ARKitのための3D算数
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KBOY
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ARKitͷͨΊͷ 3Dࢉ KBOY@ےΤϯδχΞ 2018.8.30@iOSDC 2018
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ࣗݾհ ૣҴా͕ߍͰ͢
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ےΤϯδχΞͷܦྺ
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݄ ݄ ݄ ݄ ݄ Spajam༏ल ϕετϘσΟδϟύϯग़ ے.swift։࠵ స৬υϥϑτग़ԋ ॱ෩ຬൕʂʁ
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͔ͦ͠͠͏͘ͳ͍
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ےΤϯδχΞͷ಄
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ےΤϯδχΞ ઓࠃ࣌
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ͦ͏ͩʂARͩʂ
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݄ ݄ ݄ ݄ ݄ Spajam༏ल ϕετϘσΟδϟύϯग़ స৬υϥϑτग़ԋ ے.swift։࠵
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Δ͔͠ͳ͍ ͜ͷϏοάΣʔϒʹ
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ͱ͍͏͜ͱͰ
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ࠓ1݄ʹ ARελʔτΞοϓJOIN
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Graffity Inc. Ϧʔμʔ
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͜ΜͳΞϓϦ࡞ͬͯ·͢
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ͱ͍͏͜ͱͰARKitΛ ؤுͬͯษڧ͠·ͨ͠
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͔͠͠ ͦ͏͘ͳ͍
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͜͏͍͏ྫΛ ߟ͑ͯΈ·͠ΐ͏
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εΫϦʔϯ্ͷλοϓͨ͠෦ͷ 30cmલʹ ඈߦػΛஔ͘
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༨༟ͬ͠ΐʂ
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λοϓδΣενϟʔ͔Β x, yΛऔಘ, z0.3mΛೖΕΕʂ
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݁Ռ
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શવग़ͯ͜ͳ͍…
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ཧ
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ݱ࣮
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ͬͺΓ ͦ͏͘ͳ͍
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ͦΜͳ࣌ɺϦʔμʔ͕ खΛࠩ͠৳ͯ͘Εͨ
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3DϓϩάϥϛϯάΛ ษڧ͢Ε༨༟ͩΑ
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Ϧʔμʔʂʂ
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ͦͯ͠
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3Dϓϩάϥϛϯά Λษڧͨ͠ɻ
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ษڧʹͬͨຊ IUUQTBN[OUP.4V.F( IUUQTBN[OUP1,'Z5
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ͱ͍͏͜ͱͰ
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ࠓօ͞Μʹ Θ͔Γ͘͢ 3DϓϩάϥϛϯάΛ આ໌͠·͢
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ARKitͷͨΊͷ 3Dࢉ KBOY@ےΤϯδχΞ 2018.8.30@iOSDC 2018
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ࠓͷΰʔϧ
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εΫϦʔϯ্ͷλοϓͨ͠෦ͷ 30cmલʹ ඈߦػΛஔ͘
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ษڧ͢Δ͜ͱ •࠲ඪܥΛΔ •࠲ඪมͷϝιουΛΔ
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ARKitͰ͏࠲ඪܥ
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࠲ඪ·ͱΊ ϫʔϧυ࠲ඪܥ ΦϒδΣΫτ࠲ඪܥ Χϝϥ࠲ඪܥ εΫϦʔϯ࠲ඪܥ iPad ProͰॻ͖·ͨ͠ɻ
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ϫʔϧυ࠲ඪܥ ͜ΕΑΓେ͖ͳ֎ଆͷ ࠲ඪۭؒͰදݱͰ͖ͳ͍
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ΦϒδΣΫτ࠲ඪܥ ඈߦػࣗͷϩʔΧϧ࠲ඪʂ
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Χϝϥ࠲ඪܥ ΧϝϥͷϩʔΧϧ࠲ඪ
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Χϝϥ࠲ඪܥ
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εΫϦʔϯ࠲ඪܥ
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εΫϦʔϯ࠲ඪܥ
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࠲ඪ·ͱΊ ϫʔϧυ࠲ඪܥ ΦϒδΣΫτ࠲ඪܥ Χϝϥ࠲ඪܥ εΫϦʔϯ࠲ඪܥ iPad ProͰॻ͖·ͨ͠ɻ
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ΰʔϧͷ֬ೝ
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εΫϦʔϯ্ͷλοϓͨ͠෦ͷ 30cmલʹ ඈߦػΛஔ͘
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30cm εΫϦʔϯλοϓͷ xy࠲ඪऔಘ ϫʔϧυ࠲ඪʹมͯ͠ ͦ͜ʹஔ͘ʂ Χϝϥͷ30cmલʹஔ͘ ϫʔϧυ࠲ඪʹม ᶃ ᶄ ᶅ εΫϦʔϯ࠲ඪʹม ᶆ ᶄ’ εΫϦʔϯ࠲ඪʹม
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ᶃΧϝϥ࠲ඪͰ30cmલʹஔ͘ ϚΠφε 30cm
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ᶄϫʔϧυ࠲ඪʹม
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͋Δ࠲ඪܥ͔Β ͋Δ࠲ඪܥ มͰ͖Δ
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ᶄ’εΫϦʔϯ࠲ඪʹม
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ϫʔϧυ࠲ඪܥ→εΫϦʔϯ࠲ඪܥ
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ᶅεΫϦʔϯλοϓͷxy࠲ඪऔಘ
