加速度センサを用いた図形入力

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1 ( ) 2/Sep : ( ) 2. : t a 0, a 1,..., a ( ) v 0 t v 0, v 1,..., v n ( ) p 0 t p 0, p 1,..., p n+1 3 Kentaro Yamaguchi@bandainamcogames.co.jp 1

2 ( ) a i g a i g v 1,..., v n v 0 v i+1 = v i + t (a i g) (1) p 1,..., p n+1 p 0 v 1 = v 0 + t (a 0 g) p i+1 = p i + t v i (2) v 2 = v 1 + t (a 1 g) = v 0 + t (a 0 + a 1 ) 2 t g. i 1 v i = v 0 + t a k i t g (3). v n = v 0 + t a k n t g p 1 = p 0 + t v 0 p 2 = p 1 + t v 1 = p 0 + t(v 0 + v 1 ) = p t v 0 + t 2 (a 0 g). i 1 p i = p 0 + t v k i 2 = p 0 + i t v 0 + t 2 (i k 1)a k. p n+1 = p 0 + t n v k = p 0 + (n + 1) t v 0 + t 2 (n k)a k s 1, s 2 i(i 1) t 2 g (4) 2 t 2 g 2 s 1 = a k (5) s 2 = (n k)a k (6) 2

3 s 1, s 2 v n, p n+1 v n = v 0 + t s 1 n t g (7) p n+1 = p 0 + (n + 1) t v 0 + t 2 s 2 t 2 g (8) ( ) (7), (8), (9), (10) g, v 0 p 0 = p n+1 = 0 (9) v n = 0 (10) g = 2 n s 2 1 s 2 (11) ( v 0 = t s 1 2 ) n + 1 s 2 (12) (9), (11), (12) (4) p i p i ( ) 3 (4) (1), (2) (11) g p i g 4 (0G ) e e a i g e g g g g = g + e (13) 5 ( 1) 3 4 3

4 p e p 0 = 0 (14) p n+1 = p e (15) v n = 0 (16) p e = 0 3 (7), (8), (14), (15), (16) g, v 0 g = 2 n s 2 1 s 3 (17) ( v 0 = t s 1 2 ) n + 1 s 3 (18) s 3 = s 2 p e t 2 (19) (14), (17), (18) (4) p i v n = 0 p n = p n+1 p n+1 p 0,..., p n p e (8), (20), (21), (22) g g = p 0 = 0 (20) p n+1 = p e (21) v 0 = 0 (22) 2 s 3 (23) (20), (22), (23) (4) p i v 0 = 0 p 0 = p 1 p 0 p 1,..., p n+1 4

5 (7), (25) g p 0 = 0 (24) v 0 = v n = 0 (25) g = 1 n s 1 (26) (24), (25), (26) (4) p i v 0 = v n = 0 p 0 = p 1, p n = p n+1 p 0, p n+1 p 1,..., p n 6 ( 2) p e p 0 = 0 (27) p n+1 = p e (28) v 0 = v n = 0 (29) 1 (3 1 3 ) 2 p 0 = 0, p n+1 = p e, v n = p e i (i = 0,..., n + 1) p 0 = 0, p n+1 = p e, v 0 = p s i (i = 0,..., n + 1) pe i i (n + 1 ) i p s i p s i pe i p e i, ps i v 0 = v n = 0 5

6 p 0 = p 1, p n = p n+1 p 0, p n+1 p e 1,..., p e n ps 1,..., p s n pb 0,..., p b p b i = i pe i+1 + (n i 1)ps i+1 n 1 (30) p e i+1 ps i+1 i : (n i 1) pb i p b 0 = p s 1 = 0 p b = p e n = p e ( 0) (17) g e 5.2 ( 0) (23) g s g e = 2 n s 2 1 s 3 (31) g s 2 = s 3 (32) g b g b = (g e + g s ) / 2 = 1 n s 1 (33) ( 1) 0 ( 2) ( 3) p e i, ps i (30) pb i p e i ps i p b i (34), (35) v b i+1 = v b i + t a b i (34) p b i+1 = p b i + t v b i (35) a b i = ( v b i+1 v b i ) / t (36) v b i = ( p b i+1 p b i) / t (37) 6

7 1: 0 2: 0 3: 7

8 4: 0 5: 0 6: 8

9 (30), (36), (37) v0 b ab i [ v0 b = t a ] n s 6 1 s 3 (38) a b i = a i+1 2(3i n + 4) 6(2i n + 3) s 1 + n(n 1) n(n 1)(n + 1) s 3 (39) v b 0, a b i (34) vb 1,..., v b n 2 pb 0 = 0 (35) p b 1,..., p b (2 ) A 6.1 p e i ps i a i a i 9

10 p e i a k (k = 0,..., n 1) 1 a k c i,k c i,k (k + 1)(i n)(i n 1) t 2 (0 k i 2) c i,k = (40) i(n 2 2kn n + ik k + i 1) t 2 (i 1 k n 1) p s i a k (k = 0,..., n 1) 1 a k d i,k d i,k (n i + 1)(kn in + n + ik) t 2 (0 k i 2) d i,k = (41) i(i 1)(n k) t 2 (i 1 k n 1) p e i ps i α i : (1 α i ) p m i p m i = α i p e i + (i α i )p s i (42) a i ( ) σ a D(), ( 2 ) D 2 () p m i D 2 (p m [ ] 2 i ) = [αi c i,k + (1 α i )d i,k ] σ a (43) D 2 (p m i ) α i α i d dα i D 2 (p m i ) = 0 (44) α i = i 1 n 1 α i i α i p m i p i p i (45) p i = [(i 1)p e i + (n i)p s i ] / (n 1) (46) D 2 (p i ) = i(i 1)(n i)(n i + 1)(2ni 2i2 n + 2i + 1) t 4 σa 2 (47) 6n(n 1)(n + 1) p e i, ps i D 2 (p e i ) = (c i,k σ a ) 2 = i(n i)(n i + 1)(2ni 2i2 + i + 1) t 4 σa 2 (48) 6 D 2 (p s i ) = (d i,k σ a ) 2 = i(i 1)(n i + 1)(2ni 2i2 n + 3i) t 4 σa 2 (49) 6 10

11 p i, pe i, ps i 7 D(p i ) D(pe i ), D(ps i ) 7: 11

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