Introduction to theoretical kinematics
Introduction to theoretical kinematics
Advanced animation and rendering techniques
Advanced animation and rendering techniques
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Introduction to Robotics: Mechanics and Control
Introduction to Robotics: Mechanics and Control
Metric calibration of a stereo rig
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Automated Alignment of Robotic Pan-Tilt Camera Units Using Vision
International Journal of Computer Vision
Scene point constraints in camera auto-calibration: an implementational perspective
Image and Vision Computing
PalmSpace: continuous around-device gestures vs. multitouch for 3D rotation tasks on mobile devices
Proceedings of the International Working Conference on Advanced Visual Interfaces
Analyzing and evaluating markerless motion tracking using inertial sensors
ECCV'10 Proceedings of the 11th European conference on Trends and Topics in Computer Vision - Volume Part I
International Journal of Computer Vision
Comparing ICP variants on real-world data sets
Autonomous Robots
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3D rotations arise in many computer vision, computer graphics, and robotics problems and evaluation of the distance between two 3D rotations is often an essential task. This paper presents a detailed analysis of six functions for measuring distance between 3D rotations that have been proposed in the literature. Based on the well-developed theory behind 3D rotations, we demonstrate that five of them are bi-invariant metrics on SO(3) but that only four of them are boundedly equivalent to each other. We conclude that it is both spatially and computationally more efficient to use quaternions for 3D rotations. Lastly, by treating the two rotations as a true and an estimated rotation matrix, we illustrate the geometry associated with iso-error measures.