢ΔίʔσΟϯάମݧ N  ᶈ ࣗ༝ʹίʔσΟϯά N  ᶉ ൃද N

  5. ʮؔ਺ʯͱ͸ w ॲཧͷ·ͱΊ w ύϥϝʔλʢҾ਺ʣΛ౉ͯ͠ɺ
 ฦΓ஋Λฦͯ͘͠ΕΔʢ͜ͱ΋͋Δʣ

  6. ʮؔ਺ʯͱ͸ w ॲཧͷ·ͱΊ w ύϥϝʔλʢҾ਺ʣΛ౉ͯ͠ɺ
 ฦΓ஋Λฦͯ͘͠ΕΔʢ͜ͱ΋͋Δʣ ਺ֶ΋ಉ༷ʂ

  7. ࡾ֯ؔ਺ʢ਺ֶ*ʣ

  8. ʮࡾ֯ؔ਺ʯͱ͸ ᶃ ֯౓ΛҾ਺ʹ౉͢ͱɺ͔Βͷ஋Λฦؔ͢਺ ᶄ ฦͯ͘͠ΕΔ஋͸ϥϯμϜͰ͸ͳ͘
 ֯౓ͱؔ܎ੑ͕͋Δ

  9. ʮࡾ֯ؔ਺ʯͱ͸ ᶃ ֯౓ΛҾ਺ʹ౉͢ͱɺ͔Βͷ஋Λฦؔ͢਺ ᶄ ฦͯ͘͠ΕΔ஋͸ϥϯμϜͰ͸ͳ͘
 ֯౓ͱؔ܎ੑ͕͋Δ දݱͰ࢖͏ͷ͸ओʹαΠϯ TJO ͱίαΠϯ DPT

     ͦΕͱύΠˠК<ʜ>͸›Ͱ͋Δͱ͍͏ࣄ

  10. αΠϯTJO Ҿ਺͕͍͘Β૿͑ͯ΋ʙͷ஋Λ॥؀͢Δ w .BUITJO  ˠ w .BUITJO К➗ <ʜ>ˠ

    w .BUITJO К <ʜ>ˠ w .BUITJO К К➗ <ʜ>ˠ w .BUITJO К <>ˠ

  11. αΠϯDPT Ҿ਺͕͍͘Β૿͑ͯ΋ʙͷ஋Λ॥؀͢Δ
 К➗౓෼͚ͩฦΓ஋͕Φϑηοτ͞Ε͍ͯΔ w .BUIDPT  ˠ w .BUIDPT К➗

    <ʜ>ˠ w .BUIDPT К <ʜ>ˠ w .BUIDPT К К➗ <ʜ>ˠ w .BUIDPT К <>ˠ

  12. TJOͱDPT ੨ɿTJOɹ੺ɿDPT IUUQHPPHMC.E(KM

  13. ՝୊ᶃɹTJODPTΛ࢖ͬͯԿ͔࡞Δ ੍໿ w .BUITJO .BUIDPT Λ࢖͏ ྫ w ޫ͕໌໓͢ΔΞχϝʔγϣϯ w

    IUUQHPPHMRY3[) w TJODPTΛ࢖ͬͯඳ͔ΕΔਤ w .BUI1*࢖ͬͯ΋͍͍͔΋ alpha = sin(count) x = cos(count)×10 y = sin(count)×10 ⎧ ⎨ ⎪ ⎩ ⎪

  14. ͓·͚ɿΞʔΫλϯδΣϯτBUBO ΞʔΫʙ͸஋͔Β֯౓ΛٻΊΔٯؔ਺ w .BUIBUBO Z Y ˠК ›

  15. ऄ଍ɿ.BUIBUBOͱ.BUIBUBO UBO͸›୯ҐͰ஋͕॥؀͢Δ
 BUBO΋›୯ҐͰ஋Λฦ͢
 BUBO͸›͕Θ͔ΔΑ͏ɺΑ͠ͳʹ΍ͬͯ͘ΕΔ w .BUIUBO › ˠ w .BUIUBO

    › ˠ

  16. ߦྻʢ਺ֶ$ʣ

  17. ʮߦྻʯͱ͸ w ෳ਺ͷ਺ΛߦͱྻͰอ࣋͢Δ਺ྻ 3 5 ( ) 1 0 0

    1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ a 11 … a 1n ! " ! a m1 # a mn ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟

  18. ʮߦྻʯͱ͸ w ෳ਺ͷ਺ΛߦͱྻͰอ࣋͢Δ਺ྻ w දݱͰ͸ߦྻಉ࢜ͷܭࢉ·Ͱཧղ͕͋Δͱ͍͍ײ͡ 3 5 ( ) 1

    0 0 1 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ a 11 … a 1n ! " ! a m1 # a mn ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟

  19. ߦྻͷܭࢉɿ߹ମʢDPODBUʣ M = 1 2 3 4 ⎛ ⎝ ⎜

    ⎞ ⎠ ⎟ 5 6 7 8 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

  20. ߦྻͷܭࢉɿ߹ମʢDPODBUʣ M = 1 2 3 4 ⎛ ⎝ ⎜

    ⎞ ⎠ ⎟ 5 6 7 8 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 1×5+2×7 1×6+2×8 3×5+4×7 3×6+4×8 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ҰͭΊͷߦྻ͸ԣʹɺೋͭΊͷߦྻ͸ॎʹ஋Λर͏ ύζϧΈ͍ͨͳײͩ͡Α

