rt_qinterp - interpolate unit-quaternions[view code]

Calling Sequence

qi = rt_qinterp(q1, q2, r)

QI = rt_qinterp(q1, q2, R)

Parameters

• q1 : quaternion object. It represents a first rotation.
• q2 : quaternion object. It represents a second rotation.
• r : scalar. It represents a "step" between the two rotations described by q1 and q2. It can vary between 0 and 1 inclusively.
• R : p-element vector (p is arbitrary). Each element in R represents a "step" between the two rotations described by q1 and q2. Each element in R can vary between 0 and 1 inclusively.
• qi : quaternion object. The interpolated unit quaternion.
• QI : p-element list. Each element in QI is the interpolated unit quaternion between q1 and q2, for the corresponding element in R.

Description

The first form returns a unit quaternion that interpolates between q1 and q2 as r varies between 0 and 1 inclusively. This is a spherical linear interpolation (slerp) that can be interpreted as interpolation along a great circle arc on a sphere.

The second form returns a list of quaternions corresponding to successive values of R.

Examples

   // To show how two rotations described by two unit quaternions can be
   // interpolated at different fractions between them, the following code
   // could be used.

   q1 = rt_quaternion(rt_rotx(0.3)),        // first rotation
   q2 = rt_quaternion(rt_roty(-0.5)),       // second rotation

   // slerp at r = 0 should return q1
   qi1 = rt_qinterp(q1, q2, 0),             // qi1 == q1

   // slerp at r = 1 should return q2
   qi2 = rt_qinterp(q1, q2, 1),             // qi2 == q2

   // slerp at r = 0.3
   qi3 = rt_qinterp(q1, q2, 0.3),

   // A more direct approach...
   QI = rt_qinterp(q1, q2, [0, 1, 0.3]),    // QI == list(qi1, qi2, qi3)

   // error handling
   QI = rt_qinterp(q1, q2, [0, 1.1, 0.3]),  // R(2) > 1

  

See Also

rt_quaternion,  

Authors

original Matlab version by

Peter I. Corke CSIRO Manufacturing Science and Technology

Scilab implementation by

Matteo Morelli Interdepartmental Research Center "E. Piaggio", University of Pisa

Bibliography

Corke, P.I. "A Robotics Toolbox for MATLAB", IEEE Robotics and Automation Magazine, Volume 3(1), March 1996, pp. 24-32

K. Shoemake, "Animating rotation with quaternion curves", in Proceedings of ACM SIGGRAPH, (San Francisco), pp. 245-254, The Singer Company, Link Flight Simulator Division, 1985.