Sory, I forgot to tell you a great thanks for the code. ;-) Alan Bromborsky a écrit : > projetmbc wrote: > >> Hello, >> is-it possible to use quaternions with sympy ? >> >> Christophe. >> >> >> >> > Look at - > > http://docs.sympy.org/modules/galgebra/GA/GAsympy.html > > and - > > http://www.mrao.cam.ac.uk/~clifford/introduction/intro/intro.html > > quaternions are the even sub-algebra of the 3D geometric algebra. See > section on > quaternions in introGA.pdf. To do 3D rotations we have the following code > > #!/usr/bin/python > > import sys > from sympy.galgebra.GA import * > from sympy.galgebra.latex_ex import * > from sympy import * > > set_main(sys.modules[__name__]) > > if __name__ == '__main__': > > metric = '1 0 0,'+\ > '0 1 0,'+\ > '0 0 1' > > vars = make_symbols('x y z alpha') > MV.setup('e',metric,True,vars[:-1]) > Format() > I = MV(1,'pseudo') > I.convert_to_blades() > print '$I$ Pseudo-Scalar' > print 'I =',I > u = MV('u','vector') #axis of rotation (unit vector) > v = MV('v','vector') #vector to be rotated > > print 'u =',u > print 'v =',v > U = I*u #quaternion defining plane of rotation > print 'U =',U > R = cos(alpha/2)+sin(alpha/2)*U #This is a quaternion > print 'R =',R > print 'R^{\\dagger} =',R.rev() > vp = R*v*R.rev() > vp.simplify() > MV_format(3) > print 'RvR^{\\dagger} =',vp > xdvi('rotate.tex') > > The output of the code is in the rotate.dvi file. This can be read with > 'xdvi' (I am assuming a linux system). I did not convert to pdf since > the right side of the equations get clipped at the page edge. With xdvi > you can just widen the window until you see the whole equation. If you > run the program without having latex or xdiv simple text output will > result and look ugly. Note that 'u' is the rotation axis (u*u = 1), > alpha the rotation angle, and 'v' the vector being rotated. > > Note that with geometric algebra it is just as easy to do rotations in > N-dimensions! > > > > > > > > > >
--~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
