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ίϯϐϡʔλάϥϑΟΫεͷۭ NAOMASA MATSUBAYASHI

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ۭ͕ࠇ͍

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੨ۭΛඳ͍ͨ൘ ࠓ೔΋ۭ͕੨͍ͳ

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ݱ࣮ͷۭͷ৭

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੨ۭ͸ओʹଠཅޫ͕ ۭؾதͰࢄཚ͢ΔࣄͰੜ͡Δ

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ΠϚυΩͷϦΞϧλΠϜϨϯμϦϯά ۭؾதͰͷޫͷࢄཚΛܭࢉ͢Δ

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஍ٿͷେؾʹೖ͖ͬͯͨଠཅޫͷࢄཚΛܭࢉ͢Ε͹ ݁Ռͱͯ͠ਖ਼͍͠੨ۭ͕ಘΒΕΔͷͰ͸

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https://diglib.eg.org/handle/10.1111/cgf14050 େؾதͰͷޫͷࢄཚΛܭࢉͯ͠ ۭͷ৭ΛٻΊΔ ϦΞϧλΠϜϨϯμϦϯάͰ ࢖͑Δ଎͞Ͱܭࢉ͢Δ Unreal Engineͷ ඪ४ͷۭͷϨϯμϦϯάख๏ ͜ͷ࿦จͷख๏Λ ࣮૷ͯ͠ΈΑ͏

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ۭؾΛߏ੒͢Δ෼ࢠ΍ۭؾதΛඬ͏ཻࢠʹޫ͕Ϳ͔ͭΔͱ ޫ͕޲͖Λม͑ͨΓ(ࢄཚ)ผͷΤωϧΪʔʹͳͬͨΓ(ٵऩ)͢Δ ٵऩ ࢄཚ ࢄཚ

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ٵऩ ޫͷਐΉڑ཭͕௕͘ͳΔఔ ޫͷΤωϧΪʔ͕ݮΔ

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ग़ࢄཚ ࢹ఺ʹ޲͔ͬͯ์ͨΕͨޫ͕ ࢄΒ͹͍ͬͯ͘ࣄͰ ࢹ఺ʹಧ͘ޫͷΤωϧΪʔ͕ݮΔ

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ೖࢄཚ Ͳ͔͜Ͱग़ࢄཚͨ͠ޫ͕ ࢹ఺ʹ޲͔͏ޫʹՃΘΔࣄͰ ࢹ఺ʹಧ͘ޫͷΤωϧΪʔ͕ ૿͑Δ

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͋Δ఺Ͱೖࢄཚͯ͠ࢹ఺ʹ޲͔͏ޫͷΤωϧΪʔ͸ ͦͷ఺ʹपғ͔ΒඈΜͰ͖ͨޫͷΤωϧΪʔͰܾ·Δ ͭ·Γશͯͷํ޲ʹ͍ͭͯͷੵ෼

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͋Δ఺ʹ޲͔ͬͯඈΜͰ͘ΔޫͷΤωϧΪʔ͸ ผͷ͋Δ఺Ͱ޲͖Λม͑ͨޫͩͬͨΓ͢Δ ੵ෼ͷੵ෼

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ੵ෼ͷੵ෼ͷੵ෼ͷੵ෼ ͜ΕΛΠϯλϥΫςΟϒʹܭࢉ͢Δͷ͸ແཧ

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ޫ͸1ճ͚ͩࢄཚͰ޲͖Λม͑Δࣄʹ͢Δ ࢹ఺ͱःṭ෺Λ݁Ϳઢ෼্ͷ֤఺Ͱ ޫݯ͔Βͷޫ͕ࢄཚͯ͠ ࢹ఺ʹ޲͔͏ ޫͷΤωϧΪʔʹՃΘΔ ͜ͷઢ෼ʹԊͬͯੵ෼ γϯάϧεΩϟολϦϯά

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Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei ͜ͷܦ࿏Ͱ ੜ͡Δٵऩͱ ग़ࢄཚ ͜͜ʹಧ͍ͨޫͷ͏ͪ ೖࢄཚͰࢹ఺ͷํ޲ʹ ޲͖Λม͑Δޫͷׂ߹ ͜ͷܦ࿏Ͱੜ͡Δ ٵऩͱग़ࢄཚ ඈΜͰ͖ͨ ޫͷΤωϧΪʔ v : li : ||c − x|| ଠཅͷ޲͖ x + tatmo li : ඪߴ100kmͷ໘ͱ ํ޲ʹ৳͹ͨ͠ ௚ઢͷަ఺ li c x

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T(xa , xb ) = e−∫xb x=xa σt (x)||dx|| ϥϯϕϧτɾϕʔϧͷ๏ଇ ֤఺Ͱͷޫͷ௨Γ΍͢͞ Λޫ͕௨Δܦ࿏Ͱੵ෼ σt (x) ͦͷ஋͕େ͖͍ఔಁաͰ͖ΔޫͷΤωϧΪʔ͸খ͘͞ͳΔ Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei

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100km ଠཅ͔ΒͷޫΛݦஶʹࢄཚͤ͞Δͷ͸ ஍ද͔Β100km͘Β͍ͷൣғͷۭؾ ີ౓͕ߴ͍ ີ౓͕௿͍ ۭؾͷີ౓͸ ஍ද͔Βԕ͘ͳΔఔ খ͘͞ͳΔ

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σr (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 e− ||x|| − 6.36 × 106 8 × 103 ||x|| 6.36 × 106m 1ؾѹͷۭؾதͰ ޫ͕ۭؾΛߏ੒͢Δ ෼ࢠͱͿ͔ͭͬͯ ग़ࢄཚ͢Δׂ߹ ߴ౓ ߴ౓͕ߴ͘ͳΔఔ ۭؾͷີ౓͕Լ͕Δ x ۭؾதͷ෼ࢠʹΑΔ ग़ࢄཚ

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σm (x) = (3.996 × 10−6 + 4.40 × 10−6) e− ||x|| − 6.36 × 106 1.2 × 103 6.36 × 106m ߴ౓͕ߴ͘ͳΔͱ ۭؾதΛඬ͏ཻࢠͷྔ͸ٸ଎ʹݮΔ ۭؾதΛඬ͏ཻࢠʹΑΔ ग़ࢄཚͱٵऩ ग़ࢄཚ ٵऩ ||x|| x

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6.36 × 106m ΦκϯʹΑΔޫͷٵऩ ||x|| x σo (x) = 0.650 × 10−6 1.881 × 10−6 0.085 × 10−6 max ( 0,1 − |(||x|| − 6.36 × 106) − 25 × 103 | 15 × 103 ) ٵऩ ߴ౓25kmΛϐʔΫͱ͢Δ ্Լ֤15kmͷൣғ

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T(xa , xb ) = e−∫xb x=xa σt (x)||dx|| σt (x) = σr (x) σm (x) σo (x) σr (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 e− ||x|| − 6.36 × 106 8 × 103 σm (x) = (3.996 × 10−6 + 4.40 × 10−6) e− ||x|| − 6.36 × 106 1.2 × 103 σo (x) = 0.650 × 10−6 1.881 × 10−6 0.085 × 10−6 max ( 0,1 − |(||x|| − 6.36 × 106) − 25 × 103 | 15 × 103 ) Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei

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σs (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 p (v, li) = 3 (1 + (v ⋅ li) 2 ) 16π ۭؾΛߏ੒͢Δ෼ࢠʹΑΔࢄཚ(ϨΠϦʔࢄཚ) Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei

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σs (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 p (v, li) = 3 (1 + (v ⋅ li) 2 ) 16π ۭؾΛߏ੒͢Δ෼ࢠʹΑΔࢄཚ(ϨΠϦʔࢄཚ) σs (x) = 3.996 × 10−6 p (v, li) = 3 8π (1 − g2) (1 + (v ⋅ li) 2 ) (2 + g2) (1 + g2 − 2g (v ⋅ li)) 3 2 ۭؾதΛඬ͏ཻࢠʹΑΔग़ࢄཚͱٵऩ(ϛʔࢄཚ) g = 0.8 Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei ϔχΤΠɾάϦʔϯελΠϯؔ਺

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Lscat (c, x, v) = T (c, x) T (x, x + tatmo li) σs (x) p (v, li) Ei L (c, v) = ∫ ||p−c|| t=0 Lscat (c, c − tv, v) dt c 100km p ͜ͷઢ෼ʹԊͬͯੵ෼

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Lscat (c, x, v) = T (c, x) T (x, x + tatmo li) σs (x) p (v, li) Ei T(xa , xb ) = e−∫xb x=xa σt (x)||dx|| σt (x) = σr (x) σm (x) σo (x) σr (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 e− ||x|| − 6.36 × 106 8 × 103 σm (x) = (3.996 × 10−6 + 4.40 × 10−6) e− ||x|| − 6.36 × 106 1.2 × 103 L (c, v) = ∫ ||p−c|| t=0 Lscat (c, c − tv, v) dt ਺஋ੵ෼ͷ਺஋ੵ෼͸ ϦΞϧλΠϜϨϯμϦϯάʹ͸ਏ͍

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100km ߴ౓h ఱ௖ͱଠཅͷ ͳ֯͢θ ͸ ͱ ͚ͩͰܾ·Δ e−∫xb x=xa σt (x)||dx|| θ h xa xb

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ଠཅ͔Β ʹࢸΔޫͷಁա཰ xa 1 − ( 1 − θ θmax ) 2 1 − (1 − h 1 × 105 ) 2 ଠཅͱ Λ݁Ϳ௚ઢ͕஍໘ʹ઀͢Δ֯౓ xa

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ݱ࣮ͷۭͷ৭ ۭͷ৭͸ ؇΍͔ʹ͔͠ มԽ͠ͳ͍ ݶΒΕͨ఺͚ͩ ܭࢉͯ͠ ؒ͸ิؒͰे෼

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θ ϕ θ ϕ π 2 − π 2 0 2π ͳΜ͔ബ҉͍

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σr (x) = 5.802 × 10−6 13.558 × 10−6 33.1 × 10−6 e− ||x|| − 6.36 × 106 8 × 103 ग़ࢄཚ͔͠ແ͍ ۭؾதͷ෼ࢠʹΑΔٵऩ͸ແࢹͰ͖Δ΄Ͳখ͍͞ ࢄཚͨ͠ޫ͸ ຆͲΤωϧΪʔΛࣦΘͣʹ ࢄཚΛ܁Γฦ͢ ͦͷ͏ͪزΒ͔͸ࢹ఺ʹಧ͘ ϚϧνεΩϟολϦϯάͷӨڹ͕ ແࢹ͢Δʹ͸େ͖͗͢Δ

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ίετΛ͔͚ͣʹ ࡶʹෳ਺ճͷࢄཚΛܭࢉͨ͠ࣄʹ͍ͨ͠ ͜ͷ෼Λࣄલʹ ܭࢉ͍ͨ͠

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ߴ౓ x ೖࢄཚͷ޲͖(ܦ౓) ೖࢄཚͷ޲͖(Ң౓) ଠཅͷ޲͖(Ң౓) ଠཅͷ޲͖(ܦ౓) 2ճࢄཚ͢Δޫͷࣗ༝౓ : 5࣍ݩ ࣄલʹܭࢉͨ͠஋Λ഑ྻʹ͢Δʹ͸ ࣍ݩ͕େ͖͗͢Δ y

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ࠨ͔Βདྷͨޫ͕ ϨΠϦʔࢄཚ͢Δ৔߹ͷ ࢄཚํ޲ͷ෼෍ શͯͷํ޲ʹͦΕͳΓͷେ͖͞Ͱ ෼෍͍ͯ͠Δ ࢄཚΛ܁Γฦ͢ͱ ݩͷޫͷ޲͖ͷ৘ใ͸ ٸ଎ʹࣦΘΕΔ ∴

