login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

This says don't use LaTeX output.

fricas
)set output tex off
 
fricas
)set output algebra on

Rotation matrix

fricas
rotationX(alpha) == [[1,0,0],[0,cos(alpha),-sin(alpha)],[0,sin(alpha),cos(alpha)]]
Type: Void
fricas
rotationY(beta) == [[cos(beta),0,sin(beta)],[0,1,0],[-sin(beta),0,cos(beta)]]
Type: Void
fricas
rotationZ(gamma) == [[cos(gamma),-sin(gamma),0],[sin(gamma),cos(gamma),0],[0,0,1]]
Type: Void
fricas
rotation(alpha,beta,gamma) == rotationX(alpha)*rotationY(beta)*rotationZ(gamma)
Type: Void
fricas
rotation(alpha,beta,gamma)
fricas
Compiling function rotationX with type Variable(alpha) -> List(List(
      Expression(Integer)))
fricas
Compiling function rotationY with type Variable(beta) -> List(List(
      Expression(Integer))) 
   There are 31 exposed and 40 unexposed library operations named * 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op *
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named * 
      with argument type(s) 
                       List(List(Expression(Integer)))
                       List(List(Expression(Integer)))
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need. FriCAS will attempt to step through and interpret the code.
fricas
Compiling function rotationZ with type Variable(gamma) -> List(List(
      Expression(Integer))) 
(5) [[cos(beta)cos(gamma), - cos(beta)sin(gamma), sin(beta)],
[cos(alpha)sin(gamma) + cos(gamma)sin(alpha)sin(beta), - sin(alpha)sin(beta)sin(gamma) + cos(alpha)cos(gamma), - cos(beta)sin(alpha)] ,
[sin(alpha)sin(gamma) - cos(alpha)cos(gamma)sin(beta), cos(alpha)sin(beta)sin(gamma) + cos(gamma)sin(alpha), cos(alpha)cos(beta)] ]
Type: Matrix(Expression(Integer))

Transformation for a 3d point (x1,x2,x3) by rotation and translation (t1,t2,t3)

