Two moving coordinate frames for sweeping along a 3D trajectory
Computer Aided Geometric Design
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Calculation of reference frames along a space curve
Graphics gems
Visualizing n-dimensional virtual worlds with n-vision
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Worlds within worlds: metaphors for exploring n-dimensional virtual worlds
UIST '90 Proceedings of the 3rd annual ACM SIGGRAPH symposium on User interface software and technology
Some techniques for visualizing surfaces in four-dimensional space
Computer-Aided Design - Beyond solid modelling
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
Interactive manipulation and display of surfaces in four dimensions
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Geometry for n-dimensional graphics
Graphics gems IV
Graphics gems IV
Graphics gems IV
Illumination in diverse codimensions
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Visualizing quaternion rotation
ACM Transactions on Graphics (TOG)
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Constrained optimal framings of curves and surfaces using quaternion Gauss maps
Proceedings of the conference on Visualization '98
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A computer technique for displaying n-dimensional hyperobjects
Communications of the ACM
A study in interactive 3-D rotation using 2-D control devices
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Quaternion Frame Approach to Streamline Visualization
IEEE Transactions on Visualization and Computer Graphics
Illuminating the Fourth Dimension
IEEE Computer Graphics and Applications
Practical parameterization of rotations using the exponential map
Journal of Graphics Tools
VIS '95 Proceedings of the 6th conference on Visualization '95
An Automatic Method For Determining Quaternion Field Boundaries for Ball-and-Socket Joint Limits
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
Visualizing the fourth dimension using geometry and light
VIS '91 Proceedings of the 2nd conference on Visualization '91
Four-dimensional views of 3D scalar fields
VIS '92 Proceedings of the 3rd conference on Visualization '92
Orientation maps: techniques for visualizing rotations (a consumer's guide)
VIS '93 Proceedings of the 4th conference on Visualization '93
Interactive visualization methods for four dimensions
VIS '93 Proceedings of the 4th conference on Visualization '93
Visualizing flow with quaternion frames
VIS '94 Proceedings of the conference on Visualization '94
Virtual reality performance for virtual geometry
VIS '94 Proceedings of the conference on Visualization '94
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
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This intermediate-level tutorial provides a comprehensive approach to the visualization of quaternions and their relationships to computer graphics and scientific visualization. The introduction focuses on a selection of everyday phenomena involving rotating objects whose explanation is essentially impossible without a quaternion visualization. The presentation will then pursue selected examples of quaternion-based visualization methods to help explain the behavior of quaternion manifolds: quaternion representations of orientation frames attached to curves, surfaces, and volumes.