  21. ߦྻͷܭࢉɿ߹ମʢDPODBUʣ M = 1 2 3 4 ⎛ ⎝ ⎜

    ⎞ ⎠ ⎟ 5 6 7 8 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 1×5+2×7 1×6+2×8 3×5+4×7 3×6+4×8 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 19 22 43 50 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ҰͭΊͷߦྻ͸ԣʹɺೋͭΊͷߦྻ͸ॎʹ஋Λर͏ ܭࢉ্ग़ͯ͘Δߦྻ࠷খͷେ͖͞ʹͳΔ ύζϧΈ͍ͨͳײͩ͡Α

  22. ߦྻͷܭࢉɿ߹ମʢDPODBUʣΛ൚Խ = A× E + B ×G A× F +

    B × H C × E + D×G C × F + D× H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ M = A B C D ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ E F G H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

  23. ߦྻͷܭࢉɿ߹ମʢDPODBUʣΛ൚Խ ࿈ཱํఔࣜʹͯ͠ΈΔ = A× E + B ×G A× F

    + B × H C × E + D×G C × F + D× H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ M = A B C D ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ E F G H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ → a = A× E + B ×G b = A× F + B × H c = C × E + D×G d = C × F + D× H ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

  24. ߦྻͷܭࢉɿ߹ମʢDPODBUʣΛ࣮૷ → a = A× E + B ×G b

    = A× F + B × H c = C × E + D×G d = C × F + D× H ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ function concatMatrix(A, B, C, D, E, F, G, H) {
 ...
 return [a, b, c, d]
 } IUUQHPPHMF:NX&

  25. ʮߦྻʯԿʹ࢖͏Μ ೋ࣍ݩ࠲ඪ 9 : ΍ࡾ࣍ݩ࠲ඪ 9 : ; ͷΑ͏ʹෳ਺ ͷ஋͔Β੒ΔσʔλΛૢ࡞͢Δ৔߹༗ޮ

    ྫɿʮ࠲ඪʯʹʮม׵ߦྻʯΛՃ͑Δͱ
 ɹɹʮมܗʯ͕ߦ͑ΔʢҰ࣍ม׵ɺΞϑΟϯม׵ʣ w ʮճసͷͨΊͷߦྻʯ SPUBUF  w ʮҠಈͷͨΊͷߦྻʯ USBOTMBUF  w ʮ֦େͷͨΊͷߦྻʯ TDBMF  w ʮ܏ࣼͷͨΊͷߦྻʯ TLFX

  26. ՝୊ᶄɹճసߦྻΛ࣮૷͢Δ ໰୊ɿ࠲ඪ   Λݪ఺Λத৺ʹ౓ʢКʣճ సͤͨ͞࠲ඪΛϓϩάϥϜͰٻΊΑɻ ճసߦྻ Ұ౓࿈ཱํఔࣜʹ͢ΔͱϓϩάϥϜԽ͠΍͍͢Αʂ cosθ −sinθ

    sinθ cosθ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ′ P = cosθ −sinθ sinθ cosθ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 5 10 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

  27. ՝୊ᶄɹճసߦྻΛ࣮૷͢Δ ໰୊ɿ࠲ඪ   Λݪ఺Λத৺ʹ౓ʢКʣճ సͤͨ͞࠲ඪΛϓϩάϥϜͰٻΊΑɻ ճసߦྻ cosθ −sinθ sinθ

    cosθ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ′ P = cosθ −sinθ sinθ cosθ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 5 10 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = cosθ ×5−sinθ ×10 sinθ ×5+cosθ ×10 IUUQHPPHMLO3R

  28. ՝୊ᶄ`ɹճసߦྻͰΞχϝʔγϣϯ Ͳͷ࠲ඪɾ֯౓Ͱ΋ٻΊΒΕΔΑ͏ʹɺ՝୊ᶄͷΞϧ ΰϦζϜΛؔ਺Խ͠ɺ֯౓Λ૿΍͍ͯ͘͠ͱճస͢Δ Α͏ͳΞχϝʔγϣϯΛ࡞੒͍ͯͩ͘͠͞ɻ IUUQHPPHM;9;Y/L

  29. ·ͱΊ ਺ֶ͕ࣜಡΊΔΑ͏ʹͳΕ͹͍ΖΜͳ࿦จ͕δΣωϨ ΠςΟϒදݱͰ׆༻Ͱ͖ΔΑ͏ʹͳͬͯ௙ΔΑʂ ਺ֶָ͍͠Αʂ

  30. ͓͚ͮ͘ w TJOͱDPTͷղઆͰ͔ͭͬͨΞχϝʔγϣϯ
 IUUQHPPHMC.E(KM w ՝୊ᶄճసߦྻΛ͔ͭͬͨΞχϝʔγϣϯ
 IUUQHPPHM;9;Y/L w ࢀߟɿ೥લʹॻ͍ͨϒϩά
 IUUQDSFBUPSEFOBKQBSDIJWFTIUNM

    w ਺ࣜΤσΟλʔɿ.BUI5ZQF
 IUUQXXXEFTTDJDPNFOQSPEVDUTNBUIUZQF USJBMBTQ