# Quaternions, Interpolation and Animation

@inproceedings{Dam2000QuaternionsIA, title={Quaternions, Interpolation and Animation}, author={Erik Bj{\o}rnager Dam and Martin Koch and Martin Lillholm}, year={2000} }

The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the well-known matrix implementations. We then treat di erent methods for interpolation between series of rotations. During this treatment we give complete proofs for the correctness of the important interpolation methods Slerp and Squad . Inspired by…

## 318 Citations

### Applications of Dual Quaternions in Three Dimensional Transformation and Interpolation

- Computer Science
- 2013

The findings show that while dual quaternions are useful in the context of skeletal animation, other applications may favour other representations, due to simplicity or speed.

### Dual Quaternions for Rigid Transformation Blending

- Computer Science
- 2006

This paper shows how to generalize established techniques for blending of rotations to include all rigid transformations, and demonstrates that problems which required considerable research effort recently are trivial to solve using the dual quaternion formulation.

### Efficient Representation and Derivation of Fundamental Transformation of Relationships using Euler Angles and Quaternions

- Mathematics
- 2019

This paper introduces and defines two principal rotational methods;the Euler angles and the quaternions
theories with a brief insight into their definitions and algebraic properties. These methods…

### High-Quality Mesh Deformation Using Quaternions for Orthogonality Preservation

- Mathematics
- 2014

Many mesh deformation techniques developed in the past have been widely used, but for large deformations, the mesh properties can be severely altered. In particular, the mesh lines orthogonality near…

### Rigid-Body Pose and Position Interpolation using Geometric Algebra

- Computer Science
- 2008

This paper presents the theory behind the interpolation and its description as a tool, and outlines the possible advantages of using this technique for vision and graphics applications.

### Modified Rodrigues Parameters: An Efficient Representation of Orientation in 3D Vision and Graphics

- Computer ScienceJournal of Mathematical Imaging and Vision
- 2017

A compelling case is presented for MRPs as a minimal degree-of-freedom parameterization of orientation through novel solutions to prominent problems in the fields of 3D vision and computer graphics and a novel approach for designing orientation splines by configuring their back-projections in 3D space is introduced.

### On the global interpolation of motion

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2018

### Quaternions and Rotations *

- Mathematics
- 2015

Up until now we have learned that a rotation in R3 about an axis through the origin can be represented by a 3×3 orthogonal matrix with determinant 1. However, the matrix representation seems…

### Embedding-Based Interpolation on the Special Orthogonal Group

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2018

This work studies schemes for interpolating functions that take values in the special orthogonal group $SO(n) by embedding in a linear space, interpolating in thelinear space, and mapping the result onto $SO (n) via the closest point projection via the nearest point projection.

### A quaternion-based continuation method to follow the equilibria and stability of slender elastic rods

- Engineering
- 2012

We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by…

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