A Fast and Accurate Algorithm for Computing SLERP

The SLERP of quaternions is a common operation in keyframe animation. The operation can be a significant bottleneck in an animation-heavy application. The standard implementation of SLERP for an FPU typically involves trigonometric function evaluations, divisions, and branching. Commonly available SIMD implementations will modify the standard implementation and obtain a moderate speed-up. This paper provides a novel approach to computing SLERP, using only multiplications and additions. The algorithm is based on ideas from Chebyshev polynomials, power series solutions for differential equations, and error balancing using the Chebyshev Equioscillation Theorem and the associated Remez Algorithm. Implementations are provided for the FPU and SIMD. When SLERPing a pair of quaternions in parallel using four time samples, performance measurements show a 10-fold acceleration per SLERP over the standard SLERP implementation on an FPU. Source code is available online.