Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Graphics Gems III
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
ARCBALL: a user interface for specifying three-dimensional orientation using a mouse
Proceedings of the conference on Graphics interface '92
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Visualization of rotation fields
VIS '97 Proceedings of the 8th conference on Visualization '97
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Quaternion Frame Approach to Streamline Visualization
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2006 Papers
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
Smolign: A Spatial Motifs-Based Protein Multiple Structural Alignment Method
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Quaternions play a vital role in the representation of rotations in computer graphics, primarily for animation and user interfaces. Unfortunately, quaternion rotation is often left as an advanced topic in computer graphics education due to difficulties in portraying the four-dimensional space of the quaternions. One tool for overcoming these obstacles is the quaternion demonstrator, a physical visual aid consisting primarily of a belt. Every quaternion used to specify a rotation can be represented by fixing one end of the belt and rotating the other. Multiplication of quaternions is demonstrated by the composition of rotations, and the resulting twists in the belt depict visually how quaternions interpolate rotation.This article introduces to computer graphics the exponential notation that mathematicians have used to represent unit quaternions. Exponential notation combines the angle and axis of the rotation into concise quaternion expression. This notation allows the article to present more clearly a mechanical quaternion demonstrator consisting of a ribbon and a tag, and develop a computer simulation suitable for interactive educational packages. Local deformations and the belt trick are used to minimize the ribbon's twisting and simulate a natural-appearing interactive quaternion demonstrator.