SJ SG Technical Report Group 1 Table 1 arameters of bud. arameter Show the condition of bud. A 0, A 1, A 2,, Z Condition of bud N Nourishment F Sucker
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1 SJ SG Technical Report CG 1 1 bud apical bud dormant bud ending bud internode leaf sucker CG L-system CG L-system 3 Model Generation for Climbing lants Using Growth Simulation Ari Shindo 1 and Yuji Sakamoto 1 Climbing plants attract attention because they are suited for making green spaces along the wall of buildings. articularly, model generation methods for climbing plants are useful for prediction and estimation of scenery after greening. Then, this paper presents a model generation method using growth simulation with L-system. First, the proposed method sets rules of L-system. Second, the proposed method simulates the growth using the rules, and controls growth and blanching. The positions of buds in three dimensional space are searched considering the behavior of sucker and light requirement at the top branches. At the end of this paper, we show the results of the growth simulation using the proposed method, and consider the results. 1 Graduate School of nformation Science and Technology, Hokkaido University 1 2 Fig. 1 icture of climbing plant. Fig. 2 Climbing plant s organs. 1. 1) ( 1) 2),3) CG(Computer Graphics) CG 4),5) Lindenmayer L-system 6),7) CG article system 8) L-system 2. CG 1 c 2010 nformation rocessing Society of Japan
2 SJ SG Technical Report Group 1 Table 1 arameters of bud. arameter Show the condition of bud. A 0, A 1, A 2,, Z Condition of bud N Nourishment F Sucker fixed to object or not L osition of leaf Show the position of bud. (x, y, z) Coordinates of bud V(v x, v y, v z ) Growth direction n The nearest surface number step c Step when the bud was created step d Step when the bud was dead L-system (internode) (bud) (apical bud) (dormant bud) (ending bud) 3 (sucker) L-system 5) 1 A 0, A 1, A 2,, Z A 3 2 N F L Symbol A 0, A 1, A 2 Z [ ] R(θ x, θ y, θ z ) 2 Table 2 Symbols and their order using this method. Order Translate to this coordinate. Show this point is an apical bud. Translate to this coordinate. Show this point is a dormant bud. Translate to this coordinate. Show this point is an ending bud. raw an internode and a leaf. Save state, start a new branch. / Restore state, end a branch. Rotate by θ x, θ y, and θ z degrees. step c step d step c step d 2.2 L-system L-system (L-string) 2 A 0, A 1, A 2,, Z, [, ], R(θ x, θ y, θ z ) A 0, A 1, A 2 Z 1 step c L-system (production:p) (p) predecessor : condition successor (predecessor) (condition) (successor) L-string step step c step c 2010 nformation rocessing Society of Japan
3 SJ SG Technical Report A 0 (p 0 ) A 1 Z (p 1 ) Z A 2 (p 2 ) A 0 3 Fig. 3 Change in shape corresponding to growth rules of apical bud. (p 3 ) Z R( θx, θy, θz) A 0 4 Fig. 4 Change in shape corresponding to growth rule of dormant bud. 3 L-system L-string step 3 L-string CG 3.2 L-system L-system Bud step 3 V N L Bud(step,,V,N,L) (p 0 ) (p 2 ) 3 (p 0)A 0(step c,, V,N,L) : (H 0 t 0, N t 1) Z(step c,, V,0,L)A 1(step,,V,N,L ) (p 1 )A 1 (step c,, V,N,L) : (H 0 t 0, N t 1 ) Z(step c,, V,0,L)A 2 (step,,v,n,l ) (p 2 )A 2 (step c,,v,n,l) : (H 0 t 0, N t 1 ) (step c,,v,(1 α)n,l)a 0(step,,V,αN,L ) condition t 0 t 0 H 0 step H t 1 α 0.5 α 1.0 (p 2 ) successor V 3.4 (p 3 ) 4 (p 3)(step c,,v,n,l) : (H 1 t 0, N t 2) Z(step c,,v,0,l)[r(θ x, θ y, θ z)a 0(step,,V,N,L )] condition H 1 H 0 predecessor t 2 t 2 > t 1 (p 0 ) (p 3 ) L 1, 0 1, 0 L (p 4) (p 5) (p 4 )A 0,1,2 (step c,, V,N,L) : N < t 1 A 0,1,2 (step c,, V,N + β,l) (p 5 )(step c,, V,N,L) : N < t 2 (step c,, V,N + β,l) β (p 6) (p 6 )Bud(step c,, V,N,L) : (num l > B max ) Z(step c,, V,0,L) condition num l B max 3.3 9) 5(a) 3 c 2010 nformation rocessing Society of Japan
