2010 M0107432
2010 : M0107432 3 3 CG 3DCG 3 3
1 1 1.1............................ 1 1.2.............................. 2 2 3 2.1................................. 3 2.2 3........................ 4 2.3................................. 5 2.4................................. 5 3 7 3.1.............................. 7 3.1.1..................... 8 3.1.2..................... 8 3.2............................. 9 3.2.1.......................... 10 3.2.2......................... 10 3.3.............. 11 3.3.1..................... 11 3.3.2........................ 12 3.3.3......................... 13 3.3.4........................ 14 4 16 4.1......................... 17 4.2............................... 18 4.3.............................. 19 5 21 5.1................................... 21 5.1.1................... 21 5.1.2...................... 24 I
5.1.3......................... 26 5.2......................... 28 5.3................................... 30 6 33 34 35 II
2.1............................. 6 3.1.............................. 10 3.2............................. 11 3.3............................. 13 3.4.................. 15 3.5............................... 15 4.1............................... 16 4.2............................. 17 4.3.................... 18 4.4............................. 19 4.5............................ 20 5.1................... 22 5.2 3.................. 22 5.3 60.................... 23 5.4 3.................. 23 5.5 5.................. 24 5.6 S......................... 25 5.7 S......................... 25 5.8............................... 26 5.9....................... 27 5.10 N.............................. 28 5.11............................. 30 5.12..................... 32 III
1 1.1 3 3DCG 3DCG 3DCG 3 3 3 3 [1] [2] 3DCG 1
3 Autodesk Maya 3 [3] [4][5] [6] 3 1.2 6 2 3 4 5 6 2
2 2.1 [7] 3 [1] [8] 3
2.2 3 3 [9][10] 3 2 3 4
2.3 3DCG CG 3DCG [11] [12] CG CG [13] [14] 3D 2.4 3DCG 5
2.1 2.1: 6
3 3DCG 3 3.1 3DCG 1. 2. 7
3. 4. 5. 6. 3.1.1 Bezier Bezier 3.1.2 8
3.2 3 3DCG [15][16][17] [18][19] 3.2.1 3.2.2 9
3.2.1 1 3.1 3.1: 3.1 3.2.2 1 3.2 10
3.2: 3.2 3.3 3.3.1 3.3.2 3.3.1 Bezier B 0, B 1,, B n 1 (3.1) P(t) = N 1 i=0 B i J (N 1)i (t) (3.1) J ni (t) Bernstein ( ) n J ni (t) = t i (1 t) n 1 (3.2) i 0 t 1 B 0 B N 1 11
3.3.2 Bezier 2 Bezier 5 Bezier Bezier t t 2 k r 1 k 0 t 1 P s x θ P k (3.3) k = lim θ 0 y = f(x) (3.4) θ (3.3) s k = y ) 3, r = (1 1 + (y ) 2 2 k (3.4) x = x(t), y = y(t) (3.5) x (t)y (t) x (t)y (t) k = ) 3, r = ((x 1 (t)) 2 + (y (t)) 2 2 k (3.5) 12
3.3.3 [15] [16] 3.3 3.3: 3.3 1 6 n 2n 1 1 13
6 3.3.4 3.4 3 XZ P = (P x, 0, P z ), Q = (Q x, 0, Q z ) R = (0, R y, 0) R = P Q P, Q P Q Y Q P R y > 0 R y < 0 3.5 3 14
3.5 3.4: 3.5: 15
4 3D Fine Kernel Toolkit System[20] 4.1 4.1: 16
4.1 4.2 X 100 Y 10 Z 100 4.2: 3 17
4.3 Bezier 4.3: 4.2 3 18
4.4 4.4 4.4: 4.3 19
4.5 4.5: 20
5 5.1 2 1 S 2 S S 2 5.1.1 S 5 5 60 1 1 5.1 5.5 21
図 5.1: 基本形状と初期値による変形結果 図 5.2: 深さを 3 に変更した場合の変形結果 22
5.3: 60 5.4: 3 23
5.5: 5 5.1.2 S S 2 2 5.6 5.7 24
図 5.6: 急な S 字カーブの場合 図 5.7: 緩い S 字カーブの場合 25
5.1.3 S 5.8 5.8: 26
5.9 5.8 5.9: 5.10 N N N 27
5.10: N 5.2 20 28
4 D 3D 2 20 11 D D 5 29
5.11: 5.11 4 3D 4 4 5.3 3 30
D 3 5.12 31
5.12: 32
6 3 3 33
34
[1].., Vol. 24, pp. 5 14, 2005. [2].., 2004. [3] Autodesk Inc. Autodesk Maya. http://www.autodek.co.jp. [4],,,.., Vol. vol.100, pp. 103 110, 2001. [5] Nayuko Watanabe,Takeo Igarasi. A sketching interface for terrain modeling. SIGGRAPH, Vol. poster,, 2004. [6].., 2002. [7].. 1995. [8],.., Vol. 6, pp. 25 30, 2000. [9].., http://rikanet2.jst.go.jp/contents/cp0220d/start.html. [10].., 2005. [11]. cg. pp. 1 12, 2001,8. 35
[12],,.. 615, pp. 2 9, 2004,8. [13],,,. Cg. pp. 1 4. [14],,.., pp. 115 120, 2008,2. [15],. Mathematical morphology., p. 2, 1999. [16],,,,.. p. 10. [17],,. 3. (D-2), Vol. J84-D-2, pp. 778 788, 2001. [18],. x ct., Vol. vol.5, pp. 24 27, 2001. [19],,. 3., Vol. J84-D-2, pp. 843 850, 2001. [20]. FK System Ver.2.8.9. http://fktoolkit.sourceforge.jp/. 36