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

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1 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 of Media Science, Tokyo University of Technology 3DCG 1 3DCG Abstract Visual simulation of natural phenomena is one of the most important research fields in 3DCG. Many methods were developed for representing natural phenomena. These methods are used in many fields such as education and industry. We focus on aurora which is light emission phenomena and appears the sky of Polar Regions. Visual simulation of aurora generates dynamic animations by using feature of aurora such as form and motion and colors and generating mechanism. We propose a new approach for simulating and rendering aurora. The proposed method can reproduce motion of aurora, which render the various aurora emission colors. Our method reproduces motion of aurora by simulating the movements of charged particles. In this paper, we use a square grid for simulating the electromagnetic field, which calculates forces acting on the charged particles by simulating the electromagnetic field. The particle positions are iteratively updated, and the grid size is also updated after every iteration so that all the particles are always within the region of the grid. The proposed method reproduces the various aurora emission colors by simulation of the emission process and the light attenuation. Our experimental results indicate the effectiveness of the proposed system. 24

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

3 S [11] 2km 10km km 1500km 1 1 S S 5km/s 10km/s [9] 2 S 2: ( ) 557.7nm 630.0nm 391.4nm 427.8nm 670.5nm 2.2 3DCG 2 [12] Baranoski [13] Baranoski [14] Baranoski [15] [16] Baranoski 26

4 Lawlor [17] [18] [19] 2.3 Baranoski 3 3 3: [6] [9]

5 () t k {L 0, L 1, L 2,..., L k 1 } (2) W (t) = L 0 k = 1 (1 p)l q + pl q+1 k 1, 0 t < 1 (2) L k 1 k 1, t = 1 k k q = tk p = tk q tk tk (1) (2) A(t, w) (3) A(t, w) = R(t) + ww (t)n b (t) (3) 4: N b (t) t t 0 t 1 w 1 w 1 (3) t w Bézier [] 3DCG y xz xz n Bézier m 0 t 1 t R(t) (1) R(t) = n Bi n (t)q i + i=0 { m 1 j=0 A jsin(2πf jt) } N a(t) (1) m m B n i (t) Bernstein [] Q i Bézier {Q 0, Q 1, Q 2,..., Q n} A j f j N a(t) Bézier t F m e P 0 v 0 [21] t P (4) P = P 0 + v 0 t + 1 F t 2 (4) 2 m e q 0 B E v F (5) F = q 0(E + v B) (5) v B B q 0 1 E ϕ E (6) E = ϕ (6) 28

6 ε 0 ϕ ρ 2 Poisson [22] [23] (7) 2 2 ϕ = 2 ϕ x ϕ z 2 = ρ ε 0 (7) S N ρ (8) ρ = q0n S (8) Poisson ϕ E Poisson xz ϕ Drichlet [23] ϕ = 0 Gauss-Seidel [24] ϕ xz d [23] (i, j) 2 (9) (10) ) ( 2 ϕ x 2 ϕ(i + 1, j) 2ϕ(i, j) + ϕ(i 1, j) ( d) 2 (9) ( ) 2 ϕ ϕ(i, j + 1) 2ϕ(i, j) + ϕ(i, j 1) (10) z 2 ( d) 2 (7) (9) (10) (i, j) ϕ(i, j) (11) p(i, j) = ϕ(i + 1, j) + ϕ(i 1, j) + ϕ(i, j + 1) + ϕ(i, j 1) ϕ(i, j) = 1 { } ( d) 2 ρ + p(i, j) (11) 4 ε 0 [23] (i, j) E(i, j) E(i, j) X (12) Z (13) E(i, j) Y 0 ϕ(i + 1, j) ϕ(i 1, j) ( X ) = 2 d ϕ(i, j + 1) ϕ(i, j 1) ( Z ) = 2 d (12) (13) xz ϕ xz X Z x 0 z 0 x 1 z 1 u ϕ 1 h (14) { u(x1 x 0) x 1 x 0 z 1 z 0 h = (14) u(z 1 z 0) x 1 x 0 < z 1 z 0 u ϕ 1 a 1 h d (15) d = h a (15) [6] [14] xz y 500km [25] 29

