2010 : M DCG 3 (3DCG) 3DCG 3DCG 3DCG S

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1 2010 M

2 2010 : M DCG 3 (3DCG) 3DCG 3DCG 3DCG S

3 I

3......................... 18 3.4............................. 19 3.5.............................. 20 4 22 4.1................................... 25 5 27 28 29 I

4 1.1 (Wikipedia ) II

5 4....................... 24 4.6 5....................... 24 4.7 1........................... 24 4.8 2........................... 25 4.9 3........................... 25 4.10 4.

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

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

7 2005 Baranoski [11] Baranoski S ( ) [12] 1/f [13] 3 1/f 1/f 1/f [14] 3DCG 3

8 Baranosoki Bèzier [15] sin Baranosoki

9 2 2 [5] ( ) 80km 500km 5

10 : 3 U J

11 % ( 7

12 ) ( ) ( ) : 2.2 1km km 8

13 S km km 2km 10km 20km 1500km S km km/s ( )

14 50km 100km m/s 50km/s 100km/s : 10

15 2.4: 2.5: 2.6: 11

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

17 f

18 : 14

19 DCG 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

1 3DCG y xz xz Bèzier [15] sin n Bèzier m

20 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) 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 =

21 (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

22 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

23 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

24 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 x(λ)l(λ)δλ ȳ(λ)l(λ)δλ z(λ)l(λ)δλ (3.18) x, ȳ, z k L(λ) 20

25 X, Y, Z R, G, B (3.19) ( X Y Z R = ( X Y Z G = ( X Y Z B = ) ) ) (3.19) 21

26 4 3 3D FK ToolKit System[26] 512px 360px : OS Windows 7 Enterprise CPU AMD Phenom(tm) IIX6 1090T Processor 3.20 GHz GPU GeForce GTX GB

27 4.1: : 1 4.3:

28 4.4: 3 4.5: 4 4.6: 5 4.7: 1 24

29 4.8: 2 4.9: : : S 25

30 26

31 5 27

32 28

33 [1] Yoshinobu Takahiro and Kaneda Kazufumi. Rendering rainbows based on wave optics and compositing the rainbow and photographs.. ITS, Vol. 104, No. 647, pp , [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, [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 , [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 , [5]. 2., [6]. THE AURORA WATCHER S HANDBOOK.,

34 [7].., [8]. CG. NICOGRAPH 95, pp , [9] G. V. G. Baranoski, Jon Rokne, Peter Shirley, Trond Trondsen, Rui Bastos. Simulating the aurora. Visual. Comput. Animat, pp , [10] , pp , [11] G. V. G. Baranoski J. Wan. Simulating the dynamics of auroral phenomena. ACM Transactions on Graphics, Vol. 24, pp , [12]. CG. 20, p. 137, [13]. CG. 21, p. 281, [14]... CAD, [15]. 3 CAD., [16]. [ 2]., [17]. 14., [18]..,

35 [19]. UNIX & Informatioin Science-5 C., [20]. 23., [21]. 2.., Vol. 47, No. 1, pp. 2 6, [22] NASA, Robert McGuire. MSIS-E-90 Atmosphere Model. gsfc.nasa.gov/vitmo/msis vitmo.html. [23]. 1.., Vol. 46, No. 4, pp , [24] Gabriele Lohmann. 3 Volumetric Image Analysis., [25].., [26]. Fine Kernel Tool Kit System. jp/. 31

1 3 (3DCG) [1] [2] [3] [4] [5] 3DCG [6] [7] [8] [9] ( ) 3DCG 27 NICOGRAPH [10] [6] ( ) [7] 80km 500km 1 1: 25

1 3 (3DCG) [1] [2] [3] [4] [5] 3DCG [6] [7] [8] [9] ( ) 3DCG 27 NICOGRAPH [10] [6] ( ) [7] 80km 500km 1 1: 25 Visual Simulation of Aurora based on Feature Motion Takafumi Kojima Ryota Takeuchi Taichi Watanabe Koji Mikami Graduate School of Bionics, Computer and Media Sciences, Tokyo University of Technology School