Animating rotation with quaternion curves

By Ken Shoemake. 1985

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Model Architectures

Citations in the corpus

A Style-Based Generator Architecture for Generative Adversarial Networks (2018, background): “Here slerp denotes spherical interpolation [52], which is the most appropriate way of interpolating in our normalized input latent space [56].”
Denoising Diffusion Implicit Models (2020, methodology): “Denoising diffusion probabilistic models (DDPMs, Sohl-Dickstein et al. (2015); Ho et al.”
GAN Inversion: A Survey (2021, background): “Typically, slerp(·) in Z denotes spherical interpolation [63], which is the most appropriate way of interpolating in the normalized input latent space [64].”
Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models (2022, methodology): “We choose spherical linear interpolation (SLERP(x, y, α), where we interpolate from x to y by a factor of α ∈ [0, 1]) [35].”
A bonded-particle model for cemented sand (2013, background): “A quaternion can be converted into a rotation matrix that describes the same rotation by [48]”
Sigma-point kalman filters for probabilistic inference in dynamic state-space models (2004, background): “This representation is however subject to a unit norm constraint [175].”
BioMistral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains (2024, methodology): “Among these methods, we can cite TIES (Ya-dav et al., 2023), DARE (Yu et al., 2024), and SLERP (Shoemake, 1985).”
Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs (2015, methodology): “A simple 2D visualization of LERP and SLERP mapping processes is shown in Figure 4.”
View morphing (1996, methodology): “Alternatively, if the orientations are expressed using quaternions, the interpolation is computed by spherical linear interpolation [13].”
QuaterNet: A Quaternion-based Recurrent Model for Human Motion (2018, methodology): “For quaternions, the predicted deltas are applied to the input quaternions through quaternion product [48] (QMul block in Figure 1).”
Multi-View Video Plus Depth Representation and Coding (2007, methodology): “This is achieved by using spherical linear interpolation [ 12 ], which originates from the context of quaternion curves.”
Building efficient, accurate character skins from examples (2003, methodology): “This is done by examining the rotation of a joint relative to the dress pose and computing the new joint as the halfway spherical linear interpolation [Shoemake 1985] of this rotation, located at the same position in space.”
Visualizing quaternions (2005, methodology): “• Shoemake (Siggraph ’85) proposed using quaternions instead of Euler angles to get smooth frame interpolations without Gimbal Lock : BESTCHOICE:Animateobjectsandcamerasusingro-tationsrepresentedon S 3 byquaternions 49”
Eval all, trust a few, do wrong to none: Comparing sentence generation models (2018, methodology): “3 and 4, we show the outputs obtained by encoding two sentences from the test set and using spherical linear interpolation (Slerp; Shoemake, 1985) to generate sentences ‘in between’.”
Physically Based Modeling Rigid Body Simulation (1992, background): “For a number of reasons, unit quaternions, a type of four element vector normalized to unit length, are a better choice than rotation matrices[16].”