fricas
transform(x1,x2,x3,alpha,beta,gamma,t1,t2,t3) == rotation(alpha,beta,gamma) * [[x1],[x2],[x3]]+[[t1],[t2],[t3]]
Type: Void
fricas
m := transform(x1,x2,x3,alpha,beta,gamma,t1,t2,t3);
Cannot compile map: rotation We will attempt to interpret the code.
Type: Matrix(Expression(Integer))
fricas
p := [[(m(1,1)/m(3,1))-y1,m(2,1)/m(3,1)-y2]]*[[(m(1,1)/m(3,1))-y1],[m(2,1)/m(3,1)-y2]]
(8) [ [ 2 2 2 x2 sin(alpha) + 2 x2 y2 cos(alpha)sin(alpha) + 2 2 2 2 2 (x2 y2 + x2 y1 )cos(alpha) * 2 sin(beta) + 2 2 x1 x2 y2 sin(alpha) + 2 2 (2 x1 x2 y2 + 2 x1 x2 y1 - 2 x1 x2)cos(alpha)sin(alpha) + 2 2 2 x2 y1 cos(alpha)cos(beta) - 2 x1 x2 y2 cos(alpha) * sin(beta) + 2 2 2 2 2 (x1 y2 + x1 y1 )sin(alpha) + 2 (2 x1 x2 y1 cos(beta) - 2 x1 y2 cos(alpha))sin(alpha) + 2 2 2 2 x2 cos(beta) + x1 cos(alpha) * 2 sin(gamma) + 2 - 2 x1 x2 cos(gamma)sin(alpha) + - 4 x1 x2 y2 cos(alpha)cos(gamma)sin(alpha) + 2 2 2 (- 2 x1 x2 y2 - 2 x1 x2 y1 )cos(alpha) cos(gamma) + - 2 x2 x3 y1 cos(alpha) * 2 sin(beta) + 2 2 2 ((2 x2 - 2 x1 )y2 cos(gamma) + 2 x2 x3 cos(beta))sin(alpha) + 2 2 2 2 2 2 2 (2 x2 - 2 x1 )y2 + (2 x2 - 2 x1 )y1 - 2 x2 + 2 2 x1 * cos(alpha)cos(gamma) + 4 x2 x3 y2 cos(alpha)cos(beta) + 2 t3 x2 y2 - 2 x1 x3 y1 + - 2 t2 x2 * sin(alpha) + - 4 x1 x2 y1 cos(alpha)cos(beta) + 2 2 2 (- 2 x2 + 2 x1 )y2 cos(alpha) * cos(gamma) + 2 2 2 ((2 x2 x3 y2 + 2 x2 x3 y1 )cos(alpha) - 2 x2 x3)cos(beta) + 2 2 (2 t3 x2 y2 - 2 t2 x2 y2 + 2 t3 x2 y1 - 2 t1 x2 y1)cos(alpha) * sin(beta) + 2 2 ((2 x1 x2 y2 + 2 x1 x2 y1 )cos(gamma) + 2 x1 x3 y2 cos(beta)) * 2 sin(alpha) + 2 2 ((2 x2 - 2 x1 )y1 cos(beta) - 4 x1 x2 y2 cos(alpha)) * cos(gamma) + 2 2 (2 x1 x3 y2 + 2 x1 x3 y1 - 2 x1 x3)cos(alpha)cos(beta) + 2 2 2 t3 x1 y2 - 2 t2 x1 y2 + 2 t3 x1 y1 - 2 t1 x1 y1 * sin(alpha) + 2 2 (- 2 x1 x2 cos(beta) + 2 x1 x2 cos(alpha) )cos(gamma) + 2 2 x2 x3 y1 cos(alpha)cos(beta) + 2 (- 2 x1 x3 y2 cos(alpha) + 2 t3 x2 y1 - 2 t1 x2)cos(beta) + (- 2 t3 x1 y2 + 2 t2 x1)cos(alpha) * sin(gamma) + 2 2 2 x1 cos(gamma) sin(alpha) + 2 2 2 x1 y2 cos(alpha)cos(gamma) sin(alpha) + 2 2 2 2 2 2 (x1 y2 + x1 y1 )cos(alpha) cos(gamma) + 2 2 x1 x3 y1 cos(alpha)cos(gamma) + x3 * 2 sin(beta) + 2 (- 2 x1 x2 y2 cos(gamma) - 2 x1 x3 cos(beta)cos(gamma)) * 2 sin(alpha) + 2 2 2 (- 2 x1 x2 y2 - 2 x1 x2 y1 + 2 x1 x2)cos(alpha)cos(gamma) + - 4 x1 x3 y2 cos(alpha)cos(beta) - 2 t3 x1 y2 + - 2 x2 x3 y1 + 2 t2 x1 * cos(gamma) * sin(alpha) + 2 2 2 (2 x1 y1 cos(alpha)cos(beta) + 2 x1 x2 y2 cos(alpha) )cos(gamma) + 2 2 2 ((- 2 x1 x3 y2 - 2 x1 x3 y1 )cos(alpha) + 2 x1 x3)cos(beta) + 2 2 (- 2 t3 x1 y2 + 2 t2 x1 y2 - 2 t3 x1 y1 + 2 t1 x1 y1) * cos(alpha) * cos(gamma) + 2 - 2 x3 y1 cos(alpha)cos(beta) - 2 t3 x3 y1 + 2 t1 x3 * sin(beta) + 2 2 2 2 2 (x2 y2 + x2 y1 )cos(gamma) + 2 x2 x3 y2 cos(beta)cos(gamma) + 2 2 x3 cos(beta) * 2 sin(alpha) + 2 2 (- 2 x1 x2 y1 cos(beta) - 2 x2 y2 cos(alpha))cos(gamma) + 2 2 (2 x2 x3 y2 + 2 x2 x3 y1 - 2 x2 x3)cos(alpha)cos(beta) + 2 2 2 t3 x2 y2 - 2 t2 x2 y2 + 2 t3 x2 y1 - 2 t1 x2 y1 * cos(gamma) + 2 2 2 x3 y2 cos(alpha)cos(beta) + (2 t3 x3 y2 - 2 t2 x3)cos(beta) * sin(alpha) + 2 2 2 2 2 (x1 cos(beta) + x2 cos(alpha) )cos(gamma) + 2 - 2 x1 x3 y1 cos(alpha)cos(beta) + 2 (- 2 x2 x3 y2 cos(alpha) - 2 t3 x1 y1 + 2 t1 x1)cos(beta) + (- 2 t3 x2 y2 + 2 t2 x2)cos(alpha) * cos(gamma) + 2 2 2 2 2 2 (x3 y2 + x3 y1 )cos(alpha) cos(beta) + 2 2 (2 t3 x3 y2 - 2 t2 x3 y2 + 2 t3 x3 y1 - 2 t1 x3 y1)cos(alpha) * cos(beta) + 2 2 2 2 2 2 t3 y2 - 2 t2 t3 y2 + t3 y1 - 2 t1 t3 y1 + t2 + t1 / 2 2 2 x2 cos(alpha) sin(beta) + 2 x1 x2 cos(alpha)sin(alpha)sin(beta) + 2 2 x1 sin(alpha) * 2 sin(gamma) + 2 2 - 2 x1 x2 cos(alpha) cos(gamma)sin(beta) + 2 2 (2 x2 - 2 x1 )cos(alpha)cos(gamma)sin(alpha) + 2 2 x2 x3 cos(alpha) cos(beta) + 2 t3 x2 cos(alpha) * sin(beta) + 2 2 x1 x2 cos(gamma)sin(alpha) + (2 x1 x3 cos(alpha)cos(beta) + 2 t3 x1)sin(alpha) * sin(gamma) + 2 2 2 2 x1 cos(alpha) cos(gamma) sin(beta) + 2 - 2 x1 x2 cos(alpha)cos(gamma) sin(alpha) + 2 (- 2 x1 x3 cos(alpha) cos(beta) - 2 t3 x1 cos(alpha))cos(gamma) * sin(beta) + 2 2 2 x2 cos(gamma) sin(alpha) + (2 x2 x3 cos(alpha)cos(beta) + 2 t3 x2)cos(gamma)sin(alpha) + 2 2 2 2 x3 cos(alpha) cos(beta) + 2 t3 x3 cos(alpha)cos(beta) + t3 ] ]
Type: Matrix(Expression(Integer))




  Subject:   Be Bold !!
  ( 15 subscribers )  
Please rate this page: