Graphics Gems III
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
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
Illuminating the Fourth Dimension
IEEE Computer Graphics and Applications
Visualizing the fourth dimension using geometry and light
VIS '91 Proceedings of the 2nd conference on Visualization '91
Constructing stream surfaces in steady 3D vector fields
VIS '92 Proceedings of the 3rd conference on Visualization '92
Interactive visualization methods for four dimensions
VIS '93 Proceedings of the 4th conference on Visualization '93
Virtual reality performance for virtual geometry
VIS '94 Proceedings of the conference on Visualization '94
Visualization of rotation fields
VIS '97 Proceedings of the 8th conference on Visualization '97
Interactive deformations from tensor fields
Proceedings of the conference on Visualization '98
Constrained optimal framings of curves and surfaces using quaternion Gauss maps
Proceedings of the conference on Visualization '98
Quaternion Frame Approach to Streamline Visualization
IEEE Transactions on Visualization and Computer Graphics
Virtual reality performance for virtual geometry
VIS '94 Proceedings of the conference on Visualization '94
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
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Flow fields, geodesics, and deformed volumes are natural sources of families of space curves that can be characterized by intrinsic geometric properties such as curvature, torsion, and Frenet frames. By expressing a curve's moving Frenet coordinate frame as an equivalent unit quaternion, we reduce the number of components that must be displayed from nine with six constraints to four with one constraint. We can then assign a color to each curve point by dotting its quaternion frame with a 4D light vector, or we can plot the frame values separately as a curve in the threesphere. As example, we examine twisted volumes used in topology to construct knots and tangles, a spherical volume deformation known as the Dirac string trick, and streamlines of 3D vector flow fields.