AbsoluteAngles

Description

This model determines the 3 angles to rotate the world frameinto frame_a along the axes defined by parameter sequence.For example, if sequence = {3,1,2} then the world frame isrotated around angles[1] along the z-axis, afterwards it is rotatedaround angles[2] along the x-axis, and finally it is rotated aroundangles[3] along the y-axis and is then identical to frame_a.The 3 angles are returned in the range

    -p <= angles[i] <= p

There are two solutions for "angles[1]" in this range.Via parameter guessAngle1 (default = 0) thereturned solution is selected such that |angles[1] - guessAngle1| isminimal. The transformation matrix between the world frame andframe_a may be in a singular configuration with respect to "sequence", i.e.,there is an infinite number of angle values leading to the same relativetransformation matrix. In this case, the returned solution isselected by setting angles[1] = guessAngle1. Then angles[2]and angles[3] can be uniquely determined in the above range.

The parameter sequence has the restriction thatonly values 1,2,3 can be used and that sequence[1] ≠ sequence[2]and sequence[2] ≠ sequence[3]. Often used values are:

  sequence = {1,2,3}  // Cardan or Tait-Bryan angle sequence           = {3,1,3}  // Euler angle sequence           = {3,2,1}