slerp

slerp (plural slerps)

1. Alternative form of SLERP
   • 1997, Ravi Ramamoorthi, Alan H. Barr, “Fast construction of accurate quaternion splines”, in Proceedings of the 24th annual conference of the Association for Computing Machinery:

     Shoemake [16] introduced the idea of interpolating rotations with quaternions, but the constructed curves (slerps) did not satisfy an obvious variational principle [21] as splines [2] do in flat space.

   • 2001 April, Samuel R. Buss, Jay P Fillmore, “Spherical averages and applications to spherical splines and interpolation”, in ACM Transactions on Graphics (TOG), volume 20, number 2:

     However, it should be possible to give more sophisticated spherical spline curves based on the de Castaljau method that are computed using multiple slerps between pairs of points and which work well for arbitrary knot positions (indeed, knot insertion methods for spline curves should suffice for this, cf Farin [1993])

   • 2002, G. Farin, J. Hoschek, M.-S. Kim, Handbook of Computer Aided Geometric Design, page 723:

     Unlike the slerp techniques, this approach produces motions with rational point trajectories, the socalled rational motions. In kinematical geometry, these motions had been studied since the end of the 19th century (5,43,52].

   • 2011, Zhigeng Pan, Adrian David Cheok, Wolfgang Müller, Transactions on Edutainment VI - Volume 6, page 173:

     The first describes the skeleton-driven deformation which is solved by spherical linear interpolation (slerp).

   • 2018, Chang Dau Yan, Wei-Hua Chieng, Shyr-Long Jeng, “Five-Axis Slerp for Tool-Orientation Planning in a Five-Axis CNC Machine”, in Journal of the Chinese Society of Mechanical Engineers, volume 39, number 6:

     The quaternion spherical linear interpolation method (slerp), which many researchers have adopted for numerical control, is inadequate for tool-axisorientation planning in general five-axis computer numerical control machines. This paper explains why the quaternion slerp method fails to achieve constant rotational speed.

slerp (third-person singular simple present slerps, present participle slerping, simple past and past participle slerped)

1. Alternative form of SLERP
   • 2007, X Li, “VQS Transformation with an Incremental Approach”, in Game-On Asia Conference Processing, Kyoto, Japan:

     In other words, E.3-1 says that the slerped quaternion qk can be computed by multiplication of k-th power of a constant quaternion qc and q0, where β=α/n and u is a unit vector defined by components of q0 and qn as u = (w0un – wnu0 + u0×un)/sin(α).

   • 2008, Mark Wesley, “Navigating Detailed Worlds with a Complex, Physically Driven Locomotion: NPC Skateboarder AI in EA's skate”, in Proceedings of the Fourth Artificial Intelligence and Interactive Digital Entertainment Conference:

     Board and skater orientations were slerped, and the velocity was re-computed back from the positional Hermite curve rather than being interpolated.

   • 2017, Huiwen Chang, Michael F Cohen, “Panning and zooming high-resolution panoramas in virtual reality devices”, in Proceedings of the 30th Annual ACM Symposium on User Interface Software and Technology:

     More specifically, the quaternion representing the currently reported head position, Q∗(t), is slerped (linearly interpolated in quaternion space) with the most recent quater- nion used for rendering, Qt−1.

• LPers, Sperl, lerps