2010 : M0107189 3DCG 3 (3DCG) 3DCG 3DCG 3DCG S

2010 M0107189

2010 : M0107189 3DCG 3 (3DCG) 3DCG 3DCG 3DCG S

1 1 1.1............................ 1 1.2.............................. 4 2 5 2.1............................ 5 2.2............................. 8 2.3.............................. 12 2.4....................... 13 3 15 3.1.......................... 15 3.2............................. 16 3.3......................... 18 3.4............................. 19 3.5.............................. 20 4 22 4.1................................... 25 5 27 28 29 I

1.1 (Wikipedia )............ 2 2.1 6 2.2....................... 8 2.3........................ 10 2.4....................... 11 2.5......................... 11 2.6............... 11 2.7.................... 14 4.1....................... 23 4.2 1....................... 23 4.3 2....................... 23 4.4 3....................... 24 4.5 4....................... 24 4.6 5....................... 24 4.7 1........................... 24 4.8 2........................... 25 4.9 3........................... 25 4.10 4........................... 25 4.11 5........................... 25 II

1 1.1 3 ( 3DCG) 3DCG [1][2][3][4] 3DCG [5][6][7] 1

1.1 1.1: (Wikipedia ) 2 [8] 2003 Baranoski [9] ( ) [10] ( ) 2

2005 Baranoski [11] Baranoski S ( ) [12] 1/f [13] 3 1/f 1/f 1/f [14] 3DCG 3

Baranosoki Bèzier [15] sin Baranosoki 1.2 5 2 3 4 5 4

2 2 [5] 2.1 2.2 2.3 2.4 2.1 ( ) 80km 500km 5

2.1 2.1: 3 U J 2 2 3 6

2 3 4 30 60 75% ( 7

) ( ) ( ) 2.2 2.2: 2.2 1km km 8

S km km 2km 10km 20km 1500km S km 0.06 0.2 50km/s ( ) 0.1 10 9

50km 100km 10 300m/s 50km/s 100km/s 2.3 10 2.4 2.5 2.6 2.3: 10

2.4: 2.5: 2.6: 11

2.3 1 557.7nm 630.0nm 391.4nm 427.8nm 670.5nm 630.0nm 110 630.0nm a b c d e f 6 a 120km 140km b 80km 100km c 100km 200km d 220km 250km e b 12

f 2.4 1 3 1 2 3 4 1 2 2 3 2 3 30 60 4 13

4 3 4 30 2 2.7 2.7: 14

3 3.1 3.2 3.3 3.4 3.5 3.4 3.1 3DCG y xz xz Bèzier [15] sin n Bèzier m sin R(t) (3.1) R(t) = n Bi n (t)q i + i=0 { m 1 j=0 A j sin(2πf j t) } N b (t) (0 t 1) (3.1) 15

N b (t) Bèzier t Q i Bèzier {Q 0, Q 1, Q 2,..., Q n } Bi n (t) Bernstein A j sin f j sin Bernstein (3.2) B n i (t) = n C i t i (1 t) n i (3.2) t k {W 0, W 1, W 2,..., W k 1 } (3.3) w W 0 (k = 1) 2 W (t, w) = w W tk (1 (tk tk ))+W tk +1 (tk tk ) (k 1, 0 t < 1) 2 w W k 2 (k 1, t = 1) (3.3) 1 w 1 tk tk (3.1) (3.3) A(t, w) (3.4) A(t, w) = R(t) + W (t, w)n a (t) (0 t 1, 1 w 1) (3.4) N a (t) t 3.2 [16] F P 0 v 0 t P 16

(3.5) P = ( ) t m F + v 0 t + P 0 (3.5) q 0 B E F (3.6) v B F = q 0 (E + v B) (3.6) B q 0 1 E φ E (3.7) E = φ (3.7) S N ρ (3.8) ρ = q 0N S (3.8) ε 0 ε 0 φ ρ [17][18] (3.9) 2 2 φ = 2 φ 2 x + 2 φ 2 z = ρ ε 0 (3.9) φ xz Drichlet [18] φ = 0 Gauss-Seidel [19] φ xz 17

4 4 4 d (i, j) 2 [18] (i, j) 2 (3.10) (3.11) ( ) 2 φ x 2 φ(i + 1, j) 2φ(i, j) + φ(i 1, j) ( d) 2 (3.10) ( ) 2 φ z 2 φ(i, j + 1) 2φ(i, j) + φ(i, j 1) ( d) 2 (3.11) (3.9) (3.10) (3.11) (i, j) φ(i, j) (3.12) φ(i, j) = 1 4 { ( d) 2 ρ ε 0 } + φ(i + d, j) + φ(i d, j) + φ(i, j + l) + φ(i, j d) (3.12) [18] (i, j) E(i, j) E(i, j) = ( φ(i + 1, j) φ(i 1, j), 2 d ) φ(i, j + 1) φ(i, j 1) 2 d (3.13) 3.3 [20] 18