7 B v t P P 0 P (16) P = P 0 + v B B t (16) t t t t r t l [25] n l [26] P 1 (17) P 1 = nπr 2 l (17) [27] [6] [28] r n v m t t [26] P 2 (18) ( P 2 = 1 exp ) 2nπr 2 v mt (18) v m [28] DCG [29] [30] g d c (19) c = exp( (dg) 2 ) (19) [31] σ () G(x, y) = 1 2πσ 2 exp ) ( x2 + y 2 2σ 2 () σ R, G, B CIE-XYZ X, Y, Z [32] λ L(λ) X, Y, Z (21) 780 X = k x(λ)l(λ) dλ Y = k Z = k ȳ(λ)l(λ) dλ z(λ)l(λ) dλ (21) x(λ), ȳ(λ), z(λ) k L(λ) (21) X, Y, Z R, G, B (22) [33] R = ( X Y Z G = ( X Y Z B = ( X Y Z ) ) ) (22) 3D API OpenGL 3DCG FK Toolkit System [30] 1 OS CPU 1: Windows 7 Enterprise 64bit Intel Core i GHz 8.0 GB 30

8 芸術科学会論文誌 Vol. 12, No. 1, pp ビジュアルシミュレーションを行った際のパラメー タ値は t を t を 拡大率 u を 2.0 とした また 正方領域を直行格子に分割した際の格 子点の 1 列分の個数 a を 100 としたので 格子全体 での格子点の個数は 10,000 個となる カーテン型オーロラを生成した結果を図 5 に示す 光の減衰により観測位置から見てオーロラの遠い部 分ほど発光が弱くなるのが確認できる なお 図 5 図 6 図 7 のパラメータ値は スクリーンサイズは横 幅 512px, 縦幅 360px 荷電粒子の個数は 60,000 個 とした このとき 1 フレーム毎の平均生成時間は約 5 分であった また 図 5 図 6 図 7 の放射する光の波長ごとの 発光の強度 ガウシアンフィルタのパラメータ値を次 の表 2 に示す 表 2: 図 5, 図 6, 図 7 の波長ごとのパラメータ値 図 5: カーテン型オーロラの生成結果 図 5 はカーテンが揺らめくような動きをしたオー ロラを表現できており 発光に連続性があることが確 認できる それぞれ異なる観測位置から見上げたオーロラの 生成結果を図 6 に示す 波長 557.7nm 630.0nm 391.4nm 発光の強度 σ サイズ nm 670.5nm また スプリッティングや ひだの回転運動によっ てスパイラルを形成した様子の生成結果を図 8 に示す 図 8: スパイラルの生成結果 図 6: 観測位置の異なるオーロラの生成結果 多重に出現しているオーロラの生成結果を図 7 に 示す オーロラの特徴的な運動であるスプリッティング や ひだの回転運動 反時計回りに渦を巻いている様 子が確認できる 図 8 のパラメータ値は スクリー ンサイズは横幅 7px, 縦幅 480px 荷電粒子の個数 は 160,000 個とした このとき 1 フレーム毎の平均 生成時間は約 15 分であった また 図 8 の放射する 光の波長ごとの発光の強度 ガウシアンフィルタのパ ラメータ値を次の表 3 に示す 表 3: 図 8 の波長ごとのパラメータ値 波長 発光の強度 557.7nm 630.0nm 391.4nm 427.8nm 670.5nm 図 7: 多重なオーロラの生成結果 31 サイズ σ

