In http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
is a formula what - with the following input values - will outputes an
orthogonal matrix and a vector rotation
s1=.sind 30
c1=.cosd 30
s2=.sind 45
c2=.cosd 45
s3=.sind 60
c3=.cosd 60
]R11=.c2*c3
0.353553
]R12=.(-c1*s3)+s1*s2*c3
_0.573223
]R13=.(s1*s3)+c1*s2*c3
0.739199
]R21=.c2*s3
0.612372
]R22=.(c1*c3)+s1*s2*s3
0.739199
]R23=.(-s1*c3)+c1*s2*s3
0.28033
]R31=.-s2
_0.707107
]R32=.s1*c2
0.353553
]R33=.c1*c2
0.612372
]R=.3 3$R11,R12,R13,R21,R22,R23,R31,R32,R33
0.353553 _0.573223 0.739199
0.612372 0.739199 0.28033
_0.707107 0.353553 0.612372
X=.+/ .*
w=.3 4 5
R X w
2.46376 6.19556 2.35475
In the Studio/Labs/rotations (with the same input values)
with the verbs
r=: (cosd , -@:sind) ,. (sind , cosd)
GR=: 4 : 0
res=: (i. =/ i.) 3 NB. Initialize res as identity matrix
p=: >0 1 2;1 0 2;1 2 0 NB. Permutations for axes
while. 0<# x do.
cp=. ('xyz'i.{:x){p NB. Current permutation
cr=. cp {"1 cp { 1 0 0,0 0,.r {: y NB. Current rotation
res =. cr X res
x=. }: x
y=. }: y
end.
res
)
there is the same numerical example, but instead of R there is as resultat
an other rotation matrix:
'xyz' GR 30 45 60
0.353553 0.612372 0.707107
_0.926777 0.126826 0.353553
0.126826 _0.78033 0.612372
instead of
]R=.3 3$R11,R12,R13,R21,R22,R23,R31,R32,R33
0.353553 _0.573223 0.739199
0.612372 0.739199 0.28033
_0.707107 0.353553 0.612372
After the refinement of verbs slightly we can get the same
resultats. Namenly
let be r=: (cosd , -@:sind) ,:(sind , cosd)
instead of r=: (cosd , -@:sind) ,. (sind , cosd)
and
GR=: 4 : 0
res=: (i. =/ i.) 3 NB. Initialize res as identity matrix
p=: >0 1 2;2 0 1;1 2 0 NB. Permutations for axes
while. 0<# x do.
cp=. ('xyz'i.{:x){p NB. Current permutation
cr=. cp {"1 cp { 1 0 0,0 0,.r {: y NB. Current rotation
res =. res X cr
x=. }: x
y=. }: y
end.
res
)
insted of
GR=: 4 : 0
res=: (i. =/ i.) 3 NB. Initialize res as identity matrix
p=: >0 1 2;1 0 2;1 2 0 NB. Permutations for axes
while. 0<# x do.
cp=. ('xyz'i.{:x){p NB. Current permutation
cr=. cp {"1 cp { 1 0 0,0 0,.r {: y NB. Current rotation
res =. cr X res
x=. }: x
y=. }: y
end.
res
)
Any opinion?
Istvan Kadar
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