rotationMatrix

PURPOSE ^

Performs different operations dealing with a rotation matrix

SYNOPSIS ^

function varargout=rotationMatrix(varargin)

DESCRIPTION ^

 Performs different operations dealing with a rotation matrix

 USAGE
  R = rotationMatrix( M )
  [u,theta] = rotationMatrix( R )
  R = rotationMatrix( theta )
  R = rotationMatrix( u )
  R = rotationMatrix( u, theta )

 INPUTS 1 - Finds the closest matrix to a given matrix M
  M       - 3x3 matrix

 INPUTS 2 - Extract the axis and the angle of a 3x3 rotation matrix
  R       - 3x3 Rotation matrix

 INPUTS 3 - Creates a 2x2 rotation matrix from an angle
  theta   - angle of rotation (radians)

 INPUTS 4 - Creates a 3x3 rotation matrix from a rotation vector
  u       - 1x3 or 3x1 axis of rotation - norm is theta

 INPUTS 5 - Creates a 3x3 rotation matrix from a rotation vector
  u       - axis of rotation
  theta   - angle of rotation (radians)

 INPUTS 6 - Creates a 3x3 rotation matrix from 3 angles (around fixed 
            axes)
  th1     - angle with respect to X axis
  th2     - angle with respect to Y axis
  th3     - angle with respect to Z axis

 INPUTS 7 - Creates the full 3x3 rotation matrix from its first 2 rows
  R       - 2x3 first two rows of the rotation matrix
  
 OUTPUTS 1,4,5,6,7
  R       - 3x3 rotation matrix

 OUTPUTS 2
  u       - axis of rotation
  theta   - angle of rotation (radians)

 OUTPUTS 3
  R       - 2x2 Rotation matrix

 EXAMPLE 1
  R3 = rotationMatrix( [0 0 1], pi/4 )+rand(3)/50
  R3r = rotationMatrix( R3 )
  [u,theta]  = rotationMatrix( R3r )

 EXAMPLE 2
  R3 = rotationMatrix( [0 0 1], pi/4 );
  [u,theta]  = rotationMatrix( R3 )

 EXAMPLE 3
  R3 = rotationMatrix( pi/4 )

 EXAMPLE 4
  R3 = rotationMatrix( [0 0 .5] )

 EXAMPLE 5
  R3 = rotationMatrix( [0 0 1], pi/4 )

 EXAMPLE 6
  R3 = rotationMatrix( pi/4,pi/4,0 )

 EXAMPLE 7
  R3 = rotationMatrix( pi/4,pi/4,0 )
  R3bis = rotationMatrix( R3(1:2,:) )

 See also

CROSS-REFERENCE INFORMATION ^

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