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ߴ౓ x ೖࢄཚͷ޲͖(ܦ౓) ೖࢄཚͷ޲͖(Ң౓) ଠཅͷ޲͖(Ң౓) ଠཅͷ޲͖(ܦ౓) Ͳͷ޲͖͔Βͷೖࢄཚ΋ಉ͡ ೖࢄཚͷ޲͖ຖʹ ܭࢉ݁ՌΛ࣋ͭඞཁ͸ͳ͍ ∴ y

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ߴ౓ x ଠཅͷ޲͖(Ң౓) ଠཅͷ޲͖(ܦ౓) Ͳͷ޲͖͔Βͷೖࢄཚ΋ಉ͡ ޲͖͸Ͳ͏Ͱ΋͍͍ͷͰ ଠཅͷ޲͖ͷܦ౓͸ཁΒͳ͍ ∴ y

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L2 (xs , p) = ∫ Ω4π L′ (xs , p, − ω) 1 4π dω L′ (x, p, v) = ∫ ||p−x|| t=0 T (x, x − tv) σs (x) 1 4π T (x, x + tatmo li) dt શͯͷ޲͖͔Βͷ2࣍ͷೖࢄཚ c x

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L2 (xs , p) = ∫ Ω4π L′ (xs , p, − ω) 1 4π dω L′ (x, p, v) = ∫ ||p−x|| t=0 T (x, x − tv) σs (x) 1 4π T (x, x + tatmo li) dt શͯͷ޲͖͔Βͷ2࣍ͷೖࢄཚ c x ∫ D 0 e−σt xSdx = S − Se−σt D σt Λ࢖ͬͯ Λղੳతʹղ͘ L′

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fms (xs , p) = ∫ Ω4π Lf (xs , p, − ω) 1 4π dω Lf (x, p, v) = ∫ ||p−x|| t=0 T (x, x − tv) σs (x) dt Fms (x, p) = 1 1 − fms (x, p) ψms (x, p) = L2 (x, p) Fms (x, p) L2 (xs , p) = ∫ Ω4π L′ (xs , p, − ω) 1 4π dω L′ (x, p, v) = ∫ ||p−x|| t=0 T (x, x − tv) σs (x) 1 4π T (x, x + tatmo li) dt શͯͷ޲͖͔Βͷ2࣍ͷೖࢄཚ શͯͷ޲͖͔Βͷ 2͔࣍Β ࣍·Ͱͷೖࢄཚ ∞ ∫ D 0 e−σt xSdx = S − Se−σt D σt ͜Ε΋ Ͱղ͘ ͜͜ʹ2࣍ͷೖࢄཚ͕ՃΘΔͱ͢Δͱ ઴ԽࣜʹͳΔ

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Lscat (c, x, v) = T (c, x) σs (x) p (v, li) T (x, x + tatmo li) Ei + ψms (x, li) Ei ͜ͷܦ࿏Ͱ ੜ͡Δٵऩͱ ग़ࢄཚ ͜͜ʹಧ͍ͨޫͷ͏ͪ ೖࢄཚͰࢹ఺ͷํ޲ʹ ޲͖Λม͑Δޫͷׂ߹ ͜ͷܦ࿏Ͱੜ͡Δ ٵऩͱग़ࢄཚ c x ෳ਺ճࢄཚͯ͠ ʹͨͲΓண͘෼ x

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θ ϕ θ ϕ π 2 − π 2 0 2π

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https://fadis.booth.pm/ /&8 ϦΞϧλΠϜϨϯμϦϯάͷख๏Λ ήʔϜΤϯδϯͱ͔࢖Θͣʹ ࣗྗͰ࣮૷͢Δ ϨΠϠʔ͕௿͍ਓͷͨΊͷ ίϯϐϡʔλάϥϑΟΫεղઆຊ ٕज़ॻయͰຊग़ͯ͠·͢