2007 3DCG : M DCG 3DCG 3DCG 3D (huristic method) C++

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1 2007 3DCG M

2 2007 3DCG : M DCG 3DCG 3DCG 3D (huristic method) C++

3 D I

4 D i IK IK II

5 DCG [1] 3DCG [2][3][4] Born Digital CAT(Character Animation Technologies)[5] CAT 3dMax CAT [6] 1

6 3D CG [7][8] [9] CG 2

7 1 1 3 (huristic method) 2 FK[10]

8 (African Elephant) (Elephas Maximus) [11] 2.1 [12]

9 2.1: : 10cm 2.6 5

10 2.3: 2.4:

11 2.5: 2.6: 7

12 2.7: 2.8: 8

13 D 3D D 5 : 1 P 0 P 20 P i w i (3.1) P i P i+1 l i i+1 (3.2) w i = w 0 ( 1 5 ) i 20 (3.1) l i i+1 = w i 2 (3.2) 9

14 P D 3.1: 3D 3.2: 10

15 (Inverse Kinematics)[13][14] 3 [15][16] θ X X = f(θ) θ = f 1 (X) θ (Iterative Solution) 2 [17] (Heuristic Method) i L i L i L i 1 P i P end P goal P end P goal (3.3) E = P goal P end (3.3) Li P i θ P end P i P goal P i 3.3 Li 11

16 θ θ 2 P end P i P goal P i [?] L i 1 L i 2 P end P i 1 P goal P i 1 θ L 1 0 L i 3.4 L i L i 1 θ 3.3: 12

17 3.4: i (Heuristic Method) θ P 0 i P i 13

18 P 20 P i θ i (3.4) i θ i = ai (3.4) a P food 3 P food P i P 20 P food P 20 ( ) ( ) 2 (3.5) (x i, y i, z i ) = (P 20 P i ) (P food P i ) (3.5) P i θ hi θ pi (3.6)(3.7) ai (z i > 0) θ hi = ai (z i < 0) 0 ( ) ( ) ( ) ai (x i > 0) (y i < 0) (x i < 0) (y i > 0) ( ) ( ) θ pi = ai (x i > 0) (y i > 0) (x i < 0) (y i < 0) 0 ( ) (3.6) (3.7) 14

19 X Z : 15

20 3.6: 2 P 20 P food P food 3 P 0 P 13 P 14 P 16 P 17 P 19 3 Q 1 Q 2 Q r P food (x, y, z) (x food, y food, z food ) 16

21 3 Q 1 (x food 2r, y food, z food +2.5r) Q 2 (x food, y food, z food 2.1r) Q 3 (x food + 1.8r, y food, z food 0.5r) 3.7: (3.8) (P 14 P i ) (Q 1 P i ) (0 i 13) (P 17 P i ) (Q 2 P i ) (14 i 16) (P 20 P i ) (Q 3 P i ) (17 i 19) (3.8) P 20 P food P food y Q 1 Q 2 Q 3 17

22 3.2.4 [18][19] [20] A B Q a Q b (3.9) Q(t) = (1 t)q a + tq b (1 t)q a + tq b (3.9)

23 IK(Inverse Kinematics)

24 4.1: 4.2: IK 4.3: 4.4: 4.5: 4.6: 4.7: IK 4.10 IK

25 4.14 IK 4.8: 4.9: IK 4.10: 4.11: 4.12: 4.13: 21

26 4.14: 22

27 5 (Heuristic Method) 1 IK 23

28 24

29 [1], ,, [2],,, No7, , [3] Petros Faloutsos, Michiel van de Panne, Demetri Terzopoulos3, Composable Controllers for Physics-Based Character Animatio, SIGGRAPH, [4] Harold C. Sun, Dimitris N. Metaxas, Automating gait generation, SIGGRAPH, [5] Born Digital CAT, <http://www.borndigital.co.jp/software/cat/>. [6],?,, [7] CGWORLDvol.32,,2001. [8],!,,2004. [9] Adam Kirk, James F. O Brien, David A. Forsyth, Skeletal Parameter Estimation from Optical Motion Capture Data, SIGGRAPH,

30 [10], FK Tool Kit System, <http://www.media.teu.ac.jp/~earth/fk/>. [11] DK, 4 ANIMALS,, [12], 42,, [13],,, C MAGAZINE, , 7, [14] Jeff Landar, Game Developer Magazine,Sep 1998 Sep,1998 Nov, <http://darwin3d.com/>. [15] Monacha D and Zhu Y, A Fast Algorithm and System for the Inverse Kinematics of General Serial Manipulators, IEEE International Conference on Robotics and Automation, [16] Chin K, Closed-Form and Generalized Inverse Kinematic Solutions for Animating the Human Articulated Structure, Bachelor s Thesis in Computer Science, Curtin University of Technology, [17] Welman Chris, Inverse Kinematics and Geometric Constraints for Articulated Figure Manipulation, <http://fas.sfu.ca/pub/cs/theses/1993/chriswelmanmsc.ps.gz>. [18] EricLengyel, 3D,, [19], 3D-CG,,2004. [20], 3DCG,,

[2] 2. [3 5] 3D [6 8] Morishima [9] N n 24 24FPS k k = 1, 2,..., N i i = 1, 2,..., n Algorithm 1 N io user-specified number of inbetween omis

[2] 2. [3 5] 3D [6 8] Morishima [9] N n 24 24FPS k k = 1, 2,..., N i i = 1, 2,..., n Algorithm 1 N io user-specified number of inbetween omis 1,a) 2 2 2 1 2 3 24 Motion Frame Omission for Cartoon-like Effects Abstract: Limited animation is a hand-drawn animation style that holds each drawing for two or three successive frames to make up 24 frames

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