4 SJ SG Technical Report d max light source (a) d d l 0 Fig. 5 (c) 1 V l0 3 leaf s shadow 1 V l d max Vl3 0 V l 2 0 (b) V l1 (d) 1 V l0 5 Receiving light model with branch. 3 3 sucker l θ max V' V ' surface of object 6 Fig. 6 utting the slate points. step d max d max 5(b) (c) 0 0 d l 0 0 / V l0 = 0/ h 0 1 d d l h 0 V l0 { 1 (d d l )/d max (d d l 0) h 0 = 1 (d d l < 0) V l0 = h 0 0/ 0 V l1 V l3 V l V l0 V l3 H 0 h 0 h 3 H 1 H 0 H L-system 3 Benes (rected Random Walk) 8). 6 predecessor V successor l θ max V V x, y, z θ x, θ y, θ z θ max = + lr(θ x, θ y, θ z)v 5 d f d f d = 1 d/ (0 f d 1) 0 f d 1 f d < 0 f d = 0 f v f v = (V V + 1)/2 (0 f v 1) 4 c 2010 nformation rocessing Society of Japan
5 SJ SG Technical Report unfixed branch C φ num 1 Mg sin φ Mg 0 V branch G 1 0 1' ' center of rotation num num' 1 1' 0 ' num' center of rotation (a) (b) (c) Fig. 7 7 Flow of correcting the position of branches. G f geotropism f geotropism = (( G) V + 1)/2 (0 f geotropism 1) f gravity f gravity = (G V + 1)/2 (0 f gravity 1) f gravity = V l V l f heliotropism f heliotropism = (V l V + 1)/2 (0 f heliotropism 1) f f = f d + f v + f geotropism + f gravity + f heliotropism f num 3 Table 3 arameters of growth simulations. nternode length l 30 [pixels] Threshold value t Sucker length 30 [pixels] Threshold value t Leaf s maximum size d max 60 [pixels] egree of apical dominance α 0.8 Object size 3000 x 3000 [pixels] Amount of nourishment addition β 0.05 Acceleration of gravity g 9.8 [m/s 2 ] 7(a) 0 0 1,,... num 1 num C M V branch = (C 0 )/ C 0 V branch G ϕ g F moment F moment = C 0 Mgsinϕ 0 F moment 1 num 7(b) 1 num 1 num 1 num 0 7(c) 1 F moment 4. L-system 3 1m 2 1pixel 1mm t 0 step=450 5 c 2010 nformation rocessing Society of Japan
6 情報処理学会研究報告 SJ SG Technical Report 物の違いは 3.4 節で説明した適正値の計算で 屈光性以外の性質も同じ重みで考慮してい るからであると思われる そこで 芽の周囲の環境に応じて考慮するべき適正値に重みを持 たせ 影が多い場合は屈光性に従いやすくするなどの工夫をする必要がある また ツタの 枝の伸び方の仕組みは解明されていないが 再現のためにパラメタの値の調整や別の要素の 追加を行っていくことも検討する必要がある 5. ま と め 本稿では ツタの吸盤の働きに沿った L-system のルールと 生長位置の決定方法 枝葉 が作る影を考慮した枝の伸び方の処理方法を提案した 実験では 受光量と受光ベクトルの (a) t0 =15.0 (b) t0 =20.0 導入によって 芽の周囲の影に応じて発芽を抑え 枝が互いに避け合う様子を表現した し 図 8 シミュレーション結果 Fig. 8 Results of the growth simulation. かし 本物のツタが枝を同じ方向に伸ばして交差を避けるような挙動は再現できなかった 今後は より本物に近い形が得られるようパラメタの調整や新しいパラメタの追加について 検討する び方を確認した 図 8(a) は t0 =15.0 (b) は t0 =20.0 としたときの結果である (b) の方が 参 (a) よりも枝と枝の隙間が少なく t0 が大きいときほど 周囲に影が多くても発芽している 考 文 献 1) 壁面緑化ガイドライン, 東京都, 平成 18 年 3 月発行. 2) 沖中健, 野島義照, 小林達明, 瀬戸裕直, つる性植物の被覆がコンクリート建物の壁面 温度に及ぼす影響, 千葉大学園芸学部学術報告, 第 48 号, pp , ) 梅干野晃, 茶谷正洋, 八木幸二, ツタの西日遮へい効効果に関する実験研究, 日本建 築学会計画系論文報告集, pp.11-17, ) 金山知俊, 阪田省二郎, 増山繁, さまざまな樹種に対応可能な樹木の生長モデル, 信 学技報, RU 94-87, pp.15-22, ) 大西克彦, 蓮池祥一, 北村喜文, 岸野文郎, インタラクティブな生長シミュレーション による仮想樹木モデルの生成, 日本バーチャルリアリティ学会論文誌, Vol.11, No.1, pp , Mar ) R. Mech,. rusinkiewicz, Visual Models of lants nteracting with Their Environment, n roceedings of ACM SGGRAH 96, ACM, pp , ) Z. Lam, S. A. King, Simulating Tree Growth Based on nternal and Environmental Factors, n roceedings of ACM SGGRAH 05, ACM, pp , ) B. Benes, E. U. Millan, Virtual Climbing lants Competing for Space, roc. of Computer Animation, pp.33-42, ) 甲斐 昌一, 森川 弘道, 鈴木 泰博, プラントミメティクス 植物に学ぶ, エヌ ティー エス, ことが見て取れる このことから 受光量に応じた分岐の制御ができたことが分かる ま た (a) の枝の分岐点と交差点の数は 1m2 あたり約 55 個 (b) は約 86 個だった 図 1 に 示した本物のツタについても 葉のない部分の分岐点 交差点数を数えたところ 手作業に つき誤差が見込まれるが 1m2 あたり約 88 個であった 従って 枝葉の密度の点では (b) の方が図 1 のツタに近いとみなすことができる 次に 図 8 において 枝の先端を見ると 枝同士が近付いた箇所では その先で離れるよ うに枝の生長方向が変わっていることが確認できる このことから 生長位置決定の処理で 用いた受光ベクトルによって 枝葉の影の少ない方向への生長が実現できたことが分かる 以上のことから 周囲の葉の影が多いところでは枝の分岐をせず 明るいところを求めて 枝を伸ばす性質が表現されたと考えられる また 補助物体のない右端では 付着できないまま長く伸びた枝が重みで傾く点 枝の先 端は屈地性に従って上向きになっている点が見て取れる このことから 枝が付着していな い場合の伸び方の変化が現れたと分かる 問題点として 枝同士が近付いても交差を回避できず 枝葉が重なり合う場合が挙げられ る 本物のツタでも枝が交差することは多いが 図 1 のように 枝同士がほぼ平行に伸びる ことで交差を避けており 必ずしも上に向かって伸びていない例もある この実験結果と実 6 c 2010 nformation rocessing Society of Japan
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