Rendering fur with three dimensional textures
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Calculation of reference frames along a space curve
Graphics gems
Graphics Gems III
Geometry for n-dimensional graphics
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)
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
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
Constrained optimal framings of curves and surfaces using quaternion Gauss maps
Proceedings of the conference on Visualization '98
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
Computation of rotation minimizing frames
ACM Transactions on Graphics (TOG)
Mesh quality oriented 3D geometric vascular modeling based on parallel transport frame
Computers in Biology and Medicine
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Curves in space are difficult to perceive and analyze, especially when they form dense sets as in typical 3D flow and volume deformation applications. We propose a technique that exposes essential properties of space curves by attaching an appropriate moving coordinate frame to each point, reexpressing that moving frame as a unit quaternion, and supporting interaction with the resulting quaternion field. The original curves in three-space are associated with piecewise continuous four-vector quaternion fields, which map into new curves lying in the unit three-sphere in four-space. Since four-space clusters of curves with similar moving frames occur independently of the curves驴 original proximity in three-space, a powerful analysis tool results. We treat two separate moving-frame formalisms, the Frenet frame and the parallel-transport frame, and compare their properties. We describe several flexible approaches for interacting with and exploiting the properties of the four-dimensional quaternion fields.