Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
Robot Vision
Techniques for visualizing Fermat's Last Theorem: a case study
VIS '90 Proceedings of the 1st conference on Visualization '90
Interactive manipulation and display of surfaces in four dimensions
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Illumination in diverse codimensions
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Isosurfacing in higher dimensions
Proceedings of the conference on Visualization '00
Quaternion Frame Approach to Streamline Visualization
IEEE Transactions on Visualization and Computer Graphics
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
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
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
On the intersection curve of three parametric hypersurfaces
Computer Aided Geometric Design
A framework for exploring high-dimensional geometry
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
| Hi-index | 0.00 |
We explore techniques for visualizing mathematical objects in four-dimensional space that exploit four-dimensional lighting effects. We analyze the geometry of image production, stereography, and shadows in 4D. We examine alternatives for smooth and specular shaded rendering of curves, surfaces, and solids in 4D, and propose a new approach that systematically converts curves or surfaces into uniquely renderable solids in four-dimensional space by attaching spheres or circles to each point. Analogs of 3D shading methods are used to produce volume renderings that distinguish objects whose 3D projections from 4D are identical. Analyzing the procedures needed to justify and evaluate a system such as ours for teaching humans to "see" in four dimensions leads us to propose a generally applicable four-step visualization paradigm.