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

2007 3DCG M0104402

2007 3DCG : M0104402 3DCG 3DCG 3DCG 3D (huristic method) C++

1 1 1.1............................ 1 1.2.............................. 3 2 4 2.1......................... 4 2.2.................... 4 3 9 3.1 3D....................... 9 3.2......................... 11 3.2.1................... 11 3.2.2............................. 13 3.2.3.................... 16 3.2.4......................... 18 3.2.5........................... 18 4 19 5 23 24 25 I

2.1 2............................. 5 2.2................... 5 2.3.................... 6 2.4.............. 6 2.5......................... 7 2.6....................... 7 2.7.......................... 8 2.8.......................... 8 3.1 3D............................. 10 3.2............................. 10 3.3............................... 12 3.4 i................... 13 3.5............................ 15 3.6............. 16 3.7................ 17 4.1............................... 20 4.2 IK................................ 20 4.3.............................. 20 4.4............................. 20 4.5............................... 20 4.6............................... 20 4.7................................. 20 4.8............................... 21 4.9 IK................................ 21 4.10............................... 21 4.11.............................. 21 4.12............................... 21 4.13............................... 21 4.14............................ 22 II

1 1.1 3DCG [1] 3DCG [2][3][4] Born Digital CAT(Character Animation Technologies)[5] CAT 3dMax CAT [6] 1

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

1 1 3 (huristic method) 2 FK[10] 1.2 2 3 4 5 3

2 2.1 2 (African Elephant) (Elephas Maximus) [11] 2.1 [12] 2.2 2 4

2.1: 2 2.2 2.3 2.4 2.5 2.2: 10cm 2.6 5

2.3: 2.4: 2.7 2.8 8 6

2.5: 2.6: 7

2.7: 2.8: 8

3 3.1 3D 3D 21 3.1 3D 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

P 0 25 3.2 3D 3.1: 3D 3.2: 10

3.2 3.2.1 (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

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

3.4: i 3.2.2 (Heuristic Method) θ 1 3.1 P 0 i P i 13

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

X Z 3.5 3.6 3.5: 15

3.6: 2 P 20 P food 3.2.3 P food 3 P 0 P 13 P 14 P 16 P 17 P 19 3 Q 1 Q 2 Q 3 3.7 3 r P food (x, y, z) (x food, y food, z food ) 16

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

3.2.4 [18][19] 3 2 2 [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) 3.2.5 0 18

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.1 4.2 IK(Inverse Kinematics) 4.3 4.4 4.5 4.6 4.7 19

4.1: 4.2: IK 4.3: 4.4: 4.5: 4.6: 4.7: 4.8 4.9 4.10 4.11 4.12 4.13 4.8 4.9 IK 4.10 IK 4.11 4.12 4.13 20

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

4.14: 22

5 (Heuristic Method) 1 IK 23

24

[1], 2004-2005,, 2005. [2],,, No7, 287-294, 1984. [3] Petros Faloutsos, Michiel van de Panne, Demetri Terzopoulos3, Composable Controllers for Physics-Based Character Animatio, SIGGRAPH, 2001. [4] Harold C. Sun, Dimitris N. Metaxas, Automating gait generation, SIGGRAPH, 2001. [5] Born Digital CAT, <http://www.borndigital.co.jp/software/cat/>. [6],?,, 2002. [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, 2004. 25

[10], FK Tool Kit System, <http://www.media.teu.ac.jp/~earth/fk/>. [11] DK, 4 ANIMALS,, 1993. [12], 42,, 1994. [13],,, C MAGAZINE, 110-115, 7, 2001. [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, 1994. [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, 1996. [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,, 2002. [19], 3D-CG,,2004. [20], 3DCG,, 2006. 26