bundle block adjustment with 3d natural cubic splines

+Du ′ ( t 1 + t 22)2r 11 t + Dv ′ ( t 1 + t 22)2r 21 t + Dw ′ ( t }1 + t 2)2r 31 t}2+ 1 2 f(t 2) − 1 2 {Du(t2 )r 11 t 2 + Dv(t 2 )r 21 t 2 + Dw(t 2 )r 31 t 2 }+Du ′ (t 2 )2r 11 t + Dv ′ (t 2 )2r 21 t + Dw ′ (t 2 )2r 31 t}]A 10 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 )r 11 t 3 + Dv(t 1 )r 21 t 3 + Dw(t 1 )r 31 t 3+Du ′ (t 1 )3r 11 t 2 + Dv ′ (t 1 )3r 21 t 2 + Dw ′ (t 1 )3r 31 t 2 }( ) t1 + t −1 {2 2+2fDu( t 1 + t 2)r 11 t 3 + Dv( t 1 + t 2)r 21 t 3222+Dw( t 1 + t 2)r 31 t 32+Du ′ ( t 1 + t 22)3r 11 t 2 + Dv ′ ( t 1 + t 22)3r 21 t 2 + Dw ′ ( t }1 + t 2)3r 31 t 2 }2+ 1 2 f(t 2) − 1 2 {Du(t2 )r 11 t 3 + Dv(t 2 )r 21 t 3 + Dw(t 2 )r 31 t 3 }+Du ′ (t 2 )3r 11 t 2 + Dv ′ (t 2 )3r 21 t 2 + Dw ′ (t 2 )3r 31 t 2 }]A 11 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 )r 12 + Dv(t 1 )r 22 + Dw(t 1 )r 32 }( ) t1 + t −1 {2 2+2fDu( t 1 + t 2)r 12 + Dv( t 1 + t 2)r 22 + Dw( t }1 + t 2)r 32 }2222+ 1 ]2 f(t 2) − 1 2 {+Du(t2 )r 12 + Dv(t 2 )r 22 + Dw(t 2 )r 32 }A 12 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 )r 12 t + Dv(t 1 )r 22 t + Dw(t 1 )r 32 t}Du ′ (t 1 )r 12 + Dv ′ (t 1 )r 22 + Dw ′ (t 1 )r 32 }( ) t1 + t −1 {2 2+2fDu( t 1 + t 222+Du ′ ( t 1 + t 22)r 12 + Dv ′ ( t 1 + t 22)r 12 t + Dv( t 1 + t 22)r 22 + Dw ′ ( t }1 + t 2)r 322+ 1 2 f(t 2) − 1 2 {Du(t2 )r 12 t + Dv(t 2 )r 22 t + Dw(t 2 )r 32 t}+Du ′ (t 2 )r 12 + Dv ′ (t 2 )r 22 + Dw ′ (t 2 )r 32 }]A 13 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 )r 12 t 2 + Dv(t 1 )r 22 t 2 + Dw(t 1 )r 32 t 2+Du ′ (t 1 )2r 12 t + Dv ′ (t 1 )2r 22 t + Dw ′ (t 1 )2r 32 t})r 22 t + Dw( t 1 + t 2)r 32 t}2107