→ |
mx x == [[1,0,0],[0,cos(x),- sin(x)],[0,sin(x),cos(x)]]
|
→ |
my x == [[cos(x),0,sin(x)],[0,1,0],[- sin(x),0,cos(x)]]
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→ |
mz x == [[cos(x),- sin(x),0],[sin(x),cos(x),0],[0,0,1]]
|
→ |
mx(c)*mz(b)*mx(a)
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cos (b) | - cos (a)sin (b) | sin (a)sin (b) |
cos (c)sin (b) | - sin (a)sin (c) + cos(a)cos (b)cos (c) | - cos (a)sin (c) - cos (b)cos (c)sin (a) |
sin (b)sin (c) | cos (a)cos (b)sin (c) + cos(c)sin (a) | - cos (b)sin (a)sin (c) + cos(a)cos (c) |
→ |
mx(c)*my(b)*mx(a)
|
cos (b) | sin (a)sin (b) | cos (a)sin (b) |
sin (b)sin (c) | - cos (b)sin (a)sin (c) + cos(a)cos (c) | - cos (a)cos (b)sin (c) - cos (c)sin (a) |
- cos (c)sin (b) | cos (a)sin (c) + cos(b)cos (c)sin (a) | - sin (a)sin (c) + cos(a)cos (b)cos (c) |
→ |
my(c)*mx(b)*my(a)
|
- cos (b)sin (a)sin (c) + cos(a)cos (c) | sin (b)sin (c) | cos (a)cos (b)sin (c) + cos(c)sin (a) |
sin (a)sin (b) | cos (b) | - cos (a)sin (b) |
- cos (a)sin (c) - cos (b)cos (c)sin (a) | cos (c)sin (b) | - sin (a)sin (c) + cos(a)cos (b)cos (c) |
→ |
my(c)*mz(b)*my(a)
|
- sin (a)sin (c) + cos(a)cos (b)cos (c) | - cos (c)sin (b) | cos (a)sin (c) + cos(b)cos (c)sin (a) |
cos (a)sin (b) | cos (b) | sin (a)sin (b) |
- cos (a)cos (b)sin (c) - cos (c)sin (a) | sin (b)sin (c) | - cos (b)sin (a)sin (c) + cos(a)cos (c) |
→ |
mz(c)*my(b)*mz(a)
|
- sin (a)sin (c) + cos(a)cos (b)cos (c) | - cos (a)sin (c) - cos (b)cos (c)sin (a) | cos (c)sin (b) |
cos (a)cos (b)sin (c) + cos(c)sin (a) | - cos (b)sin (a)sin (c) + cos(a)cos (c) | sin (b)sin (c) |
- cos (a)sin (b) | sin (a)sin (b) | cos (b) |
→ |
mz(c)*mx(b)*mz(a)
|
- cos (b)sin (a)sin (c) + cos(a)cos (c) | - cos (a)cos (b)sin (c) - cos (c)sin (a) | sin (b)sin (c) |
cos (a)sin (c) + cos(b)cos (c)sin (a) | - sin (a)sin (c) + cos(a)cos (b)cos (c) | - cos (c)sin (b) |
sin (a)sin (b) | cos (a)sin (b) | cos (b) |
→ |
my(c)*mz(b)*mx(a)
|
cos (b)cos (c) | sin (a)sin (c) - cos (a)cos (c)sin (b) | cos (a)sin (c) + cos(c)sin (a)sin (b) |
sin (b) | cos (a)cos (b) | - cos (b)sin (a) |
- cos (b)sin (c) | cos (a)sin (b)sin (c) + cos(c)sin (a) | - sin (a)sin (b)sin (c) + cos(a)cos (c) |
→ |
mz(c)*my(b)*mx(a)
|
cos (b)cos (c) | - cos (a)sin (c) + cos(c)sin (a)sin (b) | sin (a)sin (c) + cos(a)cos (c)sin (b) |
cos (b)sin (c) | sin (a)sin (b)sin (c) + cos(a)cos (c) | cos (a)sin (b)sin (c) - cos (c)sin (a) |
- sin (b) | cos (b)sin (a) | cos (a)cos (b) |
→ |
mz(c)*mx(b)*my(a)
|
- sin (a)sin (b)sin (c) + cos(a)cos (c) | - cos (b)sin (c) | cos (a)sin (b)sin (c) + cos(c)sin (a) |
cos (a)sin (c) + cos(c)sin (a)sin (b) | cos (b)cos (c) | sin (a)sin (c) - cos (a)cos (c)sin (b) |
- cos (b)sin (a) | sin (b) | cos (a)cos (b) |
→ |
mx(c)*mz(b)*my(a)
|
cos (a)cos (b) | - sin (b) | cos (b)sin (a) |
sin (a)sin (c) + cos(a)cos (c)sin (b) | cos (b)cos (c) | - cos (a)sin (c) + cos(c)sin (a)sin (b) |
cos (a)sin (b)sin (c) - cos (c)sin (a) | cos (b)sin (c) | sin (a)sin (b)sin (c) + cos(a)cos (c) |
→ |
mx(c)*my(b)*mz(a)
|
cos (a)cos (b) | - cos (b)sin (a) | sin (b) |
cos (a)sin (b)sin (c) + cos(c)sin (a) | - sin (a)sin (b)sin (c) + cos(a)cos (c) | - cos (b)sin (c) |
sin (a)sin (c) - cos (a)cos (c)sin (b) | cos (a)sin (c) + cos(c)sin (a)sin (b) | cos (b)cos (c) |
→ |
my(c)*mx(b)*mz(a)
|
sin (a)sin (b)sin (c) + cos(a)cos (c) | cos (a)sin (b)sin (c) - cos (c)sin (a) | cos (b)sin (c) |
cos (b)sin (a) | cos (a)cos (b) | - sin (b) |
- cos (a)sin (c) + cos(c)sin (a)sin (b) | sin (a)sin (c) + cos(a)cos (c)sin (b) | cos (b)cos (c) |
→ |
|