Graphics Gems III
Discrete groups and visualization of three-dimensional manifolds
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Geometry for n-dimensional graphics
Graphics gems IV
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th 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
Four-dimensional views of 3D scalar fields
VIS '92 Proceedings of the 3rd conference on Visualization '92
Virtual spacetime: an environment for the visualization of curved spacetimes via geodesic flows
VIS '92 Proceedings of the 3rd conference on Visualization '92
Virtual reality performance for virtual geometry
VIS '94 Proceedings of the conference on Visualization '94
Constrained 3D navigation with 2D controllers
VIS '97 Proceedings of the 8th conference on Visualization '97
Constrained Navigation Environments
Dagstuhl '97, Scientific Visualization
Automatic camera path generation for graph navigation in 3D
APVis '05 proceedings of the 2005 Asia-Pacific symposium on Information visualisation - Volume 45
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
Haptic exploration of mathematical knots
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
A framework for exploring high-dimensional geometry
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
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We propose an interactive method for exploring topological spaces based on the natural local geometry of the space. Examples of spaces appropriate for this visualization approach occur in abundance in mathematical visualization, surface and volume visualization problems, and scientific applications such as general relativity. Our approach is based on using a controller to choose a direction in which to "walk" a manifold along a local geodesic path. The method automatically generates orientation changes that produce a maximal viewable region with each step of the walk. The proposed interaction framework has many natural properties to help the user develop a useful cognitive map of a space and is well-suited to haptic interfaces that may be incorporated into desktop virtual reality systems.