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ᶆϫʔϧυ࠲ඪʹมͯ͠ஔ͘
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εΫϦʔϯ࠲ඪܥ→ϫʔϧυ࠲ඪܥ
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30cmલ λοϓͨ͠Ґஔ ม ม
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ͦΕͧΕɺ߹ͷ͍͍ ࠲ඪܥͰܭࢉ͢Δ
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ͪͳΈʹ
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εΫϦʔϯ࠲ඪܥ͚ͩ ͰશͯΛදݱͰ͖Δ
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εΫϦʔϯλοϓͷ xy࠲ඪऔಘ ϫʔϧυ࠲ඪʹมͯ͠ ͦ͜ʹஔ͘ʂ Χϝϥͷ30cmલʹஔ͘ ϫʔϧυ࠲ඪʹม ᶃ ᶄ ᶅ εΫϦʔϯ࠲ඪʹม ᶆ ᶄ’ εΫϦʔϯ࠲ඪʹม ͜͜ল͚Δ 30cm
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͜͜ল͚Δ
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ͬͪ͜ͷํָ͕͡ΌΜʂ
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͔ͨ͠ʹ
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͜ͷ͍ίʔυͰߦ͚Δ
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Ͱ
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࣮
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͜ͷ0.996 Χϝϥ࠲ඪܥͷ0.3mͱ ಉ͡ҙຯ
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0.996ͱ
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͜͜Ͱ࠲ඪܥͷ෮श
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0.0 1.0 εΫϦʔϯ࠲ඪܥͷ z 0.001m 1000m Χϝϥ࠲ඪܥͷ z
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εΫϦʔϯ࠲ඪܥͷz
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https://developer.apple.com/documentation/scenekit/scnscenerenderer/1522631-unprojectpoint εΫϦʔϯ࠲ඪܥͷ z0.0~1.0
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Χϝϥ࠲ඪܥͷzʁ
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debugͯ͠ΈΔͱ
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zNearΛ มԽͤͯ͞ΈΑ͏
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0.0 1.0 εΫϦʔϯ࠲ඪܥͷ z 0.001m 1000m Χϝϥ࠲ඪܥͷ z
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εΫϦʔϯ࠲ඪͷz vs Χϝϥ࠲ඪͷz
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http://www.alecjacobson.com/weblog/?p=3835 -0.001 -1000 0.996 screenZ = f(n + cameraZ)/((f − n)cameraZ) -0.3 screenZ cameraZ
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screenZ = f(n + cameraZ)/((f − n)cameraZ) screenZ = 1000(0.001 + (−0.3))/((1000 − 0.002)(−0.3)) f = 1000 n = 0.001 cameraZ = − 0.3 screenZ = 0.9966...
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࣮ʹ໘͍͘͞
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͜͜ল͚Δʂʁ
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ඞཁʂ
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ͱ͍͏͜ͱͰ
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࠲ඪมΛۦͯ͠
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ʂ
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͏ͪΐ͍ͬͯΈ·͠ΐ͏ʂ
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ඈߦػΛ֦େͨ͠Γɺ ճసͤ͞Α͏ʂ
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֦େɾॖখ
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ճస (SCNVector4) ࣠ ֯
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ճస(Euler angle)
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ճస (Euler angle) x
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ճస (Euler angle) Y
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ճస (Euler angle) Z
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x Y Z
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Ҏ্
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͜͜·Ͱ͕ࢉ
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·ֶ͕ͩ͋Γ·͢ɻ
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Ͱ
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࠲ඪͷ֓೦Λཧղͯ͠ SceneKitARKitΛ ͍͜ͳͤΕྑ͍ɻ
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ֶʹ͍ͭͯQiitaͰɻ
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ARKitͷͨΊͷ 3D ֶ
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ࠂ
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Graffity Inc. ΤϯδχΞืूதʂ
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࠷ޙʹ
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ݸਓͰARKitͷಈըڭࡐ࡞த
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One More Thing
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ࠓΓ·͢ .kt
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ے.kt w :BIPP-PEHF w ݄
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͓ΘΓ