B v t t t t t P (3.14) P = v B B t (3.14) r l n l [21] P 1 (3.15) P 1 = nπr 2 l (3.15) n 3.4 [22] [5] r n v m t t [21] P 2 (3.16) ( P 2 = 1 exp ) 2nπr 2 v m t (3.16) v m [23] 19

3.5 [24] σ (3.17) G(x, y) = 1 ) ( 2πσ exp x2 + y 2 2 2σ 2 (3.17) σ RGB CIE-XYZ X, Y, Z [25] λ L(λ) X, Y, Z (3.18) 780 X = k Y = k Z = k 380 780 380 780 380 x(λ)l(λ)δλ ȳ(λ)l(λ)δλ z(λ)l(λ)δλ (3.18) x, ȳ, z k L(λ) 20

X, Y, Z R, G, B (3.19) ( 3.5064X 1.7400Y 0.5441Z R = 255 100 ( 1.0690X + 1.9777Y + 0.0352Z G = 255 100 ( 0.0563X 0.1970Y + 1.0511Z B = 255 100 ) 1 2.2 ) 1 2.2 ) 1 2.2 (3.19) 21

4 3 3D FK ToolKit System[26] 512px 360px 10000 60000 9 100 40 4.1 4.1: OS Windows 7 Enterprise CPU AMD Phenom(tm) IIX6 1090T Processor 3.20 GHz GPU GeForce GTX 470 4.0 GB 4.1 22

4.1: 4.2 4.3 4.4 4.5 4.6 4.2: 1 4.3: 2 4.7 4.8 4.9 4.10 4.11 23

4.4: 3 4.5: 4 4.6: 5 4.7: 1 24

4.8: 2 4.9: 3 4.10: 4 4.11: 5 4.1 S 25

26

5 27

28

[1] Yoshinobu Takahiro and Kaneda Kazufumi. Rendering rainbows based on wave optics and compositing the rainbow and photographs.. ITS, Vol. 104, No. 647, pp. 65 70, 2005-01-28. [2] Yoshinori Dobashi, Tsuyoshi Yamamoto, and Tomoyuki Nishita. Efficient rendering of lightning taking into account scattering effects due to cloud and atmospheric particles. In Proceedings of the 9th Pacific Conference on Computer Graphics and Applications, PG 01, pp. 390, 2001. [3] TOKOI KOHE and MORIKI HIRONORI. Real-time modeling of snowcovered shape(computer graphics). Transactions of Information Processing Society of Japan, Vol. 47, No. 5, pp. 1558 1565, 2006-05-15. [4] Ye Zhao, Yiping Han, Zhe Fan, Feng Qiu, Yu-Chuan Kuo, Arie E. Kaufman, and Klaus Mueller. Visual simulation of heat shimmering and mirage. IEEE Transactions on Visualization and Computer Graphics, Vol. 13, pp. 179 189, 2007. [5]. 2., 1983. [6]. THE AURORA WATCHER S HANDBOOK., 1995. 29

[7].., 2010. [8]. CG. NICOGRAPH 95, pp. 161 170, 1995. [9] G. V. G. Baranoski, Jon Rokne, Peter Shirley, Trond Trondsen, Rui Bastos. Simulating the aurora. Visual. Comput. Animat, pp. 43 59, 2003. [10].. 2005, pp. 69 74, 2005. [11] G. V. G. Baranoski J. Wan. Simulating the dynamics of auroral phenomena. ACM Transactions on Graphics, Vol. 24, pp. 37 59, 2005. [12]. CG. 20, p. 137, 2008. [13]. CG. 21, p. 281, 2009. [14]... CAD, 2009. [15]. 3 CAD., 1991. [16]. [ 2]., 1983. [17]. 14., 2007. [18].., 1987. 30

[19]. UNIX & Informatioin Science-5 C., 2005. [20]. 23., 2011. [21]. 2.., Vol. 47, No. 1, pp. 2 6, 2004. [22] NASA, Robert McGuire. MSIS-E-90 Atmosphere Model. http://omniweb. gsfc.nasa.gov/vitmo/msis vitmo.html. [23]. 1.., Vol. 46, No. 4, pp. 31 34, 2003. [24] Gabriele Lohmann. 3 Volumetric Image Analysis., 2009. [25].., 2001. [26]. Fine Kernel Tool Kit System. http://fktoolkit.sourceforge. jp/. 31