9 芸術科学会論文誌 Vol. 12, No. 1, pp 様々な色のオーロラを生成した結果を図 9 図 10 図 11 に示す 表 4: 図 9 の波長ごとのパラメータ値 波長 発光の強度 σ サイズ 557.7nm nm 391.4nm 427.8nm 670.5nm また 図 10 の放射する光の波長ごとの発光の強 度 ガウシアンフィルタのパラメータ値を次の表 5 に 示す 図 9: 全体が緑色のオーロラの生成結果 表 5: 図 10 の波長ごとのパラメータ値 波長 発光の強度 557.7nm 630.0nm 391.4nm 427.8nm 670.5nm サイズ σ また 図 11 の放射する光の波長ごとの発光の強 度 ガウシアンフィルタのパラメータ値を次の表 6 に 示す 図 10: 上部が赤色で下部が緑色のオーロラの生 表 6: 図 11 の波長ごとのパラメータ値 成結果 波長 発光の強度 557.7nm 630.0nm 391.4nm 427.8nm 670.5nm σ サイズ 星空の写真 [34] と合成した結果を図 12 に示す 図 11: 緑色と青色のオーロラの生成結果 図 9 図 10 図 11 のパラメータ値は スクリーン サイズは横幅 1500px, 縦幅 10px 荷電粒子の個数 は 300,000 個とした このとき 1 フレーム毎の平均 生成時間は約 30 分であった また 図 9 の放射する 光の波長ごとの発光の強度 ガウシアンフィルタのパ ラメータ値を次の表 4 に示す 図 12: 星空の写真と合成した結果 図 12 のパラメータ値は スクリーンサイズは横幅 7px, 縦幅 480px 荷電粒子の個数は 60,000 個とし 32

10 : 12 σ 557.7nm nm nm nm nm S GPU(Graphics Processing Unit) [1] Yoshinori Dobashi, Tsuyoshi Yamamoto, 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 , 01. [2] Yoshinobu Takahiro, Kaneda Kazufumi. Rendering Rainbows based on Wave Optics and Compositing the Rainbow and Photographs.. ITS, Vol. 104, No. 647, pp , 05. [3] Zhao Ye, Han Yiping, Fan Zhe, Qiu Feng, Kuo Yu-Chuan, Kaufman Arie E., Mueller Klaus. Visual Simulation of Heat Shimmering and Mirage. IEEE Transactions on Visualization and Computer Graphics, Vol. 13, pp , 07. [4].. Visual Computing/ CAD, No. 15, pp , 11. [5] Chentanez Nuttapong, Müller Matthias. Real-time Eulerian Water Simulation using a Restricted Tall Cell Grid. ACM Transactions on Graphics, Vol. 30, No. 4, pp. 82:1 82:10, 11. [6]. 2.,

11 [7]. THE AU- RORA WATCHER S HANDBOOK., [8]. -., 10. [9].., 10. [10],,,.. 27 NICOGRAPH, pp , 11. [11]. ( 2)., [12],. CG. 11 NICOGRAPH, pp , [13] G. V. G. Baranoski, Jon Rokne, Peter Shirley, Trond Trondsen, Rui Bastos. Simulating the Aurora. Journal of Visualization and Computer Animation, Vol. 14, No. 1, pp , 03. [14],.. 05, pp , 05. [15] G. V. G. Baranoski, J. Wan. Simulating the Dynamics of Auroral Phenomena. ACM Transactions on Graphics, Vol. 24, pp , 05. [16],,... CAD, No. 12, pp , 09. [17] Orion Sky Lawlor, Jon Genetti. Interactive Volume Rendering Aurora on the GPU. Journal of WSCG, Vol. 19, p. H41, 11. [18] Modeling of Aurora Borealis using the Observed Data, 11. [19] Tomokazu Ishikawa, Yonghao Yue,Kei Iwasaki, Yoshinori Dobashi, Tomoyuki Nishita.. Visual Computing/ CAD, No. 19, pp , 11. [],. 3 CAD., [21]. ( 1)., [22],,. 14., 07. [23],.., [24]. UNIX & Informatioin Science-5 C., 05. [25]. 23., 11. [26]. 2.., Vol. 47, No. 1, pp. 2 6, 04. [27] NASA, Robert McGuire. MSIS-E-90 Atmosphere Model. vitmo/msis vitmo.html/. [28]. 1.., Vol. 46, No. 4, pp , 03. [29] Tomas Akenine-Möller, Eric Haines. 2 REAL-TIME REN- DERING Second Edition., [30] Fine Kernel Project. Fine kernel tool kit system. [31] Gabriele Lohmann. 3 Volumetric Image Analysis., 09. [32].., 01. [33]. 4., 04. [34]. Flickr - Photo Sharing! @N07/ /in/photostream/. 11 ACM SIGGRAPH 34

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